Thinning on binary images is an iterative layer by layer erosion until only the “skeletons ” of the objects are left. This paper presents an efficient parallel thinning algorithm which produces either curve skeletons or surface skeletons from 3D binary objects. It is important that a curve skeleton is extracted directly (i.e., without creating a surface skeleton). The strategy which is used is called directional: each iteration step is composed of a number of subiterations each of which can be executed in parallel. One iteration step of the proposed algorithm contains 12 subiterations instead of the usual six. The algorithm makes easy implementation possible, since deletable points are given by 3 × 3 × 3 matching templates. The topological correctness for (26, 6) binary pictures is proved. c ○ 1999 Academic Press 1.

We present a new method for the skeletonization of 2-dimensional or 3-dimensional objects. First, we introduce two local measures, φ and d, to characterize skeleton points, whose good localization is ensured by Euclidean distance mapping techniques. These measures allow us to control the detail of the resulting skeleton. Thresholding these measures generally does not yield well-defined skeleton: a low threshold preserves the original object's topology but produces a noise-sensitive skeleton, while a higher threshold produces a more robust skeleton but it is generally not homotopic with the original object it comes from. To overcome these drawbacks, more complex measures can be introduced. Although they generally yield good experimental results, they are still sensitive to noise. Instead, we introduce a global step, called topological reconstruction, which will provide the skeleton with robustness with respect to noise and ensure homotopy with the original object. Moreover, this method is not...

Thinning is a frequently used method for extracting skeletons in discrete spaces. This paper presents an efficient parallel thinning algorithm that directly extracts medial lines from elongated 3D binary objects Ži.e., without creating medial

We propose in this paper a new 3D fully parallel thinning algorithm that we believe to be the most concise due to its simple characterization. The algorithm is indeed completely dened by a set of ve patterns, three removing conditions and two non-removing conditions. These patterns are designed from the two fundamental and compatible constraints usually expected in skeleta: (1) Topology preservation and (2) Medial surface. From these two constraints, the removing patterns ( 1 , 2 and 3 ) detect the non-local maxima, whereas the non-removing patterns ( 1 and 2 ) prevent any topology change that the removing conditions could imply. We show that the three mentioned constraints are respected. The logical conciseness of our procedure, called MB-3D, makes it to our knowledge the easiest 3D thinning algorithm to implement. Some results are displayed, that illustrate the relevance of our approach. Keywords 3D fully parallel thinning algorithm - Discrete topology - Concise Boolean ...

Curve-skeletons are a 1D subset of the medial surface of a 3D object and are useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, mesh repair, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curve-skeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.

Thinning of a binary object is an iterative layer by layer erosion to extract an approximation to its skeleton. In order to provide topology preservation, different thinning techniques have been proposed. One of them is the directional (or border sequential) approach in which each iteration step is subdivided into subiterations where only border points of certain kind are deleted in each subiteration. There are six kinds of border points in 3D images, therefore, 6–subiteration parallel thinning algorithms were generally proposed. In this paper, we present two 8–subiteration algorithms for extracting “surface skeletons” and “curve skeletons”, respectively. Both algorithms work in cubic grid for (26,6) images. Deletable points are given by templates that makes easy implementation possible.

Many classical image processing tasks can be realized as evaluations of a boolean function over subsets of an image. For instance, the simplicity test used in 3D thinning requires examining the 26 neighbors of each voxel and computing a single boolean function of these inputs. In this article, we show how Binary Decision Diagrams can be used to produce automatically very efficient and compact code for such functions. The total number of operations performed by a generated function is at most one test and one branching for each input value (e.g., in the case of 3D thinning, 26 tests and branchings). At each stage, the function is guaranteed to examine only the pertinent input data, i.e., the values which affect the result. As an example, we consider the 2D and 3D simplicity tests in digital topology, and thinning processes. We produce functions much faster than our previously optimized implementations [18, 4], and than any other implementation we know of. In the case of 3D simplicit...

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. 1

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This paper presents a family of parallel thinning algorithms for extracting medial surfaces from 3D binary pictures. The proposed algorithms are based on sufficient conditions for 3D parallel reduction operators to preserve topology for (26, 6) pictures. Hence it is self-evident that our algorithms are topology preserving. Their efficient implementation on conventional sequential computers is also presented.