Cross Entropy Loss for Semantic Segmentation Keras

问题

I'm pretty sure this is a silly question but I can't find it anywhere else so I'm going to ask it here.

I'm doing semantic image segmentation using a cnn (unet) in keras with 7 labels. So my label for each image is (7,n_rows,n_cols) using the theano backend. So across the 7 layers for each pixel, it's one-hot encoded. In this case, is the correct error function to use categorical cross-entropy? It seems that way to me but the network seems to learn better with binary cross-entropy loss. Can someone shed some light on why that would be and what the principled objective is?

回答1:

Binary cross-entropy loss should be used with sigmod activation in the last layer and it severely penalizes opposite predictions. It does not take into account that the output is a one-hot coded and the sum of the predictions should be 1. But as mis-predictions are severely penalizing the model somewhat learns to classify properly.

Now to enforce the prior of one-hot code is to use softmax activation with categorical cross-entropy. This is what you should use.

Now the problem is using the softmax in your case as Keras don't support softmax on each pixel.

The easiest way to go about it is permute the dimensions to (n_rows,n_cols,7) using Permute layer and then reshape it to (n_rows*n_cols,7) using Reshape layer. Then you can added the softmax activation layer and use crossentopy loss. The data should also be reshaped accordingly.

The other way of doing so will be to implement depth-softmax :

def depth_softmax(matrix):
    sigmoid = lambda x: 1 / (1 + K.exp(-x))
    sigmoided_matrix = sigmoid(matrix)
    softmax_matrix = sigmoided_matrix / K.sum(sigmoided_matrix, axis=0)
    return softmax_matrix

and use it as a lambda layer:

model.add(Deconvolution2D(7, 1, 1, border_mode='same', output_shape=(7,n_rows,n_cols)))
model.add(Permute(2,3,1))
model.add(BatchNormalization())
model.add(Lambda(depth_softmax))

If tf image_dim_ordering is used then you can do way with the Permute layers.

For more reference check here.

回答2:

I tested the solution of @indraforyou and think that the proposed method has some mistakes. As the commentsection does not allow for proper code segments, here is what I think would be the fixed version:

def depth_softmax(matrix):

    from keras import backend as K

    exp_matrix = K.exp(matrix)
    softmax_matrix = exp_matrix / K.expand_dims(K.sum(exp_matrix, axis=-1), axis=-1)
    return softmax_matrix

This method will expect the ordering of the matrix to be (height, width, channels).

来源：https://stackoverflow.com/questions/42118821/cross-entropy-loss-for-semantic-segmentation-keras