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Thinning and Skeletonizing
Published in Edward R. Dougherty, Digital Image Processing Methods, 2020
The concept of the skeleton of a continuous binary image was introduced by Blum [2]. Montanari [25] also discusses skeletonizing techniques. Blum’s interest was to find possible physiological mechanisms for explaining how an animal’s vision system extracted global geometrical shape information. Several years later he introduced the concept of a “medial axis function” [3]. The medial axis function or transform (MAT) operates on the medial axis or skeleton of the object. If A is an object in a binary image, a skeleton of A is a subset I of A such that if x G I, there are at least two boundary points of A that are equidistant to x. The set I is often described by using a “brushfire” analogy [4]: if a “fire” is set on the boundary locations of A and burns inward at an equal rate, the points interior to A, where the fronts of the brush fire meet is the skeleton of A. The MAT takes a point in I to a positive real number that is its distance to the boundary of A. Given the MAT of a continuous object, the object can be recovered completely. Define a disk of radius r centered at location y to be the set Dr(y) = {z ∈ ℝ2 : |z − y| ≥ r}. If MAT (x) = rx, the original object A, with skeleton I, occupies the spatial locations in ℝ2 given by the set. The boundary of A is the envelope of.
Additive Manufacturing with Welding
Published in Jaykumar J. Vora, Vishvesh J. Badheka, Advances in Welding Technologies for Process Development, 2019
Manish Kumar, Abhay Sharma, Uttam Kumar Mohanty, S. Surya Kumar
The medial axis is the locus of the centers of circles (spheres) of the different radius that touch or are close to at least one point on the surface of the object. The contour and MAT paths have constant step-over distances that may lead to an unfilled or overfilled area as shown in Figure 5.8. The contour path plan (Figure 5.8a) generates several closed paths by offsetting the boundary curves toward its interior. In the case of the WAAM, where step-over distance is large, the contour path may leave a gap as shown in Figure 5.8b. The MAT path (Figure 5.8c) generates void-free deposition as shown in Figure 5.8d, but it deposits extra material at the boundary. Post-processing like machining removes these extra materials for enhancing the accuracy at the cost of material and energy wastage. The limitations of contour path and MAT path are overcome by adaptive path planning wherein the voids and excess material is avoided by continuously varying step-over distances (Figure 5.8e) through of adjustment of the process parameters (Ding et al. 2016b), as shown in Figure 5.8f. The WAAM is specially equipped for adaptive path planning as different width within a layer can be achieved by changing welding speed and the wire feed.
Two-Dimensional Measurements (Part 2)
Published in F. Brent Neal, John C. Russ, Measuring Shape, 2017
The practical difficulties of finding isomorphisms in graphs are reduced somewhat by constructing a directed graph from the MAT. The medial axis transform as described earlier encodes complete information about the topology of an object and its local shape. Siddiqi and Kimia (1995) proposed a method, which they call the shock graph, in which the skeleton (or MAT) of an object is encoded with values representing interesting features of the local boundary curvature of the object at each point rather than with the width. This method has the advantage of encoding information about a region of the boundary centered on the point of interest, averaging out the effects of noise or discretization error.
Identifying the pore structure and permeability anisotropy of coral reef limestone based on CT image analysis
Published in Marine Georesources & Geotechnology, 2023
Junpeng Wang, Xin Huang, Jun Xu, Shuaifeng Wang, Guolong Jin, Zixin Zhang
After three-dimensional reconstruction, the medial axis algorithm (Kwok 1988; Sirjani and Cross 1991) was used to identify the pore structure of the testing specimens. This algorithm refines the porous part of the reconstructed object into a “skeleton” that retains the topology, i.e., the medial axis. Using the medial axis to characterize the pore structure can reduce redundant information while preserving important topological features of the pore structure. The characteristic parameters of the entire pore structure can be obtained by analyzing and calculating a certain number of points on the medial axis. Currently, there are three main types of principles for calculating the medial axis: homotopic thinning (Pudney 1998), burning/erosion algorithm (Lindquist et al. 1996), and 3D (Ma and Sonka 1996; Passat, Couprie, and Bertrand 2008).
Degree of local symmetry for geometry-aware selective part visualisation on CT volumes
Published in Nondestructive Testing and Evaluation, 2022
Nobumichi Yasunami, Tatsuya Yatagawa, Yutaka Ohtake, Hiromasa Suzuki
To pay more attention to the geometric characteristics of part shapes, medial axis transform (MAT) has been used as a guide. The medial axes computed for the surface geometry of a target object are locally represented as either point, line/curve, or plane/surface. These representations are independent of the size of the target object. Hence, they are appropriate for the analysis of scale-invariant geometric characteristics [4]. Traditionally, the relative arrangement of a point on the medial axes and its nearest point on the surface has been leveraged for MAT. For example, Hesselink and Roerdink [5] calculated the direction from a point on the medial axis and its nearest surface point. They compared the directions of two neighbouring voxels and determined that medial axes are located between the pair of voxels with sufficiently different directions. MAT has been applied to segment an object into its parts based on the geometric characteristics of the parts. Zhou et al. [6] proposed a part segmentation method based on the similarity of local shapes to cylinders, which is defined using MAT. Recently, Lin et al. [7] leveraged geometric properties of points on the medial axes to classify the axes based on a graph structure. Although these approaches have demonstrated sophisticated segmentation results on simple objects, their applicability to more complicated industrial assemblies is not assured. Furthermore, these approaches do not allow the users to control the visibility of parts, although manual processes by human engineers are often preferred in the practical inspection of industrial assemblies.
Efficient preprocessing of complex geometries for CFD simulations
Published in International Journal of Computational Fluid Dynamics, 2019
Zaib Ali, James Tyacke, Rob Watson, Paul G. Tucker, Shahrokh Shahpar
The medial axis transform (MAT)-based algorithms for the domain decomposition have been presented in, for example, (Tam and Armstrong 1991; Price, Armstrong, and Sabin 1995a, 1995b; Sheehy, Armstrong, and Robinson 1995). Here the medial axis is generated using the Voronoi-based method. A subdivision is created resulting in one block for each medial vertex, medial edge and medial face. A midpoint subdivision is then used for meshing the blocks. An alternative has been presented by Rigby (2004), called the ‘TopMaker’ approach, which makes use of medial vertices and parts of medial axis to block the domain. Medial vertices are defined as the points which are equidistant from three locations from the domain boundary. Consequently, six types of medial edges and appropriate rules are defined for creating the blocks. Further enhancements have been included to produce a good quality mesh, however this technique has yet to be extended for 3D.