Aug. 29, 2018, midnight
By : Eric A. Scuccimarra
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.
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