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Spatially-variant morpho-Hessian filter: Efficient implementation and application

Abstract : 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.
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Olena Tankyevych, Hugues Talbot, Petr Dokládal, Nicolas Passat. Spatially-variant morpho-Hessian filter: Efficient implementation and application. International Symposium on Mathematical Morphology (ISMM), 2009, Groningen, Netherlands. pp.137-148, ⟨10.1007/978-3-642-03613-2_13⟩. ⟨hal-00622432⟩

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