When people try to solve the task of semantic segmentation with CNN's they usually use a softmax-crossentropy loss during training (see Fully conv. - Long). But when it comes to comparing the performance of different approaches measures like intersection-over-union are reported.
My question is why don't people train directly on the measure they want to optimize? Seems odd to me to train on some measure during training, but evaluate on another measure for benchmarks.
I can see that the IOU has problems for training samples, where the class is not present (union=0 and intersection=0 => division zero by zero). But when I can ensure that every sample of my ground truth contains all classes, is there another reason for not using this measure?
Checkout this paper where they come up with a way to make the concept of IoU differentiable. I implemented their solution with amazing results!
It is like asking "why for classification we train log loss and not accuracy?". The reason is really simple - you cannot directly train for most of the metrics, because they are not differentiable wrt. to your parameters (or at least do not produce nice error surface). Log loss (softmax crossentropy) is a valid surrogate for accuracy. Now you are completely right that it is plain wrong to train with something that is not a valid surrogate of metric you are interested in, and the linked paper does not do a good job since for at least a few metrics they are considering - we could easily show good surrogate (like for weighted accuracy all you have to do is weight log loss as well).
Here's another way to think about this in a simple manner.
Remember that it is not sufficient to simply evaluate a metric such as accuracy or IoU while solving a relevant image problem. Evaluating the metric must also help the network learn in which direction the weights must be nudged towards, so that a network can learn effectively over iterations and epochs.
Evaluating this direction is what the earlier comments mean that the errors are differentiable. I suppose that there is nothing about the IoU metrics that the network can use to say: "hey, it's not exactly here, but I have to maybe move my bounding box a little to the left!"
Just a trickle of an explanation, but hope it helps..
来源：https://stackoverflow.com/questions/40475246/why-does-one-not-use-iou-for-training