Reeb Graphs Through Local Binary Patterns

This paper presents an approach to derive critical points of a shape, the basis of a Reeb graph, using a combination of a medial axis skeleton and features along this skeleton. A Reeb graph captures the topology of a shape. The nodes in the graph represent critical points (positions of change in the topology), while edges represent topological persistence. We present an approach to compute such critical points using Local Binary Patterns. For one pixel the Local Binary Pattern feature vector is derived comparing this pixel to its neighbouring pixels in an environment of a certain radius. We start with an initial segmentation and a medial axis representation. Along this axis critical points are computed using Local Binary Patterns with the radius, defining the neighbouring pixels, set a bit larger than the radius according to the medial axis transformation. Critical points obtained in this way form the node set in a Reeb graph, edges are given through the connectivity of the skeleton. This approach aims at improving the representation of flawed segmented data. In the same way segmentation artefacts, as for example single pixels representing noise, may be corrected based on this analysis.