Learning the Hit-or-Miss Transform-Based Morphological Neural Networks

Mathematical morphology is well suited for learning interpretable shapes because of its structure-based operations. In this article, we propose techniques to improve the learning of the hit-or-miss transform, a morphological operation developed to detect object shapes by simultaneously matching the foreground and background. First, we reformulate the definition of the transform for better intuition and interpretation. Next, we enhance the selection of the "Don’t Care" elements–which are neither foreground nor background–by using an interval instead of a point, zero, proposed in prior work. We then apply linear operations to these Don’t Care elements that are by definition excluded from the transform, allowing them to be included in the parameter update during the optimization process. Finally, we propose to piece-wise linearize the hit-or-miss transform to make it robust against variations and noises. Experiment results using a deep neural network architecture, MobileNetV2, on Cifar-10 and FashionMNIST datasets demonstrate the efficacy of the proposed methods. In particular, the piecewise linear hit-or-miss transform improved the baseline accuracy for Cifar-10 by 10.7%.