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Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks

Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks. Computer Science Division University of California at Berkeley. Yizhou Yu. Previous Work. Implicit Function [ Hoppe et al. 92 ] Volumetric Reconstruction [ Curless and Levoy 96 ] Alpha Shapes

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Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks

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  1. Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks Computer Science Division University of California at Berkeley Yizhou Yu

  2. Previous Work • Implicit Function • [ Hoppe et al. 92 ] • Volumetric Reconstruction • [ Curless and Levoy 96 ] • Alpha Shapes • [ Edelsbrunner and Mucke 94 ] • 3D Voronoi-Based Reconstruction • [ Amenta , Bern & Kamvysselis 98 ]

  3. Surface from Points • Input: point clouds • Output: meshes ( vertices + connectivity ) • Bottom-to-Top Approaches • Build connectivity from or among points • Top-to-Bottom Approaches • Learn vertex coordinates given connectivity

  4. Kohonen’s Self-Organizing Maps Cells Weights Input Cell Response: some distance metric between input and weight vector Winner Cell: cell with maximum or minimum response

  5. Equivalence between Meshes andSelf-Organizing Maps • Vertices <==> Cells • Coordinates <==> Weight Vectors • Vertex Connectivity <==> Cell Connectivity • Input Points <==> Input Vectors

  6. Training Weight Vectors

  7. Property of the Training Algorithm • When the training is finished, the winner cell moves continuously in the network as the input vector changes smoothly in its vector space.

  8. Problem with Concave Structures • Large polygons fill up concave structures. • Detect: the distance from the centroid of such a polygon to the input point cloud is large.

  9. Edge Swap: Single Swap

  10. Edge Swap: Double Swap

  11. Multiresolution Learning • Start with a very low resolution. • Every triangle splits into four smaller ones in the next higher resolution. • At each resolution, first run Kohonen’s algorithm, then swap edges. • Large sturctures can be learned at low resolutions, therefore save time.

  12. An Example of Multiresolution Learning

  13. Bunny

  14. Mannequin

  15. An Open Multimodal Surface withTexture-Mapping

  16. Future Work • Improve performance. • Try different distance metrics, such as geodesic distance, among cells in self-organizing maps. • Extend to more sophisticated topology.

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