Efficient Computation of A Simplified Medial Axis

[+] Author and Article Information
Mark Foskey

Department of Radiology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7515e-mail: foskey@cs.unc.edu

Ming C. Lin, Dinesh Manocha

Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7515e-mail: dm@cs.unc.edu

J. Comput. Inf. Sci. Eng 3(4), 274-284 (Dec 24, 2003) (11 pages) doi:10.1115/1.1631582 History: Received July 01, 2003; Revised October 01, 2003; Online December 24, 2003
Copyright © 2003 by ASME
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The separation angle S(x) for a point on the medial axis. The thick border is the boundary of X.
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Computing the error bound. The angle subtended by p1and p2 is equal to θ, so no circle tangent only to the edges containing p1 and p2 is represented in Mθ. If the solid circle is enlarged into the dashed circle, then the vertex p will be included. The radius r is equal to the local radius R(p1)=R(p2).
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Computing rext=‖p−x‖. The vector (p1−x) is a normal vector from x to a face on the boundary of X. There are two other such faces; the endpoints of the normal vectors to those faces, p2 and p3, are not shown. The point q bisects p1p2, which is one side of an equilateral triangle.
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Disconnectedness. The point x is on the medial axis but has a small separation angle.
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Different Θ-SMAs for the same model. As the separation angle increases, the number of high frequency or sharp components decreases.
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The direction vectors at neighboring voxels can differ by a large angle even when the voxels are not on different sides of the medial axis.
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The first step in an iterative refinement of the approximate θ-SMA. x is the initial guess, and p is the nearest neighbor of x on the boundary. Sx,p is the center centered on x and passing through p . There is a maximal circle Smax (not shown) that is contained in X and contains Sx,p. We approach the medial axis by approaching Smax.Smax touches the boundary in at least two places. p and p are successive approximations to the second point where Smax touches the boundary of X.
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A torus and its θ-SMA. 2000 triangles. The grid resolution is 127×128×42.
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The “primer anvil” for a shotgun shell. 4,340 triangles, SMA computed at 128×73×112 resolution. (a) The model. (b) The θ-SMA. The seams and boundary curves of the θ-SMA are shown.
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Shotgun shell “charge” with 4460 triangles. The grid resolution is 126×128×126. (a) The model. (b) Cross section, showing different sheets in different shades.
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Buddha model with 1,087,474 triangles. The grid resolution is 55×128×55.
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Part of Cassini space probe model: Bus assembly. (a) The model. (b) Wireframe of the model with the θ-SMA shaded depending on the distance to the surface.
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Skeleton hand with 654,666 triangles. The grid resolution is 79×106×127. No smoothing was performed.
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Elbow pipe, at varying resolutions. (a) The model. Figures (b), (c) and (d), correspond to 128, 256, and 512 voxels along the longest side, respectively. The gap visible in (b) and (c) shows where the interior of the pipe model is separated by a surface into two compartments. The gap is not visible in (d) only because the angle of the scene is slightly different. The θ-SMA is not smoothed.
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Bunny. 69,451 triangles, 128×126×100. (a) The bunny in wireframe, with the medial axis. (b) The θ-SMA.
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Propulsion module of the Cassini spacecraft. 90,879 triangles, 94×128×96. (a) The model. (b) The model in cross section, with the θ-SMA shaded based on the distance to the boundary. In this example, the θ-SMA is not restricted to the interior of the model.




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