“One cannot say apriori which one will work better on a particular dataset. The correct way is to try both and compare the results. Also, note that when it comes to segmentation, it is not so easy to "compare the results": IoU based measures like dice coefficient cover only some aspects of the quality of the segmentation; in some applications, different measures such as mean surface distance or Hausdorff surface distance need to be used. As you see, not even the choice of the correct quality metric is trivial, let alone the choice of the best cost function.

I personally have very good experience with the dice coefficient; it really does wonders when it comes to class imbalance (some segments occupy less pixels/voxels than others). On the other hand, the training error curve becomes a total mess: it gave me absolutely no information about the convergence, so in this regard cross-entropy wins. Of course, this can/should be bypassed by checking the validation error anyways.”

The Dice coefficient is a metric used to evaluate the performance of object detection and segmentation algorithms. It is calculated as twice the intersection of the predicted and ground truth bounding boxes divided by the sum of the areas of the predicted and ground truth bounding boxes 1.

While IoU is a popular metric for evaluating object detection algorithms, it is not commonly used as a loss function for training deep learning-based segmentation models. Instead, the Dice coefficient is often used as a loss function for segmentation tasks because it is differentiable, whereas IoU is not. The Dice coefficient loss function is defined as 1 minus the Dice coefficient.

Here’s an example to help you understand the Dice coefficient better:

Let’s say we have two binary images, one is the ground truth and the other is the predicted image. The Dice coefficient is calculated as twice the number of pixels that are common in both images divided by the total number of pixels in both images. The Dice coefficient ranges from 0 to 1, where 0 indicates no overlap between the two images and 1 indicates perfect overlap

Dice Loss:

1. Spatial Overlap Emphasis:
   • Dice Loss is designed to maximize the spatial overlap between the predicted and ground truth segmentations. If spatial overlap is a crucial aspect of your segmentation task, Dice Loss can be more effective than Cross Entropy Loss.
2. Handling Class Imbalance:
   • Dice Loss can handle class imbalance more effectively than Cross Entropy Loss, especially in scenarios where one class dominates the others in terms of pixel counts. Dice Loss tends to perform well when dealing with imbalanced datasets.
3. Localization Accuracy:
   • Dice Loss tends to produce segmentations with better localization accuracy. It encourages the model to focus on capturing the precise boundaries of segmented regions.
4. Soft Segmentation Masks:
   • Dice Loss is suitable for tasks where soft segmentation masks (partial pixel assignments) are meaningful, as it operates on probabilities.

Cross Entropy Loss:

1. Class Probability Emphasis:
   • Cross Entropy Loss is designed to optimize the probability distribution over classes. It encourages the model to assign high probabilities to the correct classes for each pixel.
2. Simplicity and Stability:
   • Cross Entropy Loss is often simpler to implement and computationally more stable during training. It does not involve the explicit calculation of intersections and unions, making it easier to work with.
3. Common Choice for Multi-Class Problems:
   • Cross Entropy Loss is a standard choice for multi-class segmentation problems. It is widely used and often performs well in practice.
4. One-Hot Encoding:
   • Cross Entropy Loss typically requires one-hot encoding of the ground truth labels. If one-hot encoding is preferred or required for your task, Cross Entropy Loss may be more suitable.