Higher-Order Flux with Spherical Harmonics Transform for Vascular Analysis

Abstract

In this paper, we present a novel flux-based method to robustly identify the vasculature structure in the angiography, where the curvilinear geometry is delineated by the higher-order tensor computed in the spherical frequency domain. We first modify the vesselness measurement derived from the oriented flux and introduce an antisymmetry measurement to generate the curvilinear responses. We then extend the responses to the cylindrical model and fit them into spherical harmonics transform to perform high-order tensor analysis, in which fiber orientation distribution function is utilized. A graphical framework based on the random walker is applied for vascular segmentation. It is experimentally demonstrated that the proposed method can achieve accurate and stable segmentation performance with various noise levels, demonstrating the proposed method can deliver reliable curvilinear structure responses.