Image Processing in L1-Norm-Based Discrete Cartesian and Polar Coordinates

Abstract

This paper proposes a radial image processing method performed in an L1-norm-based discrete polar coordinate system. For this purpose, we address the problem that polar coordinates based on the L2-norm cannot exist in discrete systems and then develop a method for converting Cartesian coordinates to L1-norm-based discrete polar coordinates. The proposed method greatly reduces the directional variance occurring in the Cartesian coordinate system and so processes radial directional images along the directions of the local image signal flows. To verify the usages of the proposed method, it was applied to the stabilization of mass-type breast cancer images, a segmentation of extremely deformable objects such as biomedical objects. In all cases, the proposed method produced superior results compared to the processing in the Cartesian coordinate systems. The proposed method is useful for processing or analyzing diffusing and deformable images such as bio-cell and smoke images.