Topology Preserving Thinning of Cell Complexes

Abstract

Abstract. A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is a very active research area. It plays a central role in reducing the amount of information to be processed during image analysis and visualization, computer-aided diagnosis or by pattern recognition algorithms.This paper introduces a novel topology preserving thinning algorithm which removes simple cells-a generalization of simple points-of a given cell complex. The test for simple cells is based on acyclicity tables automatically produced in advance with homology computations. Using acyclicity tables render the implementation of thinning algorithms straightforward. Moreover, the fact that tables are automatically filled for all possible configurations allows to rigorously prove the generality of the algorithm and to obtain fool-proof implementations. The novel approach enables, for the first time, according to our knowledge, to thin a general unstructured simplicial complex. Acyclicity tables for cubical and simplicial complexes and an open source implementation of the thinning algorithm are provided as additional material to allow their immediate use in the vast number of practical applications arising in medical imaging and beyond.

Cosine-Pruned Medial Axis: A new method for isometric equivariant and noise-free medial axis extraction

“…The GIMA and the SFEMA are still the best methods measured with the Dubuisson-Jain dissimilarity, closely followed by both the CPMA and the C-CPMA. Results of using the Dubuisson-Jain dissimilarity as a metric show that the CPMA is close to methods such as BEMA The table shows the average Hausdorff distance and Dubuisson-Jain dissimilarity for different noise levels (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) over each element of the dataset.…”

“…When using thinning methods [16,27,26,32], points which belong to Ω are deleted from the outer boundary first. Later, the deletion proceeds iteratively inside until it results in a single-pixel wide medial axis.…”

“…Noise sensitivity results on Animal2000.Noise sensitivity results on Animal2000. The table shows the average Hausdorff distance and Dubuisson-Jain dissimilarity for different noise levels(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) over each element of the dataset.…”

Cosine-Pruned Medial Axis: A New Method for Isometric Equivariant and Noise-Free Medial Axis Extraction

“…When using thinning methods [34]- [37], points which belong to Ω are deleted from the outer boundary first. Later, the deletion proceeds iteratively inside until it results in a single-pixel wide medial axis.…”

Inference of Cerebrovascular Topology With Geodesic Minimum Spanning Trees

“…In [24], [56], and [57], the topological reconstruction of connected neighboring structures is traditionally addressed with the extraction of centerlines from a given segmentation by means of a skeletonisation process. Simplicial or cubical complex frameworks [16], [21]–[23] may be required when topological busy junctions are found in 2D or 3D finite raster grids. Alternatively, the skeletonisation is performed with topologically-preserving morphological operators (e.g.…”