Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application

Elongated objects are more difficult to filter than more isotropic ones because they locally comprise fewer pixels. For thin linear objects, this problem is compounded because there is only a restricted set of directions that can be used for filtering, and finding this local direction is not a simple problem. In addition, disconnections can easily appear due to noise. In this paper we tackle both issues by combining a linear filter for direction finding and a morphological one for filtering. More specifically, we use the eigen-analysis of the Hessian for detecting thin, linear objects, and a spatially-variant opening or closing for their enhancement and reconnection. We discuss the theory of spatially-variant morphological filters and present an efficient algorithm. The resulting spatially-variant morphological filter is shown to successfully enhance directions in 2D and 3D examples illustrated with a brain blood vessel segmentation problem.