Keras，循环输出的成本函数？

Question

Right now I am trying to get a neural net to colorize images. I want to do it in the HSV color space. The issue with this is that the hue channel is cyclic. The normalized values for hue are between 0 and 1. Say for instance the model predicts 0.99 but the actual hue is 0.01. With normal mean squared error loss this looks like it is way off. However the distance is really more like 0.02. How can I get a cyclic loss function in keras?

Answer 1

The true distance from predicted hue A to actual hue B is really the minimum of 3 terms:

1. (A - B)^2 (distance if you don't wrap around)
2. (A - B + 1)^2 (distance if you wrap around to the left)
3. (A - B - 1)^2 (distance if you wrap around to the right)

For instance, in your example the shortest way to get from A = 0.99 to B = 0.01 is to wrap around to the right, and the distance is (A - B - 1)^2 = (0.99 - 0.01 - 1)^2 = (-0.02)^2 = 0.02^2 .

Now that we have the math figured out, how do we implement it? Keras's implementation of mean squared error is:

from keras import backend as K

def mean_squared_error(y_true, y_pred):
    return K.mean(K.square(y_pred - y_true), axis=-1)

Here's the tweak to make it cyclic:

def cyclic_mean_squared_error(y_true, y_pred):
    return K.mean(K.minimum(K.square(y_pred - y_true), 
                            K.minimum(K.square(y_pred - y_true + 1), 
                                      K.square(y_pred - y_true - 1)), axis=-1)

To use this loss function, specify loss=cyclic_mean_squared_error when compiling the model.