# For semantic sementation, why am I getting better loss values with binary cross entropy than dice coef?

I'm learning all related to data science and how to train U-Net to do semantic segmentation.

I have a U-NET with this loss function:

def dice_coef(y_true, y_pred):
y_true_f = K.flatten(float(y_true))
y_pred_f = K.flatten(float(y_pred))
intersection = K.sum(y_true_f * y_pred_f)
return (2 * intersection + 1) // (K.sum(y_true_f) + K.sum(y_pred_f) + 1)

def dice_coef_loss(y_true, y_pred):
return 1-dice_coef(y_true, y_pred)


When the same data for training and validation, the model works better with binary_crossentropy than with dice_coef_loss.

With binary_crossentropy I get this output:

Epoch 1/50
2/698 [..............................] - ETA: 53s - loss: 0.9674 - accuracy: 0.6257WARNING:tensorflow:Callbacks method on_train_batch_end is slow compared to the batch time (batch time: 0.0432s vs on_train_batch_end time: 0.1084s). Check your callbacks.
698/698 [==============================] - 117s 168ms/step - loss: 0.0661 - accuracy: 0.9848 - val_loss: 0.0379 - val_accuracy: 0.9902
Epoch 2/50
698/698 [==============================] - 115s 165ms/step - loss: 0.0329 - accuracy: 0.9902 - val_loss: 0.0313 - val_accuracy: 0.9901
Epoch 3/50
698/698 [==============================] - 115s 165ms/step - loss: 0.0190 - accuracy: 0.9938 - val_loss: 0.0243 - val_accuracy: 0.9920
Epoch 4/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0154 - accuracy: 0.9948 - val_loss: 0.0105 - val_accuracy: 0.9963
Epoch 5/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0090 - accuracy: 0.9967 - val_loss: 0.0094 - val_accuracy: 0.9966
Epoch 6/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0083 - accuracy: 0.9970 - val_loss: 0.0143 - val_accuracy: 0.9948
Epoch 7/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0122 - accuracy: 0.9958 - val_loss: 0.0073 - val_accuracy: 0.9972
Epoch 8/50
698/698 [==============================] - 115s 165ms/step - loss: 0.0055 - accuracy: 0.9979 - val_loss: 0.0053 - val_accuracy: 0.9979
Epoch 9/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0045 - accuracy: 0.9982 - val_loss: 0.0047 - val_accuracy: 0.9982
Epoch 10/50
698/698 [==============================] - 115s 165ms/step - loss: 0.0047 - accuracy: 0.9981 - val_loss: 0.0044 - val_accuracy: 0.9982
Epoch 11/50
698/698 [==============================] - 116s 166ms/step - loss: 0.0041 - accuracy: 0.9983 - val_loss: 0.0050 - val_accuracy: 0.9980
Epoch 12/50
698/698 [==============================] - 115s 165ms/step - loss: 0.1478 - accuracy: 0.9962 - val_loss: 0.0844 - val_accuracy: 0.9849
Epoch 13/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0478 - accuracy: 0.9872 - val_loss: 0.0290 - val_accuracy: 0.9902
Epoch 14/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0218 - accuracy: 0.9924 - val_loss: 0.0167 - val_accuracy: 0.9941
Epoch 15/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0140 - accuracy: 0.9950 - val_loss: 0.0127 - val_accuracy: 0.9956
Epoch 16/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0103 - accuracy: 0.9961 - val_loss: 0.0122 - val_accuracy: 0.9956
Epoch 17/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0096 - accuracy: 0.9964 - val_loss: 0.0084 - val_accuracy: 0.9970
Epoch 18/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0086 - accuracy: 0.9967 - val_loss: 0.0074 - val_accuracy: 0.9972
Epoch 19/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0066 - accuracy: 0.9975 - val_loss: 0.0080 - val_accuracy: 0.9970
Epoch 20/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0103 - accuracy: 0.9965 - val_loss: 0.0145 - val_accuracy: 0.9951
Epoch 21/50
698/698 [==============================] - 113s 163ms/step - loss: 0.0065 - accuracy: 0.9976 - val_loss: 0.0055 - val_accuracy: 0.9979
Epoch 22/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0051 - accuracy: 0.9981 - val_loss: 0.0057 - val_accuracy: 0.9978
Epoch 23/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0058 - accuracy: 0.9977 - val_loss: 0.0051 - val_accuracy: 0.9981
Epoch 24/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0046 - accuracy: 0.9982 - val_loss: 0.0055 - val_accuracy: 0.9980
Epoch 25/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0044 - accuracy: 0.9983 - val_loss: 0.0051 - val_accuracy: 0.9981
Epoch 26/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0049 - accuracy: 0.9981 - val_loss: 0.0089 - val_accuracy: 0.9968
Epoch 27/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0045 - accuracy: 0.9982 - val_loss: 0.0043 - val_accuracy: 0.9983
Epoch 28/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0038 - accuracy: 0.9985 - val_loss: 0.0044 - val_accuracy: 0.9984
Epoch 29/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0069 - accuracy: 0.9975 - val_loss: 0.0061 - val_accuracy: 0.9978
Epoch 30/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0039 - accuracy: 0.9984 - val_loss: 0.0045 - val_accuracy: 0.9982
Epoch 31/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0033 - accuracy: 0.9986 - val_loss: 0.0038 - val_accuracy: 0.9985
Epoch 32/50
698/698 [==============================] - 112s 161ms/step - loss: 0.0032 - accuracy: 0.9987 - val_loss: 0.0041 - val_accuracy: 0.9984
Epoch 33/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0033 - accuracy: 0.9986 - val_loss: 0.0037 - val_accuracy: 0.9985
Epoch 34/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0032 - accuracy: 0.9987 - val_loss: 0.0038 - val_accuracy: 0.9985
Epoch 35/50
698/698 [==============================] - 112s 161ms/step - loss: 0.0030 - accuracy: 0.9987 - val_loss: 0.0039 - val_accuracy: 0.9985
Epoch 36/50
698/698 [==============================] - 112s 161ms/step - loss: 0.0074 - accuracy: 0.9971 - val_loss: 0.0046 - val_accuracy: 0.9982
Epoch 37/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0031 - accuracy: 0.9987 - val_loss: 0.0033 - val_accuracy: 0.9987
Epoch 38/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0027 - accuracy: 0.9989 - val_loss: 0.0032 - val_accuracy: 0.9987
Epoch 39/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0026 - accuracy: 0.9989 - val_loss: 0.0032 - val_accuracy: 0.9987
Epoch 40/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0131 - accuracy: 0.9960 - val_loss: 0.0041 - val_accuracy: 0.9984
Epoch 41/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0031 - accuracy: 0.9987 - val_loss: 0.0033 - val_accuracy: 0.9987
Epoch 42/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0025 - accuracy: 0.9989 - val_loss: 0.0032 - val_accuracy: 0.9987
Epoch 43/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0025 - accuracy: 0.9990 - val_loss: 0.0032 - val_accuracy: 0.9987
Epoch 44/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0024 - accuracy: 0.9990 - val_loss: 0.0034 - val_accuracy: 0.9986
Epoch 45/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0026 - accuracy: 0.9989 - val_loss: 0.0036 - val_accuracy: 0.9986
Epoch 46/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0025 - accuracy: 0.9989 - val_loss: 0.0031 - val_accuracy: 0.9988
Epoch 47/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0024 - accuracy: 0.9990 - val_loss: 0.0036 - val_accuracy: 0.9987
Epoch 48/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0025 - accuracy: 0.9990 - val_loss: 0.0032 - val_accuracy: 0.9987
Epoch 49/50
698/698 [==============================] - 113s 162ms/step - loss: 0.0024 - accuracy: 0.9990 - val_loss: 0.0030 - val_accuracy: 0.9988
Epoch 50/50
698/698 [==============================] - 113s 161ms/step - loss: 0.0049 - accuracy: 0.9981 - val_loss: 0.0034 - val_accuracy: 0.9987


With dice_coef_loss I get this output:

Epoch 1/50
2/582 [..............................] - ETA: 1:36 - loss: 0.9994 - accuracy: 0.9923WARNING:tensorflow:Callbacks method on_train_batch_end is slow compared to the batch time (batch time: 0.0626s vs on_train_batch_end time: 0.1113s). Check your callbacks.
582/582 [==============================] - 95s 163ms/step - loss: 0.9160 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 2/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8988 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 3/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9240 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 4/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9027 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 5/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8840 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 6/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8894 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 7/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9052 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 8/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8961 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 9/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9190 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 10/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9085 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 11/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9150 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 12/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9162 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 13/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9103 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 14/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9028 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 15/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8866 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 16/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9127 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 17/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9006 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 18/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8809 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 19/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9080 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 20/50
582/582 [==============================] - 93s 160ms/step - loss: 0.8952 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 21/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8952 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 22/50
582/582 [==============================] - 93s 160ms/step - loss: 0.8969 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 23/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8919 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 24/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8935 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 25/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9035 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 26/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9073 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 27/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9005 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 28/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9041 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 29/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8902 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 30/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8909 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 31/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9097 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 32/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9130 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 33/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9026 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 34/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9002 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 35/50
582/582 [==============================] - 93s 161ms/step - loss: 0.9153 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 36/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8931 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 37/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9148 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 38/50
582/582 [==============================] - 94s 161ms/step - loss: 0.9007 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 39/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8901 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 40/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8930 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 41/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8991 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 42/50
582/582 [==============================] - 94s 161ms/step - loss: 0.8946 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 43/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8978 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 44/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9179 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 45/50
582/582 [==============================] - 93s 160ms/step - loss: 0.8976 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 46/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9051 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 47/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9082 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 48/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9040 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 49/50
582/582 [==============================] - 93s 161ms/step - loss: 0.8989 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853
Epoch 50/50
582/582 [==============================] - 93s 160ms/step - loss: 0.9231 - accuracy: 0.9862 - val_loss: 0.9218 - val_accuracy: 0.9853


Any advice about why am I getting better loss values with binary cross entropy than with dice coef?

This result makes me doubt whether I have chosen the best loss function with the binary cross-entropy.