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
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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
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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 ]
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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
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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
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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
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Vis’99
Yizhou Yu
Training Weight VectorsTraining Weight VectorsTraining Weight VectorsTraining Weight Vectors
otherwise. ),();())(,(
], )()( [ ),(
)1()(
tttCCDistd
twtxdtK
t
k
wk
ktk
k
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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.
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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.
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Vis’99
Yizhou Yu
Edge Swap: Single SwapEdge Swap: Single SwapEdge Swap: Single SwapEdge Swap: Single Swap
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Vis’99
Yizhou Yu
Edge Swap: Double SwapEdge Swap: Double SwapEdge Swap: Double SwapEdge Swap: Double Swap
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Vis’99
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.
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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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Vis’99
Yizhou Yu
BunnyBunnyBunnyBunny
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Vis’99
Yizhou Yu
MannequinMannequinMannequinMannequin
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Vis’99
Yizhou Yu
An Open Multimodal Surface withAn Open Multimodal Surface withTexture-MappingTexture-MappingAn Open Multimodal Surface withAn Open Multimodal Surface withTexture-MappingTexture-Mapping
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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.