The authors suggest that the classical approach of using only data fidelity term to train CNN is insufficient.

Inspired by past work on energy functional minimization techniques (ASM, graph-based methods …), they propose to adapt Veksler star shape prior as a loss term.

Star shape Prior

The idea is to penalize predictions that wouldn’t amount to a star shaped object.

“Assuming c is the center of object O, object O is a star shape object if, for any point p interior to the object, all the pixels q lying on the straight line segment connecting p to the object center c are inside the object”.

Here is the expression of the new loss term that they combine to a binary cross entropy loss :

Basically, it enforces that with p and q any incident pixel on line l_pc, c being the groundtruth center, q should have the same label as p if they have the same grountruth labels and if p is assigned to the wrong class. Discontinuities of pixel labels on l_pc are only allowed on lesion boundaries and if the givel label is true.

Experiments

They use two CNN architectures : U-Net and ResNet-DUC (Res-Net-152 pretrained on ImageNet).

They apply this on the Skin Lesion Analysis Towards Melanoma Detection Challenge (ISBI 2017), composed of 2000 (train) + 150 (valid) + 600 (test) images. Only 0.14% of the groundtruths skin lesions are not star-shaped.

They add the second term loss after 5 epochs. In practice, they only consider the m closest pixels to p on d directions (m = 6, d = 8).

Here are the Jaccard index results :

For each experiment, they also computed a non-parametric Wilcoxon test that showed that the networks with and without the prior are statistically different at p < 0.05.

Here is a visualization of the results :