surface reconstruction from unorganized points using self-organizing neural networks
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Vis’99
Yizhou Yu
Surface Reconstruction from Surface Reconstruction from Unorganized Points Using Unorganized Points Using
Self-Organizing Neural NetworksSelf-Organizing Neural Networks
Surface Reconstruction from Surface Reconstruction from Unorganized Points Using Unorganized Points Using
Self-Organizing Neural NetworksSelf-Organizing Neural Networks
Computer Science Division
University of California at Berkeley
Computer Science Division
University of California at Berkeley
Yizhou Yu
Vis’99
Yizhou Yu
Previous WorkPrevious WorkPrevious WorkPrevious 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 ]
• 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 ]
Vis’99
Yizhou Yu
Surface from PointsSurface from PointsSurface from PointsSurface 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
• 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
Vis’99
Yizhou Yu
Kohonen’s Self-Organizing MapsKohonen’s Self-Organizing MapsKohonen’s Self-Organizing MapsKohonen’s Self-Organizing Maps
Cells
Input
Weights
Cell Response: some distance metric between input and weight vectorWinner Cell: cell with maximum or minimum response
Vis’99
Yizhou Yu
Equivalence between Meshes andEquivalence between Meshes andSelf-Organizing MapsSelf-Organizing MapsEquivalence between Meshes andEquivalence between Meshes andSelf-Organizing MapsSelf-Organizing Maps
• Vertices <==> Cells
• Coordinates <==> Weight Vectors
• Vertex Connectivity <==> Cell Connectivity
• Input Points <==> Input Vectors
• Vertices <==> Cells
• Coordinates <==> Weight Vectors
• Vertex Connectivity <==> Cell Connectivity
• Input Points <==> Input Vectors
Vis’99
Yizhou Yu
Training Weight VectorsTraining Weight VectorsTraining Weight VectorsTraining Weight Vectors
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Vis’99
Yizhou Yu
Property of the Training AlgorithmProperty of the Training AlgorithmProperty of the Training AlgorithmProperty 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.
• When the training is finished, the winner cell moves continuously in the network as the input vector changes smoothly in its vector space.
Vis’99
Yizhou Yu
Problem with Concave StructuresProblem with Concave StructuresProblem with Concave StructuresProblem 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.
• Large polygons fill up concave structures.
• Detect: the distance from the centroid of such a polygon to the input point cloud is large.
Vis’99
Yizhou Yu
Edge Swap: Single SwapEdge Swap: Single SwapEdge Swap: Single SwapEdge Swap: Single Swap
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Yizhou Yu
Edge Swap: Double SwapEdge Swap: Double SwapEdge Swap: Double SwapEdge Swap: Double Swap
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Yizhou Yu
Multiresolution LearningMultiresolution LearningMultiresolution LearningMultiresolution 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.
• 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.
Vis’99
Yizhou Yu
An Example of Multiresolution LearningAn Example of Multiresolution LearningAn Example of Multiresolution LearningAn Example of Multiresolution Learning
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Yizhou Yu
BunnyBunnyBunnyBunny
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Yizhou Yu
MannequinMannequinMannequinMannequin
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Yizhou Yu
An Open Multimodal Surface withAn Open Multimodal Surface withTexture-MappingTexture-MappingAn Open Multimodal Surface withAn Open Multimodal Surface withTexture-MappingTexture-Mapping
Vis’99
Yizhou Yu
Future WorkFuture WorkFuture WorkFuture Work
• Improve performance.
• Try different distance metrics, such as geodesic distance, among cells in self-organizing maps.
• Extend to more sophisticated topology.
• Improve performance.
• Try different distance metrics, such as geodesic distance, among cells in self-organizing maps.
• Extend to more sophisticated topology.