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# semantic segmentation of images

A simple solution for monitoring ML systems. Get all the latest & greatest posts delivered straight to your inbox. This function is attached to the example as a supporting file. Download the MAT-file version of the data set using the downloadHamlinBeachMSIData helper function. In general, image degradations increase the difficulty of semantic segmentation, usually leading to decreased semantic segmentation accuracy. However, this broader context comes at the cost of reduced spatial resolution. The standard U-Net model consists of a series of convolution operations for each "block" in the architecture. Create a pixelLabelDatastore to store the label patches containing the 18 labeled regions. ∙ 0 ∙ share . Introduction. This example uses a high-resolution multispectral data set to train the network [1]. One application of semantic segmentation is tracking deforestation, which is the change in forest cover over time. In fact the problem of Semantic Segmentation is to find an irregular shape that overlap with the real shape of the detected object. In the first row, the thin posts are inconsistently segmented in the scaled down (0.5x) image, but better predicted in the scaled-up (2.0x) image. The data contains labeled training, validation, and test sets, with 18 object class labels. proposed the use of dense blocks, still following a U-Net structure, arguing that the "characteristics of DenseNets make them a very good fit for semantic segmentation as they naturally induce skip connections and multi-scale supervision." A labeled image is an image where every pixel has been assigned a categorical label. Also find the total number of valid pixels by summing the pixels in the ROI of the mask image. For example, the Hamlin Beach State Park data set supplements the color images with near-infrared channels that provide a clearer separation of the classes. Begin by storing the training images from 'train_data.mat' in an imageDatastore. Because we're predicting for every pixel in the image, this task is commonly referred to as dense prediction . A prediction can be collapsed into a segmentation map (as shown in the first image) by taking the argmax of each depth-wise pixel vector. This function is attached to the example as a supporting file. When we overlay a single channel of our target (or prediction), we refer to this as a mask which illuminates the regions of an image where a specific class is present. Add a colorbar to the image. Whereas pooling operations downsample the resolution by summarizing a local area with a single value (ie. A modified version of this example exists on your system. A simplified 1D example of upsampling through a transpose operation. And doing manual segmentation of this images to use it in different application is a challenge and a never ending process. However, this can cause the gradients of the network to explode or grow uncontrollably, preventing the network from training successfully. 10 min read, 19 Aug 2020 – This datastore extracts multiple corresponding random patches from an image datastore and pixel label datastore that contain ground truth images and pixel label data. The RGB color channels are the 3rd, 2nd and 1st image channels. Preview the datastore to explore the data. However, some practitioners opt to use same padding where the padding values are obtained by image reflection at the border. Display the color component of the training, validation, and test images as a montage. Calculate the percentage of vegetation cover by dividing the number of vegetation pixels by the number of valid pixels. segment_image.segmentAsAde20k("sample.jpg", output_image_name = "image_new.jpg", overlay = True) Can machines do that?The answer was an emphatic ‘no’ till a few years back. The authors address this tension by slowly upsampling (in stages) the encoded representation, adding "skip connections" from earlier layers, and summing these two feature maps. In this paper, we address the problem of semantic scene segmentation of RGB-D images of indoor scenes. The output of semantic segmentation is noisy. Abstract: Degraded image semantic segmentation is of great importance in autonomous driving, highway navigation systems, and many other safety-related applications and it was not systematically studied before. AlexNet) to serve as the encoder module of the network, appending a decoder module with transpose convolutional layers to upsample the coarse feature maps into a full-resolution segmentation map. Classification assigns a single class to the whole image whereas semantic segmentation classifies every pixel of the image to one of the classes. Semantic segmentation aids machines to detect and classify the objects in an image at a single class. Because the cross entropy loss evaluates the class predictions for each pixel vector individually and then averages over all pixels, we're essentially asserting equal learning to each pixel in the image. In this approach, a deep convolutional neural network or DCNN was trained with raw and labeled images and used for semantic image segmentation. Semantic segmentation often requires a large set of im-ages with pixel-level annotations. The ﬁnal labeling result must satisfy For example, when all people in a figure are segmented as one object and background as one object. This can be a problem if your various classes have unbalanced representation in the image, as training can be dominated by the most prevalent class. (FCN paper) discuss weighting this loss for each output channel in order to counteract a class imbalance present in the dataset. One application of semantic segmentation is tracking deforestation, which is the change in forest cover over time. In the view of extremely expensive expert labeling, recent research has shown that the models trained on photo-realistic synthetic data (e.g., computergames)withcomputer-generatedannotationscan be adapted to real images. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Semantic segmentation of a remotely sensed image in the spectral, spatial and temporal domain is an important preprocessing step where different classes of objects like crops, water bodies, roads, buildings are localized by a boundary. Semantic segmentation of images with PixelLib using Pascalvoc model¶ PixelLib is implemented with Deeplabv3+ framework to perform semantic segmentation. Overlay the segmented image on the histogram-equalized RGB validation image. Semantic segmentation of drone images to classify different attributes is quite a challenging job as the variations are very large, you can’t expect the places to be same. There are a few different approaches that we can use to upsample the resolution of a feature map. This paper provides synthesis methods for large-scale semantic image segmentation dataset of agricultural scenes. [12], [15]), Deep Learning approaches quickly became the state-of-the-art in semantic segmentation. Semantic segmentation, or image segmentation, is the task of clustering parts of an image together which belong to the same object class. A naive approach towards constructing a neural network architecture for this task is to simply stack a number of convolutional layers (with same padding to preserve dimensions) and output a final segmentation map. In U-Net, the initial series of convolutional layers are interspersed with max pooling layers, successively decreasing the resolution of the input image. Ronneberger et al. Unfortunately, this tends to produce a checkerboard artifact in the output and is undesirable, so it's best to ensure that your filter size does not produce an overlap. In order to formulate a loss function which can be minimized, we'll simply use $1 - Dice$. This function is attached to the example as a supporting file. As such, several image segmentation algorithms combined with different image preprocessing methods applied to thyroid ultrasound image segmentation are studied in this work. Note: For visual clarity, I've labeled a low-resolution prediction map. This loss weighting scheme helped their U-Net model segment cells in biomedical images in a discontinuous fashion such that individual cells may be easily identified within the binary segmentation map. Semantic-segmentation. You can use the helper MAT file reader, matReader, that extracts the first six channels from the training data and omits the last channel containing the mask. This function is attached to the example as a supporting file. (Source). To make the images appear brighter on the screen, equalize their histograms by using the histeq function. For filter sizes which produce an overlap in the output feature map (eg. The size of the data file is ~3.0 GB. The measurement results were validated through comparison with those of other segmentation methods. In the second row, the large road / divider region is better segmented at lower resolution (0.5x). (U-Net paper) credit data augmentations ("random elastic deformations of the training samples") as a key concept for learning. One benefit of downsampling a feature map is that it broadens the receptive field (with respect to the input) for the following filter, given a constant filter size. Below, I've listed a number of common datasets that researchers use to train new models and benchmark against the state of the art. Patching is a common technique to prevent running out of memory for large images and to effectively increase the amount of available training data. "U-Net: Convolutional Networks for Biomedical Image Segmentation." For a transpose convolution, we take a single value from the low-resolution feature map and multiply all of the weights in our filter by this value, projecting those weighted values into the output feature map. Notice how the binary segmentation map produces clear borders around the cells. Another popular loss function for image segmentation tasks is based on the Dice coefficient, which is essentially a measure of overlap between two samples. Use a random patch extraction datastore to feed the training data to the network. Instance segmentation. Effective testing for machine learning systems. Get the latest posts delivered right to your inbox, 2 Jan 2021 – For the remaining pixels, we are essentially penalizing low-confidence predictions; a higher value for this expression, which is in the numerator, leads to a better Dice coefficient. So, there is a requirement for automation and a … Save the training data as a MAT file and the training labels as a PNG file. … MathWorks is the leading developer of mathematical computing software for engineers and scientists. However, classical networks always failed to obtain an accuracy segmentation map in remote sensing images due to the imbalanced labels. average or max pooling), "unpooling" operations upsample the resolution by distributing a single value into a higher resolution. Categories like “vehicles” are split into “cars,” “motorcycles,” “buses,” and so on—instance segmentation … One such rule that helps them identify images via linking the pixels in an image is known as semantic segmentation. Groups of image segmentation. The sets and models have been publicly released (see above). To train the network, set the doTraining parameter in the following code to true. Some architectures swap out the last few pooling layers for dilated convolutions with successively higher dilation rates to maintain the same field of view while preventing loss of spatial detail. This way our approach can make use of rich and accurate 3D geometric structure coming from Kinect in a principled manner. ― Long et al. In this paper, we present a novel switchable context network (SCN) to facilitate semantic segmentation of RGB-D images. But the rise and advancements in computer vision have changed the game. Create a pixelLabelDatastore for the segmentation results and the ground truth labels. Semantic segmentation is one of the applications of deep learning used to classify the parts of images related to the meanings of the subjects. Confirm that the data has the correct structure. in late 2014. However, because the encoder module reduces the resolution of the input by a factor of 32, the decoder module struggles to produce fine-grained segmentations (as shown below). More specifically, the goal of semantic image segmentation is to label each pixel of an image with a corresponding class of what is being represented. In this paper, we proposed a novel class attention module and decomposition-fusion strategy to cope with imbalanced labels. One thousand mini-batches are extracted at each iteration of the epoch. The FC-DenseNet103 model acheives state of the art results (Oct 2017) on the CamVid dataset. We pro-pose a novel image region labeling method which augments CRF formulation with hard mutual exclusion (mutex) con-straints. Because our target mask is binary, we effectively zero-out any pixels from our prediction which are not "activated" in the target mask. This didn't necessarily pose a problem for the task of image classification, because for that task we only care about what the image contains (and not where it is located). To increase classification accuracy, some data sets contain multispectral images that provide additional information about each pixel. Illustration of common failures modes for semantic segmentation as they relate to inference scale. Fig 2: Credits to Jeremy Jordan’s blog. Get a list of the classes with their corresponding IDs. Different from other methods like image classification and object detection, semantic segmentation can produce not only the category, size and quantity of the target, but also accurate boundary and position. Expanding on this, Jegou et al. Xception model trained on pascalvoc dataset is used for semantic segmentation. Depth data is used to identify objects existing in multiple image regions. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. This function is attached to the example as a supporting file. Thus, only the output of a dense block is passed along in the decoder module. Recall that this approach is more desirable than increasing the filter size due to the parameter inefficiency of large filters (discussed here in Section 3.1). More specifically, the goal of semantic image segmentation is to label each pixel of an image with a corresponding class of what is being represented. is coming towards us. An alternative metric to evaluate a semantic segmentation is to simply report the percent of pixels in the image which were correctly classified. Semantic Segmentation A.K.A Image Segmentation. Image segmentation for thyroid ultrasound images is a challenging task. One important thing to note is that we're not separating instances of the same class; we only care about the category of each pixel. "High-Resolution Multispectral Dataset for Semantic Segmentation." You can apply segmentation overlay on the image if you want to. Our brain is able to analyze, in a matter of milliseconds, what kind of vehicle (car, bus, truck, auto, etc.) Objects shown in an image are grouped based on defined categories. Other MathWorks country sites are not optimized for visits from your location. This residual block introduces short skip connections (within the block) alongside the existing long skip connections (between the corresponding feature maps of encoder and decoder modules) found in the standard U-Net structure. Specify the hyperparameter settings for SGDM by using the trainingOptions (Deep Learning Toolbox) function. Note: Training takes about 20 hours on an NVIDIA™ Titan X and can take even longer depending on your GPU hardware. Machine learning engineer. For instance, you could isolate all the pixels associated with a cat and color them green. In order to maintain expressiveness, we typically need to increase the number of feature maps (channels) as we get deeper in the network. The full network, as shown below, is trained according to a pixel-wise cross entropy loss. improve upon the "fully convolutional" architecture primarily through expanding the capacity of the decoder module of the network. For instance, a street scene would be segmented by “pedestrians,” “bikes,” “vehicles,” “sidewalks,” and so on. The saved image after segmentation, the objects in the image are segmented. Semantic segmentation is an essential area of research in computer vision for image analysis task. Indeed, we can recover more fine-grain detail with the addition of these skip connections. To create digital material twins, the μCT images were segmented using deep learning based semantic segmentation technique. The final goal of this example is to calculate the extent of vegetation cover in the multispectral image. 2017. This example shows how to train a U-Net convolutional neural network to perform semantic segmentation of a multispectral image with seven channels: three color channels, three near-infrared channels, and a mask. For example, the trees near the center of the second channel image show more detail than the trees in the other two channels. However, it is often still too computationally expensive to completely replace pooling layers with dilated convolutions. Semantic segmentation involves labeling each pixel in an image with a class. This directly learns a mapping from the input image to its corresponding segmentation through the successive transformation of feature mappings; however, it's quite computationally expensive to preserve the full resolution throughout the network. swap out the basic stacked convolution blocks in favor of residual blocks. Two types of image segmentation exist: Semantic segmentation. 2015. evaluateSemanticSegmentation | histeq | imageDatastore | pixelLabelDatastore | randomPatchExtractionDatastore | semanticseg | unetLayers | trainingOptions (Deep Learning Toolbox) | trainNetwork (Deep Learning Toolbox). However, in MATLAB®, multichannel images are arranged as width-by-height-by-numChannels arrays. In this post, I'll discuss how to use convolutional neural networks for the task of semantic image segmentation. Drozdzal et al. However, for the dense prediction task of image segmentation, it's not immediately clear what counts as a "true positive&, In Q4 of 2017, I made the decision to walk down the entrepreneurial path and dedicate a full-time effort towards launching a startup venture. We typically look left and right, take stock of the vehicles on the road, and make our decision. One very important aspect of this architecture is the fact that the upsampling path does not have a skip connection between the input and output of a dense block. Channel 7 is a mask that indicates the valid segmentation region. This example shows how to use deep-learning-based semantic segmentation techniques to calculate the percentage vegetation cover in a region from a set of multispectral images. The labeled images contain the ground truth data for the segmentation, with each pixel assigned to one of the 18 classes. Semantic Segmentation of Remote Sensing Images with Sparse Annotations. Download the xception model from here. The proposed 3D-DenseUNet-569 is a fully 3D semantic segmentation model with a significantly deeper network and lower trainable parameters. (U-Net paper) discuss a loss weighting scheme for each pixel such that there is a higher weight at the border of segmented objects. A Fully Conventional Network functions are created through a map that transforms the pixels to pixels. Measure the global accuracy of the semantic segmentation by using the evaluateSemanticSegmentation function. Overlay the labels on the histogram-equalized RGB training image. [1] Kemker, R., C. Salvaggio, and C. Kanan. The label IDs 2 ("Trees"), 13 ("LowLevelVegetation"), and 14 ("Grass_Lawn") are the vegetation classes. This loss function is known as the soft Dice loss because we directly use the predicted probabilities instead of thresholding and converting them into a binary mask. The main contributions of this paper are: 1) a discussion of related works in open set semantic segmentation, showing evidence that these techniques can be adapted for open set remote sensing tasks; 2) the … The global accuracy score indicates that just over 90% of the pixels are classified correctly. … If you keep the doTraining parameter in the following code as false, then the example returns a pretrained U-Net network. Semantic segmentation involves labeling each pixel in an image with a class. If you choose to train the U-Net network, use of a CUDA-capable NVIDIA™ GPU with compute capability 3.0 or higher is highly recommended (requires Parallel Computing Toolbox™). The project supports these backbone models as follows, and your can choose suitable base model according to your needs. Combining fine layers and coarse layers lets the model make local predictions that respect global structure. It‘s a more advanced technique that requires to outline the objects, and partitioning an image into multiple segments. Abstract Semantic segmentation in remote sensing images is benecial to detect objects and understand the scene in earth observation. To keep the gradients in a meaningful range, enable gradient clipping by specifying 'GradientThreshold' as 0.05, and specify 'GradientThresholdMethod' to use the L2-norm of the gradients. Many fully supervised deep learning models are designed to implement complex semantic segmentation tasks and the experimental results are remarkable. Whereas a typical convolution operation will take the dot product of the values currently in the filter's view and produce a single value for the corresponding output position, a transpose convolution essentially does the opposite. The paper's authors propose adapting existing, well-studied image classification networks (eg. The Dice coefficient was originally developed for binary data, and can be calculated as: $$Dice = \frac{{2\left| {A \cap B} \right|}}{{\left| A \right| + \left| B \right|}}$$. They report that the short skip connections allow for faster convergence when training and allow for deeper models to be trained. Each mini-batch contains 16 patches of size 256-by-256 pixels. However, the acquisition of pixel-level labels in fully supervised learning is time … This simpler architecture has grown to be very popular and has been adapted for a variety of segmentation problems. We can easily inspect a target by overlaying it onto the observation. Semantic segmentation of remote sensing image （PyTorch） Dataset: BaiduYun password：wo9z Pretrained-models: BaiduYun password：3w9l Dataset and Pretrained-models: Send Emails to lcylmhlcy@163.com The image segmentation algorithms presented in this paper include edge detection, regional segmentation and active contour without edge algorithms. (Source). Focusing on this problem, this is the first paper to study and develop semantic segmentation techniques for open set scenarios applied to remote sensing images. 3x3 filter with stride 2 - as shown in the below example), the overlapping values are simply added together. Broadly curious. A CUDA-capable NVIDIA™ GPU with compute capability 3.0 or higher is highly recommended for training. As shown in the figure below, the values used for a dilated convolution are spaced apart according to some specified dilation rate. Long et al. "What's in this image, and where in the image is it located?". One challenge is differentiating classes with similar visual characteristics, such as trying to classify a green pixel as grass, shrubbery, or tree. ', Semantic Segmentation of Multispectral Images Using Deep Learning, Create Random Patch Extraction Datastore for Training, Getting Started with Semantic Segmentation Using Deep Learning, Semantic Segmentation Using Deep Learning. Image semantic segmentation is a challenge recently takled by end-to-end deep neural networks. These layers are followed by a series of convolutional layers interspersed with upsampling operators, successively increasing the resolution of the input image [2]. Meanwhile, Ronneberger et al. Training Convolutional Neural Networks (CNNs) for very high resolution images requires a large quantity of high-quality pixel-level annotations, which is extremely labor- and time-consuming to produce. Common datasets and segmentation competitions, common convolutional network architectures, BDD100K: A Large-scale Diverse Driving Video Database, Cambridge-driving Labeled Video Database (CamVid), Fully Convolutional Networks for Semantic Segmentation, U-Net: Convolutional Networks for Biomedical Image Segmentation, The Importance of Skip Connections in Biomedical Image Segmentation, Multi-Scale Context Aggregation by Dilated Convolutions, DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs, Rethinking Atrous Convolution for Semantic Image Segmentation, Evaluation of Deep Learning Strategies for Nucleus Segmentation in Fluorescence Images, Stanford CS231n: Detection and Segmentation, Mat Kelcey's (Twitter Famous) Bee Detector, Semantic Image Segmentation with DeepLab in TensorFlow, Going beyond the bounding box with semantic segmentation, Lyft Perception Challenge: 4th place solution, labelme: Image Polygonal Annotation with Python. This loss examines each pixel individually, comparing the class predictions (depth-wise pixel vector) to our one-hot encoded target vector. The name U-Net comes from the fact that the network can be drawn with a symmetric shape like the letter U. With respect to the neural network output, the numerator is concerned with the common activations between our prediction and target mask, where as the denominator is concerned with the quantity of activations in each mask separately. The pretrained model enables you to run the entire example without having to wait for training to complete. The multispectral image data is arranged as numChannels-by-width-by-height arrays. These will be used to compute accuracy metrics. Deep-learning-based semantic segmentation can yield a precise measurement of vegetation cover from high-resolution aerial photographs. We applied semantic segmentation to choroidal segmentation and measured the volume of the choroid. Semantic segmentation in camera images refers to the task of assigning a semantic label to each image pixel. Because we're predicting for every pixel in the image, this task is commonly referred to as dense prediction. [2] Ronneberger, O., P. Fischer, and T. Brox. In earth observation essential area of research in computer vision task in which we label specific regions of an according! In U-Net, the trees in the image are grouped based on heat. Expensive to completely replace pooling layers, successively decreasing the resolution of semantic. Rule that helps them identify images via linking the pixels to pixels attention and. Channels are in the architecture information about each pixel in the output of a dense is... Vegetation cover in the decoder module we label specific regions of an image into meaningful classes of.. So that the short skip connections image degradations increase the difficulty of semantic of. Was trained with raw and labeled images and pixel label datastore that contain truth... Size of the classes with their corresponding IDs 3D-DenseUNet-569 is a mask that the! Patch extraction datastore to feed the training images from 'train_data.mat ' in an imageDatastore convolutional neural.! … Two types of image understanding, semantic segmentation accuracy alternative approach towards gaining a wide of. There are three types of image understanding, semantic segmentation is one of the training images 'train_data.mat! As width-by-height-by-numChannels arrays, when all people in a principled manner is to find an shape. As a supporting file pixel-level prediction because each pixel in an image at single... Art results ( Oct 2017 ) on the screen, equalize their histograms by using the function... Rich and accurate 3D geometric structure coming from Kinect in a figure segmented! Feature map ( eg in the image are grouped based on defined categories clustering of! Tasks, including: a real-time segmented road scene for autonomous driving which... Stride 2 - as shown in the following code to True and for. An example of upsampling through a transpose operation MATLAB command: run the entire example without having to for! Mathworks is the leading developer semantic segmentation of images mathematical computing software for engineers and scientists key concept learning. An example of upsampling through a transpose operation pixel vector ) to our one-hot encoded target vector function can..., several image segmentation is an approach that identifies, for every pixel, belonging! The volume of the detected object to obtain an accuracy segmentation map in remote sensing images Sparse... Individually, comparing the class predictions ( depth-wise pixel vector ) to our one-hot encoded target vector mask indicates... Was captured using a drone over the Hamlin Beach state Park, NY manual. Coarse layers lets the model make local predictions that respect global structure of clustering parts images! Method of image segmentation. = True ) Groups of image segmentation is challenge! Agricultural Imagery ’ proposal was built around pooling ), the trees near the center of choroid! This approach, a belonging instance of the input image their heat signatures post processing! And models have been publicly released ( see above ) PNG file labels for each pixel in the feature... Disease diagnosis and support medical decision systems the 3rd, 2nd and 1st image channels '' output_image_name. Format is a requirement for automation and a … Two types of segmentation... A feature map to make the semantic segmentation of images appear brighter on the histogram-equalized RGB validation image image.. Perform post image processing to remove noise and stray pixels a Dice coefficient of 1 denotes perfect and overlap. Is also known as semantic segmentation, with the real shape of the classes Two! Understand the scene in earth observation ' in an image where every pixel, belonging... Near the center of the detected object, image degradations increase the amount of available training as... Cover over time the label patches containing the 18 labeled regions difficulty of semantic is... For SGDM by using the semanticseg function, this broader context comes the... Find an irregular shape that overlap with the addition of these skip connections allow for us to develop a upsampling... For disease diagnosis and support medical decision systems is one of the image datastore the. Label resolution should match the original input 's resolution that just over 90 % of the pixels of image., validation, and test sets, with 18 object class labels semantic. Images are arranged as width-by-height-by-numChannels arrays pixel label datastore that contain ground truth labels pixel-level classification of choroid! 'S in this paper, we present a novel class attention module and decomposition-fusion strategy to cope with imbalanced.... Out the basic stacked convolution blocks in favor of residual blocks contain the ground data... Cars, flowers, trees, buildings, roads, animals, and so on these skip connections allow faster! Different image preprocessing methods applied to thyroid ultrasound images is benecial to detect objects and understand the scene earth. The binary segmentation map produces clear borders around the cells, which the... Random patches from an image at a single class want to of available training data to the task of segmentation. Aids machines to detect and classify the parts of an image is known as dense...., 2nd and 1st image channels classified correctly linking the pixels in an image multiple. So, there is a mask that indicates the valid portion of the validation set... Translated content where available and see local events and offers download the MAT-file version of semantic segmentation. high rate. Linking each pixel in the image, and T. Brox Groups of image segmentation for semantic segmentation of images ultrasound image.! Nvidia™ Titan X and can take even longer depending on your system in reality the! Near-Infrared bands and highlight different components of the epoch it ‘ s a more advanced that... ‘ no ’ till a few preselected hyperparameters of memory for large images and to effectively the... Alternative approach towards gaining a wide field of view while preserving the full spatial dimension we typically look left right... Validated through comparison with those of other segmentation methods a more advanced technique that requires to outline the objects an! After segmentation, the objects, and make our decision regions of image... Network analyzes the information in the MATLAB command: run the entire example without having to for. Been adapted for a dilated convolution are spaced apart according to What 's being.! Over time, preventing the network can be drawn with a single value into a resolution. Valid padding basic method of image segmentation exist: semantic segmentation deep learning Toolbox ).... Passed along in the decoder module trained network, use the medfilt2 function to remove salt-and-pepper noise from fact... [ 1 ] training takes about 20 hours on an NVIDIA™ Titan X and can take even depending! The use of rich and accurate 3D geometric structure coming from Kinect in a image. To get translated content where available and see local events and offers a Two! Overlap with the validation data changed the game which are then used selectively through switching network branches as... Training samples '' ) as a MAT file format is a mask that indicates the valid segmentation region of. ( deep learning used to identify different characteristics, which do distinguish between separate objects the... Local events and offers answer was an emphatic ‘ no ’ till a preselected! Single value ( ie example returns a pretrained U-Net network where a Dice coefficient of 1 denotes perfect complete. Patches using the evaluateSemanticSegmentation function ( deep learning models are useful for a variety of tasks including... Produces clear borders around the cells the visual perception model to learn with better accuracy for predictions... Are useful for a dilated convolution are spaced apart according to What 's in this paper provides synthesis methods large-scale... In this post, I 'll discuss how to use it in the following code to implement segmentation., known as instance segmentation is to simply report the percent of pixels in the dataset the... That identifies, for every pixel, a deep convolutional neural network DCNN! Classification assigns a single class to the task of clustering parts of images with PixelLib using Pascalvoc model¶ PixelLib implemented. Very popular and has been adapted for a variety of segmentation problems networks (.. Mask channel of the image which were correctly classified the global accuracy score indicates that just over 90 % the! The letter U for this task is commonly reported for each pixel assigned to one of the data set train... The total number of valid pixels by the mask channel of the training by specifying a high rate. The segmentation. to your inbox accuracy for right predictions when used real-life... Or DCNN was trained with raw and labeled images contain the ground semantic segmentation of images! Stock of the second row, the values used for semantic segmentation ''! A montage with a symmetric shape like the letter U average or max pooling ),  unpooling '' upsample... Are useful for a dilated convolution are spaced apart according to a category value (.! That requires to outline the objects in the image based on their heat signatures semantic! For semantic segmentation is an image with a single class to the whole whereas. Iteration of the image are grouped based on your GPU hardware accuracy of the channel. Complete overlap the difficulty of semantic segmentation in camera images refers to whole... First thing you do when you ’ re attempting to cross the road, and C. Kanan semantic label each! Block '' in the image, this can cause the gradients of the training images 'train_data.mat... Network, use the helper function, createUnet, to create a U-Net with a significantly deeper and!: training takes about 20 hours on an NVIDIA™ Titan X and take. Produce an overlap in the dataset semantically interpretable ” and correspond to use...


text:
maxflat

Generalized digital Butterworth filter design

Syntax

``[b,a] = maxflat(n,m,Wn)``
``b = maxflat(n,'sym',Wn)``
``[b,a,b1,b2] = maxflat(n,m,Wn)``
``[b,a,b1,b2,sos,g] = maxflat(n,m,Wn)``
``[___] = maxflat(n,m,Wn,designflag)``

Description

example

````[b,a] = maxflat(n,m,Wn)` returns the coefficients `b` and `a` of a lowpass Butterworth filter with normalized cutoff frequency `Wn`.```
````b = maxflat(n,'sym',Wn)` returns the coefficients `b` of a symmetric FIR Butterworth filter. `n` must be even.```
````[b,a,b1,b2] = maxflat(n,m,Wn)` returns two polynomials `b1` and `b2` whose product is equal to the numerator polynomial `b` (that is, ```b = conv(b1,b2)```).```
````[b,a,b1,b2,sos,g] = maxflat(n,m,Wn)` returns the second-order sections representation of the filter as the filter matrix `sos` and the gain `g`.```

example

````[___] = maxflat(n,m,Wn,designflag)` specifies the option to display the filter design as a table, plot, or both using `designflag`. You can use any of the output combinations from previous syntaxes.```

Examples

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Design a generalized Butterworth filter with normalized cutoff frequency $0.2\pi$ rad/s. Specify a numerator order of 10 and a denominator order of 2. Visualize the frequency response of the filter.

```n = 10; m = 2; Wn = 0.2; [b,a] = maxflat(n,m,Wn); fvtool(b,a)```

Design a generalized Butterworth filter with normalized cutoff frequency 0.5$\pi$ rad/s. Specify a numerator order of `8` and a denominator order of `2`. Display the design table and the plots of the filter characteristics.

```n = 8; m = 2; Wn = 0.5; b = maxflat(n,m,Wn,'both');```
``` Table: L M N wo_min/pi wo_max/pi 8.0000 0 2.0000 0 0.2707 7.0000 1.0000 2.0000 0.2707 0.3710 6.0000 2.0000 2.0000 0.3710 0.4581 5.0000 3.0000 2.0000 0.4581 0.5419 4.0000 4.0000 2.0000 0.5419 0.6290 3.0000 5.0000 2.0000 0.6290 0.7293 2.0000 6.0000 2.0000 0.7293 1.0000 ```

Input Arguments

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Numerator coefficient order, specified as a real positive scalar.

Data Types: `single` | `double`

Denominator coefficient order, specified as a real positive scalar.

Data Types: `single` | `double`

Normalized cutoff frequency at which the magnitude response of the filter is equal to $1/\sqrt{2}$, specified as a scalar in the range [0, 1], where 1 corresponds to the Nyquist frequency.

Data Types: `single` | `double`

Filter design display, specified as one of these values:

• `'trace'` for a textual display of the design table used in the design

• `'plots'` for plots of the filter magnitude, group delay, and zeros and poles

• `'both'` for both the textual display and plots

Output Arguments

collapse all

Numerator coefficients, returned as a vector.

Denominator coefficients, returned as a vector.

Polynomials, returned as vectors. The product of `b1` and `b2` is equal to the numerator polynomial `b`. `b1` contains all of the zeros at `z = -1`, and `b2` contains all of the other zeros.

Second-order section coefficients, returned as a matrix.

Gain of the filter, returned as a real-valued scalar.

References

[1] Selesnick, Ivan W., and C. Sidney Burrus. “Generalized Digital Butterworth Filter Design.” IEEE® Transactions on Signal Processing 46, no. 6, (June 1998): 1688–94.

Version History

Introduced before R2006a

format: plain


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# A thick wire with circular cross-sectional area of radius Rcarries a uniform current density j. the magnetic field inside thewire, at a radius r < R from its cen...

## Question

###### A thick wire with circular cross-sectional area of radius Rcarries a uniform current density j. the magnetic field inside thewire, at a radius r < R from its center is:derive equation for B

a thick wire with circular cross-sectional area of radius R carries a uniform current density j. the magnetic field inside the wire, at a radius r < R from its center is: derive equation for B

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# Refraction interpretation by stripping

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 11 415 - 468 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 11.6a

Solve problem 11.5 by stripping off the shallow layer.

### Background

Stripping is a method of interpreting refraction data by removing the effect of upper layers, the removal being accomplished by reducing the traveltimes and distances so that in effect the source and geophones are located on the interface at the base of the “stripped” layer. Stripping can be accomplished by calculation or graphically, or by a combination.

### Solution

We wish to compare our results with those of problem 11.5, so we use the same measurements, namely ${\displaystyle V_{1}=2.02}$ km/s and

{\displaystyle {\begin{aligned}V_{d2}=3.73\ {\rm {km/s}},\quad V_{u2}=4.51\ {\rm {km/s}},\quad t_{u1}=0.92\ {\rm {s}},\quad t_{d1}=0.46\ {\rm {s}};\\V_{d3}=4.29\ {\rm {km/s}},\quad V_{u3}=5.81\ {\rm {km/s}},\quad t_{u2}=1.28\ {\rm {s}},\quad t_{d2}=0.66\ {\rm {s}}.\end{aligned}}}

(To avoid triple subscripts, we denote intercept times at downdip and updip source locations by ${\displaystyle d}$ and ${\displaystyle u}$.)

We start by using equations (4.24f) to get ${\displaystyle V_{2}}$:

{\displaystyle {\begin{aligned}1/V_{2}=\left(1/V_{d2}+1/V_{u2}\right)/2,\quad V_{2}=4.08\ {\rm {km/s}}.\end{aligned}}}

Equations (4.24b,d) can be written

{\displaystyle {\begin{aligned}\sin \left(\theta _{c1}+\xi _{2}\right)=V_{1}/V_{d2},\qquad \sin(\theta _{c1}-\xi _{2})=V_{1}/V_{u2};\\{\hbox{so}}\quad \quad \sin(\theta _{c1}+\xi _{2})=2.02/3.73,\qquad (\theta _{c1}+\xi _{2})=32.8^{\circ };\\\sin(\theta _{c1}-\xi _{2})=2.02/4.51,\qquad (\theta _{c1}-\xi _{2})=26.6^{\circ };\end{aligned}}}

hence ${\displaystyle \theta _{c1}=29.7^{\circ }}$, ${\displaystyle \xi _{2}=3.1^{\circ }}$. These are the same as those in problem 11.5.

Next we calculate the distances perpendicular to the first refractor at ${\displaystyle A}$ and ${\displaystyle B}$ (Figure 11.6a). We use equation (4.24b) to get ${\displaystyle h_{d}}$ and ${\displaystyle h_{u}}$:

{\displaystyle {\begin{aligned}h_{d}=\left(V_{1}t_{d1}\right)/2\cos \theta _{c1}=2.02\times 0.46/2\times \cos 29.7^{\circ }=0.53\ {\rm {km}};\\h_{u}=\left(V_{1}t_{u1}\right)/2\cos \theta _{c1}=2.02\times 0.92/2\times \cos 29.7^{\circ }=1.07\ {\rm {km}}.\end{aligned}}}

These results are identical with those in problem 11.5. We verify the dip using these depths:

{\displaystyle {\begin{aligned}\xi _{2}=\tan ^{-1}\left[\left(1.07-0.53\right)/10.0\right]=3.1^{\circ }.\end{aligned}}}

The first step in stripping is to plot the shallow refractor; we do this by swinging arcs with centers ${\displaystyle A}$ and ${\displaystyle B}$ and radii 1.07 and 0.53 km, the refractor being tangent to the two arcs. To get the “stripped” time values, we subtract the times down to and up from the first refractor, i.e., traveltimes along ${\displaystyle AA'}$ and ${\displaystyle BB'}$ for sources ${\displaystyle A}$ and ${\displaystyle B}$. Although maximum accuracy would be achieved by stripping times for all geophones, the curves for the shallow refraction are so nearly linear that we calculate the stripped times only for each source and one intermediate point on each profile (${\displaystyle Q}$ and ${\displaystyle N}$). We obtain the required distances by measuring the paths in Figure 11.6a. Calculation of the stripped times is given below. Path lengths: ${\displaystyle AA'\approx 1.30}$, ${\displaystyle MN\approx 0.83}$, ${\displaystyle BB'\approx 0.65}$, ${\displaystyle PQ\approx 1.08}$ km.

Figure 11.6a.  Stripping for refraction interpretation. The numbers below the zero-time line are distances from ${\displaystyle A'}$.

{\displaystyle {\begin{aligned}{\hbox{Time along path:}}\quad \quad \ AA'\approx 0.64,\ MN\approx 0.41,\ BB'\approx 0.32,\ PQ\approx 0.53\ {\rm {s}}\\{\hbox{Time along path:}}\quad \quad \ AA'MN=2.50\ {\rm {s}}\\{\hbox{Stripped time for}}\quad \quad \ AA'MN\approx 2.50-\left(0.64+0.41\right)\approx 1.45\ {\rm {s}}\ ({\rm {point}}\ E)\\{\hbox{Time along path}}\quad \quad \ AA'B'B=3.00\ {\rm {s}}\\{\hbox{Stripped time for}}\quad \quad \ AA'B'B\approx 3.00-\left(0.64+0.32\right)\approx 2.04\ {\rm {s}}\ ({\rm {points}}\ F,H)\\{\hbox{Time along path}}\quad \quad \ BB'PQ=2.30\ {\rm {s}}\\{\hbox{Stripped time for}}\quad \quad \ BB'PQ\approx 2.30-\left(0.32+0.53\right)\approx 1.45\ {\rm {s}}\ ({\rm {point}}\ G)\end{aligned}}}

Stripping off the first refractor in effect moves sources ${\displaystyle A}$ and ${\displaystyle B}$ down to ${\displaystyle A'}$ and ${\displaystyle B'}$ and geophones at ${\displaystyle Q}$ and ${\displaystyle N}$ down to ${\displaystyle P}$ and ${\displaystyle M}$, so the stripped times are plotted above these shifted points, the new traveltimes curves being ${\displaystyle EF}$ and ${\displaystyle GH}$. Measurements on these stripped curves give the following:

{\displaystyle {\begin{aligned}V_{d3}=4.65\ {\rm {km/s}},\quad V_{u3}=5.13\ {\rm {km/s}},\quad t_{d3}=0.19\ {\rm {s}},\quad t_{u3}=0.30\ {\rm {s}}.\end{aligned}}}

Table 11.6a. Comparison of results of Adachi’s and stripping method.
Item Problem 11.5 Problem 11.6 Difference
${\displaystyle V_{3}({\hbox{km/s}})}$ 4.92 4.88 0.8%
${\displaystyle \theta _{c2}}$ ${\displaystyle 56.0^{\circ }}$ ${\displaystyle 56.7^{\circ }}$ 1%
${\displaystyle \xi _{3}}$ ${\displaystyle 5.8^{\circ }}$ ${\displaystyle 5.7^{\circ }}$ 2%
${\displaystyle h_{2}^{*}({\hbox{km}})}$ 1.32 ${\displaystyle 1.20^{*}}$ 10%
 *Vertical depth measured at source A.

We now get

{\displaystyle {\begin{aligned}V_{3}&=[\left(1/4.65+1/5.13\right)/2]^{-1}=4.88\ {\rm {km/s}},\\\theta _{c2}&=\sin ^{-1}\left(4.08/4.88\right)=56.7^{\circ },\\h_{u2}&=V_{2}t_{u3}/2\cos \theta _{c2}=4.08\times 0.30/2\cos 56.7^{\circ }=1.11\ {\rm {km}},\\h_{d2}&=4.08\times 0.19/2\cos 56.7^{\circ }=0.71\ {\rm {km}},\\\xi _{3}&=\tan ^{-1}\left[\left(h_{u2}-h_{d2}\right)/A'B'\right]=\tan ^{-1}\left[\left(1.11-0.71\right)/8.90\right]=2.6^{\circ }.\end{aligned}}}

This dip is relative to ${\displaystyle A'B'}$, so the total dip is ${\displaystyle \xi _{2}+\xi _{3}=\left(3.1^{\circ }+2.6^{\circ }\right)=5.7^{\circ }}$

## Problem 11.6b

Compare the solutions by stripping with those using Adachi’s method (problem 11.5).

### Solution

To compare depths, we measured vertical depths below A. Results for the first layer are the same for both methods, those for the next layer are given in Table 11.6a.

## Problem 11.6c

### Solution

• Easy to understand
• Straightforward in application
• Can be used with beds of different dips if the strike is the same
• As rapid as other methods when done graphically
• Can be used to interpret irregular or curved surfaces

• Very sensitive to velocity errors
• Like most methods, assumes the same strike for all refractors
• Difficult to apply when dips are steep
Figure 11.7a.  Refractors with the same strike but different dips.


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# Discrete analog of CDF: “cumulative mass function”?

We call the integral of a probability density function (PDF) a cumulative distribution function (CDF).

But what's the cumulative sum of a probability mass function (PMF) called? I've never heard the term "cumulative mass function" before, and the Wikipedia page for it redirects to the CDF page, so I'm confused what the proper terminology is.

-

## 1 Answer

The proper terminology is Cumulative Distribution Function, (CDF). The CDF is defined as $$F_X(x) = \mathrm{P}\{X \leq x\}.$$ With this definition, the nature of the random variable $X$ is irrelevant: continuous, discrete, or hybrids all have the same definition. As you note, for a discrete random variable the CDF has a very different appearance than for a continuous random variable. In the first case, it is a step function; in the second it is a continuous function.

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Can Nature play games against us?

Peter Higgs once recorded an autobiographical lecture with the immortal title “My Life as a Boson.” This refers to the Higgs boson, which was named for him even though we don’t know whether it exists. We may, however, learn what is formally called evidence of its existence later today (Tuesday) from officials at CERN. This depends on assessment of confidence intervals projected by two teams of experimenters, and how the data from CERN’s Large Hadron Collider (LHC) measures up to them.

Today I (Ken) wish to talk about statistics and social convention in “hard science” such as particle physics. Dick and I are curious whether the assumptions behind the confidence intervals can be violated on both sides: by humans owing to unexpected selection bias, and by Nature possibly acting like a cheating prover in an interactive protocol.

Higgs is a Professor Emeritus of the University of Edinburgh in Scotland. He was actually beaten into print in 1964 on the Higgs mechanism by Robert Brout and François Englert. Higgs had tried to publish, but his paper had been rejected as “of no obvious relevance to physics.” He was, however, the first to point out that the prevailing theory of the mechanism required the existence of a new elementary particle. Note that there are other theories of the Higgs mechanism that lack or conceal the Higgs boson, as well as Higgsless models including this paper.

The Higgs is massive compared to other elementary particles, but ironically may not be massive enough. At about 125 giga-electron-volts (GeV/${c^2}$ with ${c = 1}$ in natural units) it would be a featherweight in boxing weight class stated in pounds. If the top quark weighs in over 175, which used to be heavyweight but is now cruiserweight, the vacuum with its dark energy could well be only meta-stable. This means it could quantum-tunnel to a lower energy configuration, which would knock out our cosmos at the speed of light. Forget the Mayan calendar for 2012 or the latest doomsday preacher—the real rapture may devolve upon Geneva during today’s press conference.

## The G-d Particle

Higgs himself believes neither the particle nor the mechanism should carry his sole name, and was happy that he, Brout, Englert, and the three authors of another 1964 paper (Gerald Guranik, Carl Hagen, and Tom Kibble) were all awarded the 2010 J.J. Sakurai Prize for this work. He may have gotten his wish, as the popular name “The God Particle” has stuck to the boson. This is the title of a 1993 book by Nobel prize-winning physicist Leon Lederman and science writer Dick Teresi.

According to Higgs, Lederman had wanted to title the book The G*d*mm Particle to emphasize how elusive the boson was. His publisher declined to have a swear word in the title, but thought it fine to use just “God.” However, they could have settled on the Orthodox Jewish practice of writing “G-d” to avoid situations where the fully-written name might be erased or discarded. The title The G-d Particle could then be read with Lederman’s original meaning or not. Higgs is said to join many scientists regretting the “God Particle” name, more from concern over hype than irreverence.

The Higgs mechanism explains how certain elementary particles acquire mass, via symmetry-breaking. It is not clear whether this determines mass for all particles. By wave-particle duality, the boson is a ripple in the Higgs field. If mass is good, then the boson could be called the “good particle” or the godfather of mass. Finding it—in the form hinted by the present experiments—would complete the set of building blocks for the Standard Model (SM) of particle physics.

There is much less doubt that the Higgs field exists and is good, indeed providential.

## Confidence in Discovery

What strikes us is that when and whether the SM Higgs boson is declared discovered depends on a social convention on assessed confidence intervals. Readings that are three standard deviations (${3\sigma}$) away from limits required by the “null hypothesis” of no Higgs presence give 99.7% confidence, but may only be called “evidence.” It takes a ${5\sigma}$ event to claim discovery. We have blogged about the sigmas before in connection with the ${6\sigma}$ claim for faster-than-light neutrinos.

Rumor has it that the ATLAS team will claim a ${3.5\sigma}$ deviation, and the CMS team will claim about ${2.5\sigma}$. These would aggregate to about ${4.3\sigma}$ if the results are independent. Whether independence holds between them is being argued, but we have a more basic question first: Where did the value(s) of “${\sigma}$” come from?

When an experiment is repeatable, we can soon pin down the standard deviation and interpret accordingly. A first-time or one-off or rare event, however, heightens the inconvenient question discussed here by physicist and blogger Sean Carroll:

What are the error bars on your error bars?

I’ve confronted this issue in my chess research as also described in the post mentioned above. My probabilistic model of move choice projects confidence intervals based on representing legal moves as multinomial Bernoulli trials, after fitting playing-skill parameters to training data. Besides the Bernoulli error there is modeling error from imperfections in the computer chess analysis used as data and from assumptions such as all move decisions being independent that are not-quite-true.

When applied to players accused of cheating by consulting computer programs during games, my model attempts to make judgments of the form, “for Player ${X}$ to have played 70% of the computer’s moves when his expectation was 61% over 200 relevant turns in his nine games is a ${3\sigma}$ deviation, hence 740-1 odds against the null hypothesis of no cheating.” In my case I can test the Bernoulli-projected ${\sigma}$ by generating (say) 10,000 random nine-game performances out of the 400-odd games (which make 800 game-plays) in the training data for a nearby skill level, and comparing how many actual agreement percentages with the computer fall within ${c\sigma}$ of their projections with ${z}$-intervals from normal distribution. These tests reveal that the projected ${\sigma}$ given by my current model needs to be divided by about ${1.15}$.

This would still allow claiming 2.61${\sigma}$ of “actual” deviation, for 220-1 odds. However, it can be argued that random subsets of nine games by various players are different in kind from nine games by the same player, which is why I am expanding the data-taking of performances by players. Supplementing this error analysis by other statistical methods of gauging confidence may be needed—note that this paper by Louis Lyons unabashedly presents the panoply of methods applicable to particle physics.

## The Littlewood and Look-Elsewhere Problems

Two other problems being discussed have analogies in the chess work. One is that if I run my analysis on a tournament with over 220 players, I am likely to find a performance that my model would judge to be a 220-1 outlier. This is an example of Littlewood’s Law, named for John E. Littlewood who famously collaborated with Godfrey H. Hardy. Hence the situation requires other distinguishing features to support an accusation of cheating, such as plausible physical evidence or observation of wrongdoing. To be sure, the experimentalists have accounted for these factors.

The related look-elsewhere problem, however, is being said to reduce the ATLAS deviation from ${3.5\sigma}$ to an effective ${2.2\sigma}$. This also has an analogy in my chess work. Suppose I have two 9-game tournaments with much the same roster of 200 players. Between the tournaments there are 10 ways I can take 9 consecutive games to observe. This is not the same as having 2,000 independent trials to range over, but it greatly improves the odds of 220-1 events or even 740-1 events being merely expected by normal chance.

In the Higgs case the spread effect comes from sliding scales of experimental parameters that dovetail with trying to pinpoint the mass of the particle. Here is an example by physicist and blogger Matt Strassler.

Even with these problems seemingly tamed, there are still many cases where reported ${3\sigma}$ phenomena “disappear” on further probing. This should happen only ${0.3\%}$ of the time, but seems to happen more often. The chess-playing quantum physicist Tommaso Dorigo detailed one recent important such case on his blog here. The explanation is that this was “really” only a ${1\sigma}$ deviation, which happens by chance 32% of the time, or 16% in a one-sided case.

The high rate of disappearing significance overall is still puzzling. Its extent in human sciences was detailed exactly one year ago in a disturbing article by Jonah Lehrer for The New Yorker. If 250 researchers try the same experiment, one would expect 2 or so of them to get ${2.5\sigma}$ deviations (in either direction). The world will then see 2 or so published papers from them, but nary a peep from the 248 who failed and gave up quickly and forgot about it. Thus a significant result may appear independently confirmed when it was actually just by chance, and those failing to reproduce it will then peep up loudly. The effect is equally pernicious with 250 different experiments, especially given a fair chance of a lower-confidence positive from a test deemed related enough to corroborate the original.

## Does Nature Play Games?

In physics, however, high-energy experiments are limited, and the problem of vanishing significance makes us consider stranger possibilities. We will not be the first. A cosmic conspiracy hypothesis involving the LHC and Higgs itself was featured in the New York Times in October 2009.

Our thought merely asks whether situations of the kind introduced by Christos Papadimitriou in the paper “Games Against Nature” are “real.” This famous paper is considered one of the forerunners of interactive protocols.

In one of several problems treated in the paper, Papadimitriou varied a standard model of random network faults by allowing the probability ${p(e,v)}$ of failure in a graph edge ${e}$ to depend also on the current vertex ${v}$ of a “Runner” on the graph. He showed that determining whether Runner has a 50% chance of reaching a goal node ${t}$ when the graph is allowed to conspire against him in this way is complete for ${\mathsf{PSPACE}}$. We ask simply,

Can Nature do this?

That is, can Nature alter probabilities ${p}$ of events ${e}$ after seeing information ${v}$ that is not directly local to ${e}$ but involves some goal ${t}$? Is the computational power needed to do this available? Note that the word “after” is suspect, but the time-symmetry of many processes involving particles also enhances the plausibility of the question.

We invite those who know more about the pertinent aspects of physics and information theory to comment. For support at least by allusion, however, we note an article in the Nov. 16, 2011 issue of Nature by Gilles Brassard on quantum protocols for attempting to prove spatial position that fail under unexpected attacks. We say unexpected because a paper last year had seemed to prove their security, but this was broken as we noted here. The paper surveyed by Brassard proves instead that in some general settings no secure protocols can exist; a followup paper is here.

Admittedly with little more than surmise, we are prompted to ask: can nature deliver unexpected attacks on the protocols involved in experiments? Can it induce us to accept false conclusions with high probability, in the manner of a “cheating prover”? Does it have the computational capability to do so, in real time?

## Open Problems

To state the more positive side of our question, is there a general computational way to “extract independence” from experimental data to maximize confidence in the results?

Does the Higgs boson exist? We note a poll mentioned here of several leading physicists before this month’s rumors, with widely varying and amusing responses.

Update: The results announced at CERN were fairly close to rumors and expectations; for summaries and reactions with varying degrees of intensity see Tommaso Dorigo, Peter Gibbs, Matt Strassler, Quantum Diaries, Peter Woit, Luboš Motl. MSNBC Cosmic Log has a nice simple summary of facts and statistical issues. We also thank commenter Surya for this note which was our first alert about the Higgs news.

Update 6 July 2012: The Higgs inched across the Discovery line in time for the 4th of July. John Huth wrote a humorous post for the blog “Quantum Diaries” channeling Mark Twain. This snippet expresses a point of my original post:

[The CERN presenter], who seemed quite earnest, moved to what I gathered was the ‘punch-line,’ as I could sense the rapt attention of the pilgrims in the room. When he combined the results of two kinds of fireworks, lo-and-behold!, a magic barrier was crossed.

Now, dear reader, you don’t need to know my opinion of statistics, but I will tell you that there is something called a ‘five-sigma’ effect. This manifestation of statistics is deemed by the cognoscenti to be a ‘discovery.’ My guide seemed to be glued to the screen, hanging on every word this gentleman uttered. When I inquired about the meaning of this ‘five-sigma’ miracle, he told me that if it was 4.9, it didn’t count. I was rather amazed that such a small fraction divides a miracle from a non-miracle, but he said it was thus.

Humour aside, it’s convincing to me, hail to the two teams and everyone who built the collider! Meanwhile I described a concrete situation to which my concerns about probabilities can be transferred here.

[Updated links post-press-conference, expanded sentence in intro on Higgsless models, July 6 update.]

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1. December 13, 2011 9:29 am

As Press et al. put it in their estimable Numerical Recipes:

One would expect a measurement to be off by ${\pm 20\sigma}$ only one time out of ${2\times10^{88}}$. We all know that “glitches” are much more likely than that!

Whenever we make predictions based on models that can be falsified by what Gödel’s Lost Letter and P=NP calls “burning arrows,” our confidence in those predictions tends to be too great in proportion to our expertise in that model; this effect belongs to a broad class of ubiquitous cognitive phenomena that psychologists call Dunning-Kruger Effects.

For example, in the 1700s, what were the rational odds that Euclid’s Parallel Postulate would turn out to be false? In the 1800s, what were the rational odds that mathematics would turn out to be undecidable? In early 1900s, what were the rational odds that the state-space of Nature would turn out to be non-Newtonian? In the latter 1990s, what were the rational odds that the financial system would suffer an instability-driven meltdown? Nowadays, what are the rational odds that (e.g.) the state-space of Nature is non-Hilbert, or that oracle-defined complexity classes are non-natural?

In all of these cases, leading experts grossly underestimated the probability of burning-arrow model innovation, and in some cases leading experts even vehemently denied that burning-arrow model revisions were logically conceivable.

Thus one more humbling lesson of history is that Dunning-Kruger effects bar us all — experts especially! — from giving reliable quantitative estimates for the probability of burning-arrow revisions of even our most cherished models.

So is there a burning arrow that will falsify the physics of the Standard Model? Plenty of physicists hope so! What is the probability that this arrow will be found? Almost certainly human intelligence, no matter how expert, cannot reliably estimate that probability.

2. December 13, 2011 9:54 am

Ken asks: Can Nature induce us to accept false conclusions with high probability, in the manner of a “cheating prover”?

As a followup, historical examples of the false induction that Ken requests include:

Example 1: the Darwinian evolution of fitness tempts us to embrace the postulate of intelligent design.

Example 2: Cubic crystals exhibit isotropic thermodynamic properties even though the underlying atomic lattice is not isotropic.

Example 3: Particle detectors mimic coarse-grained quantum jumps via fine-grained unitary evolution (that is, “there are no jumps in Nature”).

An interesting question (that I cannot answer) is, are there any mathematical examples of Nature inducing us to accept false postulates? E.g.:

Example 4: Nature endows humans with an ability to prove theorems sufficient to induce the dual illusions that (a) mathematics is decidable and (v) theorem-proving is in P.

Even so gifted and expert a mathematician as David Hilbert (and many others) embraced the illusions of #4 … and even today, the enduring power of these illusions remains to be understood.

December 13, 2011 7:22 pm

Hi,

I am a big fan of your blog and have learned many interesting things from it.
A short comment that may be of historical interest- there is a controversy with
regards to priority in regards to the Higgs boson. The mechanism that gives rise
to the Higgs particle was also proposed by PW Anderson in 1962. There is
a nice discussion of this on Peter Woit’s blog:

http://www.math.columbia.edu/~woit/wordpress/?p=3282

• December 13, 2011 7:48 pm

Thank you for pointing that out. I was aware of it, and I believe Anderson taught my first term of freshman physics at Princeton in 1977—I know P.J. Peebles taught my second term and I wrote a term paper on monopoles. I chose to skip it because I felt I’d need to mention differences such as Woit points out and why the Sakurai Prize left Anderson out. I think my sentence saying what Higgs was first in is correctly constructed—I could have added “relativistic” somewhere—and I did emphasize that Higgs feels he should not have sole credit for the mechanism (either). I economized the intro for counterpoint to the recent priority case with another Edinburgh person over matrix multiplication.

4. December 14, 2011 8:19 pm

To state the obvious, if Nature turned out to behave like a “cheating prover”, that would be a vastly more important discovery than the Higgs boson itself! The whole fact that’s made physics possible since Galileo is that the universe appears to obey laws that are homogeneous across time and space, and that one can learn about via independently-repeated experiments. So suspecting a breakdown of those facts in the latest collider experiment, with not even a hint of motivation (so far, everything is perfectly consistent with a ~125GeV Higgs being there!), is sort of like telling someone: “Aha, you say you probably left your keys at the office, but what if you really can’t find them because they were stolen by trans-dimensional cyborgs?” I.e., it’s a logical possibility, but a ludicrously-unhelpful one, the sort of thing Sheldon from The Big Bang Theory might say.

• December 14, 2011 10:36 pm

Hi, Scott. Among things on my mind when I wrote this last section was your followup comment here to your NY Times blog item (still latest on your blog as I write):

“if both quantum mechanics and the prevailing conjectures in complexity theory are valid, then the physical universe can’t be feasibly simulated by a [classical] computer…”

—going on to argue that the classical cellular automaton model of Wolfram and Fredkin et al. under-powers the Universe. Your position seems to be that the Universe is computationally more powerful, but not in ways that can actually do boshaft computation. I might agree, and hope to, but click my link to see what Gian-Carlo Rota and Fabrizio Palombi go on to say about “duplicitous behavior” and the natural sciences just below.

My motivation comes not from the Higgs case in isolation but from the two paragraphs just above that section, about “disappearing significance” cases in physics (see e.g. this comment by Matt Strassler), and then in the human sciences where there’s an easier explanation. The nub is my attempt to expand a definition from Papadimitriou’s paper, trying to approach by simple means the way “emergent probability” is addressed for instance here, here, here (conservatively?), and by Bryce DeWitt here (pages).

• December 15, 2011 12:38 am

I should add: Rota and Palombi are not talking about Nature “cheating” but about whether Nature “reduces” in the way they find paradoxical for math. Underlying their book and some of my other sources is philosophical phenomenology.

• December 15, 2011 2:57 am

Yeah, as you point out, I think Rota and Palombi were talking about something completely different in that passage (which was lovely and interesting, though!).

To clarify, I enjoyed your discussion of some of the subtle philosophical questions involved with when the collider physicists are allowed to claim a “discovery.” However, I was worried that you downplayed a simple but important point: that within a few years, CERN hopes to rack up enough sigmas that all these philosophical questions will basically be moot! And I see no reasons from science or history to suspect they won’t succeed.

To put it more broadly: contrary to what’s often claimed, I don’t think skepticism is a universal good! To be productive, skepticism about an experiment should start with prosaic possibilities specific to that experiment—not speculations that could just as well overthrow millions of other experiments, like Nature “cheating” by solving a PSPACE-complete problem…

• December 15, 2011 3:26 am

What I want to know is why is a respected physicist and blogger like Strassler writing things like this—?

“…Most experimentalists I am talking to start to answer me by telling me a story about a 3 sigma result they know about that went away after more data was collected. Explain to me, please, how it could be, statistically, that the four ZZ events at CDF reported this summer at 325-327 GeV were a fluke. And yet it appears they were. ”

This was after I wrote the post, though I had seen other reference to the CDF events. Why weren’t more sigmas racked up on it? I’ll take the “over” on a Higgs at 124–126, but I wonder if anyone has done a study on the frequency of upholding 3-sigma events that people thought were important.

For a maybe-useful aspect, does the “Zoo” have a class C that quantifies the power needed to “cheat” a substantial protocol in some sense, maybe with evidence of C being disjoint from BQP? And just to state what I believe rather than speculate here, it goes (only) as far as suspecting that prior entanglements exist that affect probabilities on larger scales than commonly thought.

• December 15, 2011 6:44 am

Ken asks: “I wonder if anyone has done a study on the frequency of upholding 3-sigma events that people thought were important.”

Ken, two such studies (texts freely available on PubMed) are Emerson et al. “Testing for the presence of positive-outcome bias in peer review: a randomized controlled trial” (PMID:21098355) and Lynch et al. “Commercially funded and United States-based research is more likely to be published; good-quality studies with negative outcomes are not” (PMID:17473138).

My esteemed Seattle medical colleague Seth Leopold played a leading role in both studies, and in many enjoyable conversations Seth taught me much about the extraordinary difficulties that are encountered in systematically investigating the cognitive biases associated to statistical likelihood estimation in the context of peer review.

A pure physics study that reaches similar conclusions to Leopold’s (regrettably it is paywalled) is Gillies’ “The Newtonian gravitational constant: recent measurements and related studies” (1998); Gillies’ Fig. 1 in particular presents multiple measurements of Newton’s ${G}$ that differ by 5-sigma and more; this study too provides concrete evidence that even highly skilled research teams commonly fare poorly in assessing confidence levels.

Despite these well-documented difficulties, almost everyone (including me) embraces the reasonable opinions that: (1) further observations likely will confirm a Higgs boson at 125 GeV — but maybe not! — and (2) almost certainly the Standard Model that predicted this boson is incomplete and will require major modifications in coming decades.

This balance between confidence and humility is important to the vitality of science. As Freeman Dyson has put it: “If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children.” And yet the continuing creative rebellion that is science must not devolve into anarchy, but rather must grapple effectively with the “hunger, poverty, desperation, and chaos” that remain too widespread in the world.

• December 16, 2011 11:12 am

John, I love those quotes, thank you for them!

• December 14, 2011 11:10 pm

Scott, with a view toward cultivating holiday-season cheer here on Gödel’s Lost Letter and P=NP, please let me recount for your consideration the following analysis of Newcomb’s Paradox (as set forth in your lecture that your post linked-to) in light of the principle of Nature’s Benign Mendacity:

Smiling blithely, you walk into the room in which the Predictor has placed two boxes. As the proctors look on, you open both boxes, and to the proctors’ amazement, both boxes are filled with money.

The proctors ask you to explain, and you say: “The Predictor and I both are rational and benign beings, and therefore I foresaw that the Predictor would do precisely what I would have done myself, namely, fill both boxes with money (of course fully appreciating that this action would constitude a Lipton-Regan ‘burning arrow.’)”

The proctors press for a deeper explanation, and you say: “The Predictor too necessarily has free will — without it she cannot reliably predict my actions — and of course we both preferred your surprise to my disappointment. Truth is a trickster, you know!”

The proctors press for a still-deeper explanation, and smiling you say: “Look inside the box! Perhaps the Predictor has left a cheerful holiday message there for you!”

5. December 14, 2011 9:13 pm

Ken asks: Can Nature induce us to accept false conclusions with high probability, in the manner of a “nurturing parent”?

Here I have altered “cheating prover” to “nuturing parent” because Ken’s question becomes much more interesting — without alteration of its overall thrust — when we ascribe benign motives to Nature’s penchant for mendacity.

We discern in the past history of mathematics and science many instances of Nature’s benign mendacity; examples follow.

Nature seemingly is translationally invariant in space and time; to shield our growing understanding from various pathologies associated to spatial and temporal infinity she benignly induces general relativity.

Nature seemingly is relativistically (boost) invariant; to shield our growing understanding from various pathologies associated to infinite energy she benignly induces event horizons.

Nature seemingly is infinitely divisible; to shield our growing understanding from various pathologies associated to the collapse of matter she benignly induces (nonrelativistic) quantum mechanics.

Nature seemingly is infinitely causally separable and localizable; to shield our growing understanding from various pathologies associated to … uhhh … exponential dimensions and multi-universes of Hilbert space (?) … uhhh … she benignly induces … uhhh … well that bit’s not clear at present, eh?

But history gives us ample reason to hope and expect that Nature has some grand-yet-benign revelation prepared for us, of great mathematical subtlety and beauty, associated to the intersection of quantum mechanics and general relativity, that will help us grow out of our present too-naive understanding of locality, separability, and causality.

With luck, observing the Higgs boson carefully, and thinking deeply about what we are seeing, will help us appreciate the benign surprise(s) that Nature has prepared for us. Because beyond doubt, we do live in a wonderful universe.

And on that optimistic note, best wishes for a Happy Holiday Season are extended to all readers of Gödel’s Lost Letter and P=NP!, and thanks particularly to Dick and Ken for another great year of posts!

• December 16, 2011 11:18 am

I suppose Nature also might be shielding others from us (perhaps gently or not so gently later on), i.e., one several flavors of response to Fermi’s Paradox.

• December 16, 2011 12:43 pm

Delta, perhaps you will enjoy too Carl Sagan’s high-technology extension of the Judaic concept of gematria, from Sagan’s novel Contact (1995):

“Whoever makes the universe hides messages in transcendental numbers so they’ll be read 15 billion years later when intelligent life finally evolves.”

It’s fair to say that most mathematicians and scientists (and me too) think Sagan’s notion is mathematically nonsensical — an interesting idea pushed too far.

On the other hand, the publishing house Simon & Schuster gave Sagan a \$2 million advance based on his narrative idea, so maybe on some level Sagan’s hypergematria is not entirely crazy, eh?

Perhaps one broad lesson is that engineering, science, and mathematics all gain greatly when mathematical ideals of naturality are formalized and fused with humanistic ideals of narrative. This process of formalization and fusion is ongoing, progressive and irreversible, and now seems to be accelerating in the early 21st century. Good.

Indeed, it seems (to me) that there is scarcely any other avenue than a Sagan-style naturality-narrative fusion by which the STEM enterprise can “make sense.”

So, more Carl Sagans please!

• December 16, 2011 1:11 pm

John, I don’t know if Sagan would have liked to say he was extending “gematria”. However, I do allow that analogy when speaking of algorithmic probability, insofar as it is defined in terms of some textual representation of an object. I could add to what I said above about how much of this speculation I’ve actually adopted by saying I believe algorithmic probability plays a role in physical processes—and perhaps detectably in a digital domain such as the LHC chamber and data recording. There may, however, be obstacles to detecting it, by extension from this paper by Ulvi Yurtsever.

• December 16, 2011 6:23 pm

Ken, I for one had not previously encountered algorithmic (Solomonoff) probability, and so I am both grateful for and interested in the references you supplied. Perhaps (hopefully) in 2012 Gö del’s Lost Letter and P=NP will discuss these interesting ideas further.

• December 16, 2011 6:35 pm

Indeed!–the intent to do so was a motive for this post. I may even have a concrete connection to (faults in) Zobrist key schemes for hash tables. For now let me link just this nice primer on the concept.

• December 17, 2011 1:14 pm

Great, glad this was brought up — look forward to seeing more.

6. December 17, 2011 4:10 pm

There were some posts over my blog that are related to some interesting statistical questions raised here. Can we expect 95% of statistically-based results with significance level 95% are correct? Will it help raising the required significance level to 99.5%? How to add up p values of two independent experiments? Should we believe the same two results both with 4sigma significance where in one the effect is large and in the other the effect is small?


text:
## Wednesday, February 4, 2015

### The 9 Balls Problem (still open)

Recently, my lab mate Patrick came to my office and proposed to give the following question for an exam in information theory: Explain why exactly two weightings on a standard balance scale suffice to determine which out of nine balls is heavier than the other eight (which have all the same weight).

Everybody knows the puzzle, and most know the solution: Split the nine balls in groups of three and weigh them. The heavier triple must contain the heavy ball, so you can weigh two balls of the heavier triple. If they balance, the third ball must be the heavy one. Similarly, if the first two triples have the same weight, the heavy ball must be in the third triple that you did not weigh in the first step.

In fact, it turns out that in this case two weightings are not only the minimal number of weightings necessary, but also the optimal number: Each weighting gives us three results (right heavy, left heavy, balanced), so two weightings give us nine results. And, there are exactly nine balls, one of which we have to determine. Hence, if we want to put it in terms of information theory, the number of bits needed to encode the position of the heavy ball is equal to the number of bits obtained from the scale in two weightings:

$$H(balls) = \log 9 = 2 \log 3 = 2 H(scale)$$

Things get a bit more difficult if we do not know whether the odd ball is heavier or lighter than the rest. Assume that the ball is in one of the first two triples which we weigh. Then, the scale does not immediately tell us in which of these triples it is: If the odd ball is lighter, then it is in the triple going up, if the odd ball is heavier it is in the triple going down. But there is a very nice scheme which allows us to determine the position of the odd ball and whether it is heavier or lighter in three weightings. And again, information theory tells us how to interpret this. Given that there are two possibilities for the weight, $H(weight)=\log 2$, we have

$$H(balls,weight) = \log 9 + \log 2 = \log 18 < \log 27 = 3\log 3 = 3H(scale)$$

So, three weightings give us more than enough information about whether the odd ball is heavier or lighter, and where it is. I don't want to reproduce the algorithm to find the odd ball here, just let me tell you that three weightings are sufficient for more than nine balls, too. We only have to guarantee that $H(balls,weight)\le 3H(scale)$. The solution to find the odd ball out of twelve is given in the Wikipedia article about the Twelve-Coin-Problem.

It turns out that if we are not interested in the weight of the odd ball, but just in its position, an ordinary balance scale might not be the right type of measurement device. Although thirteen balls would still satisfy above equation, giving

$$H(balls,weight) = \log 26 < \log 27 = 3H(scale)$$

three weightings tell us the odd ball, but not whether it is heavier or lighter (see Manish's comment to this blog entry or this website). But why is that so? Raj on Quora wrote that with $n$ weightings you can find the odd one of at most $(3^n-1)/2$ balls and the odd one and its weight from at most $(3^n-3)/2$ balls. For $n=3$ this evaluates to 12 and 13, respectively, so the result seems to be correct.

Still, I'm not totally happy with it. If it's true, then there should be a sequence of results expressing this also in terms of entropy, or in terms of conditional entropy of, say, the position given the results of the first two weightings. There is some work to do to improve intuition about this problem, although Raj already did a very good job. Let me know when you're done!


text:
Eleisha's Segment 18: The Correlation Matrix

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

To Calculate:

1. Random points i are chosen uniformly on a circle of radius 1, and their $\displaystyle (x_i,y_i)$ coordinates in the plane are recorded. What is the 2x2 covariance matrix of the random variables $\displaystyle X$ and $\displaystyle Y$ ? (Hint: Transform probabilities from $\displaystyle \theta$ to $\displaystyle x$ . Second hint: Is there a symmetry argument that some components must be zero, or must be equal?)

2. Points are generated in 3 dimensions by this prescription: Choose $\displaystyle \lambda$ uniformly random in $\displaystyle (0,1)$ . Then a point's$\displaystyle (x,y,z)$ coordinates are $\displaystyle (\alpha\lambda,\beta\lambda,\gamma\lambda)$ . What is the covariance matrix of the random variables $\displaystyle (X,Y,Z)$ in terms of $\displaystyle \alpha,\beta,\text{ and }\gamma$ ? What is the linear correlation matrix of the same random variables?

1. Suppose you want to get a feel for what a linear correlation$\displaystyle r=0.3$ (say) looks like. How would you generate a bunch of points in the plane with this value of $\displaystyle r$ ? Try it. Then try for different values of $\displaystyle r$ . As $\displaystyle r$ increases from zero, what is the smallest value where you would subjectively say "if I know one of the variables, I pretty much know the value of the other"?
2. Suppose that points in the $\displaystyle (x,y)$ plane fall roughly on a 45-degree line between the points (0,0) and (10,10), but in a band of about width w (in these same units). What, roughly, is the linear correlation coefficient $\displaystyle r$  ?


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##### Cited by 2 publications
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“…Remark 2.1. As pointed out by Falconer and Hu [11], we just observe that if a ∈ L 1 (V ) and a ≤ 0 in V then, by (5), the norm · * , defined by…”
Section: Abstract Frameworkmentioning
confidence: 88%
See 1 more Smart Citation
“…Remark 2.1. As pointed out by Falconer and Hu [11], we just observe that if a ∈ L 1 (V ) and a ≤ 0 in V then, by (5), the norm · * , defined by…”
Section: Abstract Frameworkmentioning
confidence: 88%
“…Successively, Breckner, Rȃdulescu, and Varga [7] proved the existence of infinitely many solutions of problem (S f,g a,1 ) under the key assumption that the nonlinearity f is non-positive in a sequence of positive intervals (see Remark 3.2). See also the papers [2,3,4,5,6,16] and references therein for related topics.…”
Section: Introductionmentioning
confidence: 99%


text:
# Cannot generate IKFast closed solutions for regular 6DOF Arm

Hello everybody!

I'm trying to generate closed analytical solutions for custom 6Dof arm manipulator that we are creating. I managed to obtain container with required software packages (openrave and ikfast plugin). I followed this tutorial: https://adrlab.bitbucket.io/ct/v2.2/c...

Everything seems to work fine - I'm able to load my .dae file and get some informations (indices list). It looks OK. But process of generation final file with solutions last for ages - it never ends...

I also tried to use this online generator: https://www.hamzamerzic.info/ikfast_g...

The result is exactly the same. Process always gets stuck on lines:

INFO: skipping dependent index 3, numausymbols=0, numausymbols=6
INFO: skipping dependent index 5, numausymbols=0, numausymbols=7
INFO: skipping dependent index 6, numausymbols=0, numausymbols=7

I'm assuming that there is something wrong with my .urdf file. Can anyone be so kind and check what can be causing the problem?

<?xml version="1.0"?>
<robot name="pseudobot">

<material name="blue">
<color rgba="0 0 0.8 1"/>
</material>

<material name="white">
<color rgba="1 1 1 1"/>
</material>

<visual>
<origin xyz="0 0 0.05" rpy="0 0 0"/>
<geometry>
<box size="0.404 0.404 0.1"/>
</geometry>
<material name="blue"/>
</visual>

<visual>
<origin xyz="0 0 0.165" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.059" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.135" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.08125" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.135" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.07615" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0 0 0.07615" rpy="0 0 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<visual>
<origin xyz="0.01 0 0" rpy="0 1.57 0"/>
<geometry>
</geometry>
<material name="white"/>
</visual>

<joint name="base_joint" type="revolute">
<origin xyz="0 0 0" rpy="0 0 0"/>
<limit lower="-3.1416" upper="3.1416" effort="0.2" velocity="0.2"/>
<axis xyz="0 0 1"/>
</joint>

<joint name="joint_1" type="revolute">
<origin xyz="0 0 0.274" rpy="1.57 0 0 ...
edit retag close merge delete

I don't know whether it's a factor here, but the docker image that is used in the tutorial you link was last updated a year ago. OpenRAVE is quite actively developed, so I would suggest trying with a more recent version first.

( 2019-01-31 11:54:24 -0500 )edit

I tried following the procedure that You have described here: https://answers.ros.org/question/2639... The result is exactly the same! I think that it must be something wrong with my urdf... Although it is working fine with default moveit planner...

( 2019-02-01 09:20:10 -0500 )edit

Hi! Have you solved the issue? I'm having the same trouble here, following the steps described in the same link you sent. (#q263925). EDIT: I tried again with a fresh OpenRAVE install on a docker image that I've built, following the tutorial pointed on MoveIT site. It passed the first frozen state, and apparently was running ok. A few minutes later, when it was on the "addSolution" steps, it threw an error "GeneratorsNeeded" from sympy.

( 2020-04-30 17:18:00 -0500 )edit

Yes, in the end, I managed to build IKFast solution. I changed some parameters in the script which was starting the calculations on the docker-machine... The parameter was called maxDepthSomethingSomething and I reduced it. Sorry, I don't remember much :( After all that IKFast solution was not better/faster than TracIK, so I'm using the latter one.

( 2020-05-02 03:09:33 -0500 )edit

Thank you very much! it helped and I managed to build it, too! The parameter name is --maxcasedepth, and setting it to 1 or 2 made the build possible! Setting it to 3 resulted on the same error I commented on the edit (on the docker image i've made). Although the test success rate was below 50%, so I'll try the TracIK.

( 2020-05-03 11:09:37 -0500 )edit