Morphological image regularization with a smoothness criterion of structuring elements

Abstract

In this paper, a novel image denoising method with a morphological opening is proposed. In many image recovery, the regularization has been introduced to prevent overfitting between a recovered image and a noisy observation. In the regularization of an image, the smoothness of the image is assumed. The cost function, which is minimized during the regularization, is defined as a sum of the approximation error term and the smoothness penalty of the image. In morphological image processing, an image is approximated as a union of structuring elements (SEs) by the morphological image opening. In the approximation with the opening, the SE represents the local intensity surface of the image. We hence impose the smoothness penalty on the SE, instead of the recovered image itself, and propose an image opening method with the regularization penalty for the SE. In denoising, the approximation error is minimized under the constraint of the penalty for the SE. In experiments, we show that the proposed filtering method has ability to remove impulsive noises from degraded texture images.