  The sigmoid activation is the standard output activation function in binary
classification and segmentation with neural networks. Still, there exist a
variety of other potential output activation functions, which may lead to
improved results in medical image segmentation. In this work, we consider how
the asymptotic behavior of different output activation and loss functions
affects the prediction probabilities and the corresponding segmentation errors.
For cross entropy, we show that a faster rate of change of the activation
function correlates with better predictions, while a slower rate of change can
improve the calibration of probabilities. For dice loss, we found that the
arctangent activation function is superior to the sigmoid function.
Furthermore, we provide a test space for arbitrary output activation functions
in the area of medical image segmentation. We tested seven activation functions
in combination with three loss functions on four different medical image
segmentation tasks to provide a classification of which function is best suited
in this application scenario.
