Morphological regularization for adaptation of image opening

In this paper, an adaptation method for structuring elements of morphological filters is proposed. Morphological filters provide set theoretic image processing with structuring elements. The structuring element specifies a shape of a local image structure that is eliminated or preserved in a filter output. The adaptation of the structuring element is crucial problem for morphological image processing. For existing adaptation methods of structuring element, the training images that contain the pairs of a supposed input image and an ideal output image are required. In this paper, we propose an adaptation method for the structuring element without preliminary training for image opening. Our approach is based on a regularization technique for inverse problems of image recovery. The morphological regularization is defined as a minimization of the cost function which consists of a fidelity term and a regularization term that corresponds to a smoothness criteria of the structuring element. For this minimization problem, the morphological filters are approximated as differentiable functions in order to employ a gradient descent method. In experiments, we demonstrate the impulsive noise reduction from texture images by using the proposed morphological regularization.