  Dice loss is widely used for medical image segmentation, and many improvement
loss functions based on such loss have been proposed. However, further Dice
loss improvements are still possible. In this study, we reconsidered the use of
Dice loss and discovered that Dice loss can be rewritten in the loss function
using the cosine similarity through a simple equation transformation. Using
this knowledge, we present a novel t-vMF Dice loss based on the t-vMF
similarity instead of the cosine similarity. Based on the t-vMF similarity, our
proposed Dice loss is formulated in a more compact similarity loss function
than the original Dice loss. Furthermore, we present an effective algorithm
that automatically determines the parameter $\kappa$ for the t-vMF similarity
using a validation accuracy, called Adaptive t-vMf Dice loss. Using this
algorithm, it is possible to apply more compact similarities for easy classes
and wider similarities for difficult classes, and we are able to achieve an
adaptive training based on the accuracy of the class. Through experiments
conducted on four datasets using a five-fold cross validation, we confirmed
that the Dice score coefficient (DSC) was further improved in comparison with
the original Dice loss and other loss functions.
