A New 3D Parallel Thinning Scheme Based on Critical Kernels

Abstract

Abstract. Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. We take advantage of the properties of this framework, and we derive a general methodology for designing parallel algorithms for skeletons of objects in 3D grids. In fact, this methodology does not need to handle the structure of abstract complexes, we show that only 3 masks defined in the classical cubic grid are sufficient to implement it. We illustrate our methodology by giving two new types of skeletons.

Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

“…The methodology presented in this paper has been extended to the important case of parallel thinning of 3D objects [6]. In future works, we will study the case of general skeletons (i.e., which are not necessarily principal subcomplexes), the computation of Euclidean skeletons, and the link between critical kernels, minimal non-simple sets and P-simple points for the 3D-and 4D-cases.…”

A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing

“…For example, if the input is a corridor (the void of the corridor), then the skeleton should be a line following the main direction of the corridor. Generally, two strategies are possible to achieve this goal: find, during the skeletonization process, points whose neighbourhood configuration seems interesting and keep them in the result [6] [7] [5], or choose, before skeletonization, interesting points of the object which should remain untouched, based on a function on these points and a filtering parameter [2] [12].…”

New Characterizations of Simple Points, Minimal Non-simple Sets and P-Simple Points in 2D, 3D and 4D Discrete Spaces

“…cubes, squares, edges, vertices) glued together according to certain rules. In this section, we recall briefly some basic definitions on complexes, see also [7,5,6] for more details. We consider here n-dimensional complexes, with 0 ≤ n ≤ 4.…”

“…26-simple, 80-simple) point in the framework of 2D (resp. 3D, 4D) digital topology (see [16,17,7,6]). …”

“…It allows easy design of parallel thinning algorithms which produce new types of skeletons, with specific geometrical properties, while guaranteeing their topological soundness [7,5,6]. A new definition of a simple point is proposed in [3,4], based on the collapse operation which is a classical tool in algebraic topology and which guarantees topology preservation.…”