Quaternion Color Curvature
Lilong Shi, Brian Funt, Ghassan Hamarneh · 2008
In this paper we propose a novel approach to measuring curvature in color or vector-valued images (up to 4-dimensions) based on quaternion singular value decomposition of a Hessian matrix. This approach generalizes the existing scalar-image curvature approach which makes use of the eigenvalues of the Hessian matrix [1]. In the case of vector-valued images, the Hessian is no longer a 2D matrix but rather a rank 3 tensor. We use quaternion curvature to derive vesselness measure for tubular structures in color or vector-valued images by extending Frangi’s [1] vesselness measure for scalar images. Experimental results show the effectiveness of quaternion color curvature in generating a vesselness map.