Learning of structuring elements for morphological image model with a sparsity prior

This paper presents a learning method of a structuring element for morphological image generative model by using a maximum a posterior (MAP) estimation. Mathematical morphology provides set-theoretic image processing methods. In the morphological processing, an image is approximated as a union of translated and level-shifted structuring elements. The specification of the structuring element is crucial to application of the morphology for image processing tasks. In this paper, we introduce the MAP estimation of the structuring element from an input image for the morphological modeling. Sparse prior density functions of approximation errors and occurrence of the structuring elements are assumed for the learning. The structuring element is optimized to maximize the likelihood that is estimated from the prior density functions. In experiments, we show that the proposed learning method is capable to extract fundamental micro-structures of texture images as the structuring elements.