When doing binary image segmentation, segmenting images into foreground and background, cross entropy is far from ideal as a loss function. As these datasets tend to be highly unbalanced, with far more background pixels than foreground, the model will usually score best by predicting everything as background. I have confronted this issue during my work with mammography and my solution was to use a weighted sigmoid cross entropy loss function giving the foreground pixels higher weight than the background.

While this worked it was far from ideal, for one thing it introduced another hyperparameters - the weight - and altering the weight had a large impact on the model. Higher weights favored predicting pixels as positive, increasing recall and decreasing precision, and lowering the weight had the opposite effect. When training my models I usually began with a high weight to encourage the model to make positive predictions and gradually decayed the weight to encourage it to make negative predictions.

For these types of segmentation tasks Intersection over Union tends to be the most relevant metric as pixel level accuracy, precision and recall do not account for the overlap between predictions and ground truth. Especially for this task, where overlap can be the difference between life and death for the patient, accuracy is not as relevant as IOU. So why not use IOU as a loss function?

The reason was because IOU was not differentiable so can not be used for gradient descent. However Wang et al have written a paper - Optimizing Intersection-Over-Union in Deep Neural Networks for Image Segmentation - which provides an easy way to use IOU as a loss function. In addition, this site provides code to implement this loss function in TensorFlow.

The essence of this method is that rather than using the binary predictions to calculate IOU we use the sigmoid probability output by the logits to estimate it which allows IOU to provide gradients. At first I was skeptical of this method, mostly because I understood cross entropy better and it is more common, but after I hit a performance wall with my mammography models I decided to give it a try.

My models using cross-entropy loss had ceased to improve validation performance so I switched the loss function and trained them for a few more epochs. The validation metrics began to improve, so I decided to train a copy of the model from scratch with the IOU loss. This has been a resounding success. The IOU loss accounts for the imbalanced data, eliminating the need to weight the cross entropy. With the cross entropy loss the models usually began with recall of near 1 and precision of near 0 and then the precision would increase while the recall slowly decreased until it plateaued. With IOU loss they both start near 0 and gradually increase, which to me seems more natural. 

Training with an IOU loss has two concrete benefits for this task - it has allowed the model to detect more subtle abnormalities which models trained with cross entropy loss did not detect; and it has reduced the number of false positives significantly. As the false positives are on a pixel level this effectively means that the predictions are less noisy and the shapes are more accurate.

The biggest benefit is that we are directly optimizing for our target metric rather than attempting to use an imperfect substitute which we hope will approximate the target metric. Note that this method only works for binary segmentation at the moment. It also is a bit slower than using cross entropy, but if you are doing binary segmentation the performance boost is well worth it.

Etiketten: python, machine_learning, mammography, convnets
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I wrote about this paper before, but I am going to again because it has been so enormously useful to me. I am still working on segmentation of mammograms to highlight abnormalities and I recently decided to scrap the approach I had been taking to upsampling the image and start that part from scratch.

When I started I had been using the earliest approach to upsampling, which basically was take my classifier, remove the last fully-connected layer and upsample that back to full resolution with transpose convolutions. This worked well enough, but the network had to upsample images from 2x2x1024 to 640x640x2 and in order to do this I needed to add skip connections from the downsizing section to the upsampling section. This caused problems because the network would add features of the input image to the output, regardless of whether the features were relevant to the label. I tried to get around this by adding bottleneck layers before the skip connection in order to only select the pertinent features, but this greatly slowed down training and didn't help much and the output ended up with a lot of weird artifacts.

In "Deconvolution and Checkerboard Artifacts", Odena et al. have demonstrated that replacing transpose convolutions with nearest neighbors resizing produces smoother images than using transpose convolutions. I tried replacing a few of my tranpose convolutions with resizes and the results improved.

Then I started reading about dilated convolutions and I started wondering why I was downsizing my input from 640x640 to 5x5 just to have to resize it back up. I removed all the fully-connected layers (which in fact were 1x1 convolutions rather than fully-connected layers) and then replaced the last max pool with a dilated convolution.

I replaced all of the transpose convolutions with resizes, except for the last two layers, as suggested by Odena et al, and the final tranpose convolution has a stride of 1 in order to smooth out artifacts.

In the downsizing section, the current model reduces the input from 640x640x1 to 20x20x512, then it is upsampled by using nearest neighbors resizing followed by plain convolutions to 320x320x32. Finally there is a tranpose convolution with a stride of 2 followed by a transpose convolution with a stride of 1 and then a softmax for the output. As an added bonus, this version of the model trains significantly faster than upsampling with transpose convolutions.

I just started training this model, but I am fairly confident it will perform better than previous upsampling schemes as when I extracted the last downsizing convolutional layer from the model that layer appeared closer to the label (although much smaller) than the final output did. I will update when I have actual results.

Update - After training the model for just one epoch, with the downsizing layer weights initialized from a previous model, the results are already significantly better than under the previous scheme.

Etiketten: coding, data_science, tensorflow, mammography, convnets, ddsm
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My original work with the DDSM and CBIS-DDSM dataset yielded good accuracy and recall on the test and validation data, but the model didn't perform so well when applied to the MIAS images, which came from a completely different dataset. Additional analysis of the images indicated that the negative images (from the DDSM) and the positive images (from the CBIS-DDSM) were different in some subtle but important ways:

1. The negative images had a lower mean, lower maximum and higher minimum. 
2. The negative images also had lower contrast.

We had become concerned about point 2 when we discovered that increasing the contrast of any image made it more likely to be predicted as positive and discovered point 1 while investigating this further. When applying our fully convolutional model trained on the combined data to complete scans, rather than the 299x299 images we had trained on, we noticed that more than 50% of the sections of a positive image were predicted as positive, even if the ROI was, in fact, only present in one section. This indicates that the model was using some feature of the images other than the ROI in its prediction.

When starting this project, we had initially planned to segment the CBIS-DDSM images and use images which did not contain an ROI as negative images, but we were not certain that there were not differences in the tissue of positive and negative scans which might make this approach not generalize to completely negative scans. When we realized that the scans had been pre-processed differently we attempted to adjust the negative images in such a way as to make them more similar to the positive images but were unable to do so without knowledge of how they had been processed.

Our solution to both of these issues was to train the model to do the segmentation of the scans rather than simple classification, using the masks as the labels. This approach had several advantages:

1. Using the mask as the label tells the model where it needs to look, so we can ensure that it actually uses the ROIs rather than other features of the images, such as the contrast or maximum pixel value.
2. This allows us the exclude the DDSM images and only use images from one dataset, as the ROI of most scans only encompasses a small portion of the image.

We recreated the model to do semantic segmentation by removing the last "fully connected" layer (which were implemented as a 1x1 convolution) and the logits layer and upsampling the results with transpose convolutions. In order for the upsampling to work properly we needed to have the size of the images be a multiple of 2 so that the dimension reduction could be properly undone, so we used images of size 320x320.

We were able to get fairly good results training on this data with a pixel level accuracy of about 90% and a pixel recall of 70%. The image level accuracy and recall were 70% and 87%, respectively. While these results were respectable, we noticed certain patterns of incorrect predictions. Images which were mostly dark, with patches that were much brighter, tended to have the bright patches predicted positive regardless of the actual label. This pattern was mostly observed when the bright patch ran off the edge of the image. 

We know that the context of an ROI is important in detecting and diagnosing it, and we suspected that in the absence of context the model was predicting any patch substantially brighter than it's surroundings to be positive. While for cancer detection, it is better to make a false positive than a false negative we thought that this pattern might become problematic when applying the model to images larger than those it was trained on. To address this issue we decided to create a dataset of larger images and continue training our model on those.

We created a dataset of 640x640 images and adjusted our existing model to take those as input. As the model is fully convolutional we can restore the model trained on 320x320 images and continue training it on the larger images with no problems, which we are currently in the process of doing. If the results of this are promising we may create another dataset of even larger images are fine-tune this model on those images until we have a model which takes complete images as input.

Etiketten: machine_learning, tensorflow, mammography, convnets, ddsm
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For a course I was taking at EPFL I was working on classifying images from the DDSM dataset with ConvNets. I had some success, although not as much as I would have liked, and I posted an edited version of my report on Medium.

The source code used to create and train the models is available in this GitHub repo, and the code used to create the data and do EDA is available here.

Although the course is over I am still working on this project, attempting to fix some of the issues that came up during the first stage.

Etiketten: python, machine_learning, mammography, convnets
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