Vector-Based Morphological Operations on Polygons Using Straight Skeletons for Digital Pathology

International audienceIn this work we present an efficient implementation of vector-based mathematical morphology operators applied to simple polygons by performing wavefront propagation and computing polygon straight skeletons. In Digital Pathology (DP), the slide scanner generates important volume of images from tissues called Whole Slide Image (WSI). The main goal of the DP is to detect the biological stained structures in order to quantify the tissue pathology, such as lesions or cancerous regions. We propose the use of Adapted Straight Skeletons on polygons as an efficient technique in time and memory, to improve image segmentation and image analysis. Thanks to the use of polygons instead of bitmaps to store segmentation results, the performance of straight skeletons depends only on the polygon control points. These straight skeletons can be applied in order to perform fast morphological operations such as dilation, erosion, closing, opening, skeletonizing. When combined, these operations offer different interesting outcomes: (i) multiple disjoint-segmented shapes can be linked together to create a joint skeleton, (ii) the topological structure of segmentation can be extracted as a straight skeleton. Then, it can be used as features for structural and spatial tissue analysis

Computing a family of skeletons of volumetric models for shape description

Abstract. Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed via an iterative thinning process. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons on volumes by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and medical images, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes.

Enhancing 3D Mesh Topological Skeletons with Discrete Contour Constrictions

International audienceThis paper describes a unified and fully automatic algorithm for Reeb graph construction and simplification as well as constriction approximation on triangulated surfaces. The key idea of the algorithm is that discrete contours - curves carried by the edges of the mesh and approximating the continuous contours of a mapping function - encode both topological and geometrical shape characteristics. Therefore, a new concise shape representation, enhanced topological skeletons, is proposed, encoding contours' topological and geometrical evolution. Firstly, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Secondly, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes and constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, that we refer as enhanced topological skeletons. Extensive experiments showed that, without preprocessing stage, proposed algorithms are fast in practice, affine-invariant and robust to a variety of surface degradations (surface noise, mesh sampling and model pose variations). These properties make enhanced topological skeletons interesting shape abstractions for many computer graphics applications