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Research Papers

Extracting Manifold and Feature-Enhanced Mesh Surfaces From Binary Volumes

[+] Author and Article Information
Charlie C. Wang

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kongcwang@mae.cuhk.edu.hk

For a set of solid voxels, a voxel which has any empty face neighbor is a boundary voxel of the voxel set.

J. Comput. Inf. Sci. Eng 8(3), 031006 (Aug 19, 2008) (10 pages) doi:10.1115/1.2960489 History: Received July 14, 2007; Revised June 06, 2008; Published August 19, 2008

Abstract

This paper presents an approach to automatically recover mesh surfaces with sharp edges for solids from their binary volumetric discretizations (i.e., voxel models). Our method consists of three steps. The topology singularity is first eliminated on the binary grids so that a topology correct mesh $M0$ can be easily constructed. After that, the shape of $M0$ is refined, and its connectivity is iteratively optimized into $Mn$. The shape refinement is governed by the duplex distance fields derived from the input binary volume model. However, the refined mesh surface lacks sharp edges. Therefore, we employ an error-controlled variational shape approximation algorithm to segment $Mn$ into nearly planar patches and then recover sharp edges by applying a novel segmentation-enhanced bilateral filter to the surface. Using the technique presented in this paper, smooth regions and sharp edges can be automatically recovered from raw binary volume models without scalar field or Hermite data Compared to other related surface recovering methods on binary volume, our algorithm needs less heuristic coefficients.

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Figures

Figure 8

Comparison of position updates (c) all together versus (d) separately for smooth and shape regions, where unwanted slopes are generated in (c). (a) The segmentation result and (b) all patch boundary edges.

Figure 9

Results of our approach on various models

Figure 13

Results of the sharpened flower model from (a) our filter, (b) the normal-based bilateral filter (62), and (c) the position-based bilateral filter (61) with the same σc and σs

Figure 5

2D illustration for the progressive results from the out-of-core implementation of the CubeMerge algorithm—every 2D quadrilateral denotes a cubic cell in 3D

Figure 6

By a given binary volume model H in the left, the region holding a reasonable approximation of ∂H is shown in the right

Figure 7

Results of L2,1 planar segmentation (a) with 68 patches and the followed boundary refinements (b) with 14 patches and (c) with 12 patches on the two-cube example

Figure 10

The output of our approach gives more and more accurate results while increasing the sampling rate on input binary models with (a) 92×92×92, (b) 128×128×128, (c) 160×160×160, and (d) 192×192×192 voxels. The left column shows the results from a smooth surface reconstruction (step 2), and the right column gives the result after recovering sharp edges (step 3).

Figure 11

Results of a sharpened mechanical part from (a) our segmentation-enhanced bilateral filter, (b) the normal-based bilateral filter (62), and (c) the position-based bilateral filter (61) with the same σc and σs

Figure 12

Results of the sharpened anchor plate from (a) our filter, (b) the normal-based bilateral filter (62), and (c) the position-based bilateral filter (61) with the same σc and σs

Figure 1

A model contoured using the marching cube algorithm (17) resulting in (a) many triangles and our approach resulting in (b) good shape triangles. (c) Nonmanifold edges (the bold ones are produced by using Ref. 29 to construct the connectivity of the isosurface.

Figure 2

Step results for a sample model with two cubes to illustrate the overview of our approach: (a) the binary volume model is shown on three cross-section planes, (b) the two-manifold coarse mesh M0 approximating ∂H with correct topology, (c) duplex distance fields—the left one is generated by the boundary voxels in H and the right one is from the boundary voxels in Z3\H (where blank represents the point with a negative distance value), (d) the resultant mesh Mn of smooth shape reconstruction, (e) the segmented patches by variational shape approximation, (f) the sharpening result from segmentation-enhanced bilateral filtering

Figure 3

Illustration for the vertex neighbors, the face neighbors, the singular vertex, and the singular edge

Figure 4

Illustration for topology reconstruction

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