A New Volume Warping Method for Surface Reconstruction

[+] Author and Article Information
Sergei Azernikov

Laboratory for CAD & Life Cycle Engineering, Department of Mechanical Engineering,  Technion — IIT, Haifa 32000, Israelmesergei@technion.ac.il

Anath Fischer

Laboratory for CAD & Life Cycle Engineering, Department of Mechanical Engineering,  Technion — IIT, Haifa 32000, Israel

J. Comput. Inf. Sci. Eng 6(4), 355-363 (May 30, 2006) (9 pages) doi:10.1115/1.2356500 History: Received August 09, 2005; Revised May 30, 2006

Volumetric models of 3D objects have recently been introduced into the reverse engineering (RE) process. Grid-based methods are considered as the major technique for reconstructing surfaces from these volumetric models. This is mainly due to the efficiency and simplicity of these methods. However, these grid-based methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid in general is not well adapted to the surface, neither in size nor in orientation. In order to overcome the above obstacles a new iso-surface extraction method is proposed for volumetric models. The main idea is first to construct a geometrical field that is induced by the object’s shape. This geometrical field represents the natural directions and a grid cell size for each point in the domain. Then, the imposed volumetric grid is deformed by the produced geometrical field toward the object’s shape. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique. The proposed method provides better approximation of the unknown surface and exhibits anisotropy, which is present inherently in the surface. Moreover, since the produced meshes are quad-dominant, Catmull-Clark subdivision surfaces are directly constructed from these meshes.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Partition of unity implicit surfaces (25): (a) polynomial fitting to 3321 points sampled from a torus, (b) polynomial fitting to 3721 points sampled from an ellipsoid, and (c), (d) implicit surfaces produced by blending the local approximations (error <0.01%)

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Figure 2

A block scheme of the proposed surface reconstruction approach

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Figure 3

The geometric tensor field construction: (a) octree for a synthetic model (3032 nodes), with maximal depth 6, and (b) tensors of curvature evaluated on the model

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Figure 4

Synthetic example with complex topology: (a) initial grid 25×25×25 (shown 1752 voxels which contain a portion of the iso-surface), (b) after 100 relaxation iterations (2450 voxels), and (c) mesh extracted from the adaptive grid (2374 faces)

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Figure 5

Tangle surface: (a) anisotropic adaptive grid (2240 voxels), (b) iso-surface extracted with marching cubes (2240 faces), (c) iso-surface extracted with dual contouring (2248 faces), and (d) dual contour after decimation (1950 faces)

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Figure 6

Subdivision surface fitting process: (a) anisotropic mesh (1320 faces), (b) subdivision surface after one iteration of subdivision-projection (5280 faces), and (c) subdivision surface after two iterations of subdivision-projection (21,120 faces)

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Figure 7

Robustness of the proposed method to noise: (a) noisy cloud of points scanned from a human thoracic vertebra (6659 points); (b) triangular mesh reconstructed with Delaunay-based approach (39) (13320 faces); (c) anisotropic mesh reconstructed with the proposed approach (1809 faces)

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Figure 8

Anisotropic meshes reconstructed from point clouds

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Figure 9

Anisotropic adaptation vs isotropic refinement: (a) triangular mesh constructed with isotropic refinement (43014 triangles) (45); (b), (c) all-quad anisotropic mesh (556 quads)




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