A Class of 2D Directional Filters with Applications in Biomedical Image Analysis

Abstract

In this paper we present a design method for a class of 2D recursive filter banks with wedge-shaped channels, based on frequency transformations and 1D prototype filters. The design starts from a given analog prototype filter with specified parameters and a transfer function which is factorized into elementary functions. Applying adequate frequency transformations to these functions, the desired 2D filters are directly obtained in a factorized form, preserving the selectivity properties of their 1D counterparts. The approach is mainly analytical but also uses numerical approximations and is simple, efficient and versatile. These filter banks find applications in medical image analysis, as shown on some angiography images, for instance the detection of blood vessels with a specified orientation. A design example starting from imposed specifications and also some simulation results are provided.