Quaternion Color Curvature

Shi, L., Funt, B. and Hamarneh, G., "Quaternion Color Curvature," Proc. IS&T Sixteenth Color Imaging Conference, Portland, Nov. 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 Frangiís [1] vesselness measure for scalar images. Experimental results show the effectiveness of quaternion color curvature in generating a vesselness map.

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