Segmentation of 3D volumes using second derivatives

The second derivatives of a 2D or 3D signal is claimed to be of fundamental value for image analysis, segmentation, visualization and many other tasks. But to serve this purpose, the derivative responses at each point must be converted to three features: magnitude, shape, and orientation. This paper presents a recently developed derotation algorithm for this task based on eigenvalues analysis of the Hessian matrix and spherical harmonics. Scale invariance is achieved by combining results from different scale detectors. The algorithm has been successfully implemented and applied to magnetic resonance volume data to segment string-like cerebral vessels, for which case some preliminary experimental results are presented