1 / 26

Curvature Based Triangle Mesh Segmentation with Boundary Rectification

Curvature Based Triangle Mesh Segmentation with Boundary Rectification. Guillaume Lavoué , Florent Dupont, Atilla Baskurt. Plan. Context. Method overview. The region segmentation process. Vertex classification. Region growing. Region merging. The boundary rectification process. Why ?

stasia
Download Presentation

Curvature Based Triangle Mesh Segmentation with Boundary Rectification

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Curvature Based Triangle Mesh Segmentation with Boundary Rectification Guillaume Lavoué, Florent Dupont, Atilla Baskurt WorkShop Télégéo 6/11/03

  2. Plan • Context. • Method overview. • The region segmentation process. • Vertex classification. • Region growing. • Region merging. • The boundary rectification process. • Why ? • The Boundary Score definition. • General algorithm. • Correct boundary marking. • Contour tracking. • Perspectives. WorkShop Télégéo 6/11/03

  3. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Context • Semantic-3D RNRT national project. • Request and transmission of 3D CAD objects, multi-bandwidths, multi- platforms. Topics are Indexing, Watermarking and Compression. • Research of an adaptive, multi-resolution compression method. • Chosen approach. • Subdivision surface fitting. • Arbitrary topology. • Intrinsically Multi-resolution. • Represented by a mesh. • Prior segmentation of the mesh into patches. • To simplify the fitting algorithm. • To permit adaptiveness. WorkShop Télégéo 6/11/03

  4. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Subdivision Surface fitting Subdivision Surface fitting Subdivision Surface fitting Manifold CAD mesh Complete process diagram Patch Compressed model Assembling Segmentation Patch Patch Adaptive precision

  5. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Plan • Context. • Method overview. • The region segmentation process. • Vertex classification. • Region growing. • Region merging. • The boundary rectification process. • Why ? • The Boundary Score definition. • General algorithm. • Correct boundary marking. • Contour tracking. • Perspectives. WorkShop Télégéo 6/11/03

  6. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Constant curvature region segmentation Vertex curvature classification Region growing Region merging 3D Triangle mesh Classified vertices Segmented regions Boundary edges extraction Boundary Score processing Rectified boundaries Boundary edges Correct boundary edges Contour tracking boundary rectification Method overview We need known curvature surface patches with regular boundaries for the fitting process. WorkShop Télégéo 6/11/03

  7. Plan • Context. • Method overview. • The region segmentation process. • Vertex classification. • Region growing. • Region merging. • The boundary rectification process. • Why ? • The Boundary Score definition. • General algorithm. • Correct boundary marking. • Contour tracking. • Perspectives. WorkShop Télégéo 6/11/03

  8. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Vertex classification • Extraction of discrete curvature. [Meyer, Discrete Differential-Geometry Operators for Triangulated 2-Manifolds (VisMath 2002)] • Mean Curvature: • Gauss Curvature: • Principal Curvatures: avec WorkShop Télégéo 6/11/03

  9. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Vertex classification • Principal curvature directions dmaxet dmin. Eigenvectors of the curvature tensor, found by least square fitting.. 0,25 2,5 -7,0 4,5 0,0 2,3 2,7 4,5 Mean Gauss abs(Min) Max dmin dmax WorkShop Télégéo 6/11/03

  10. Context - Method Overview - Region segmentation - boundary rectification -Perspectives kmax kmax Classification 5 clusters Classification 5 clusters kmin kmin Vertex classification • Curvature classification. • K-Means clustering applied to Kmin and Kmax. • Cluster regularization. WorkShop Télégéo 6/11/03

  11. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Region growing • Region growing. • Triangle growing and labeling operation. triangle regions with holes between them. • Crack filling process. Not-labeled triangles are assigned to regionsaccording to: • Their neighbor triangles labels. • Boundary criteria. Triangle growing Crack filling WorkShop Télégéo 6/11/03

  12. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Region merging • Purpose: • Reduce the over-segmentation resulting from region growing. • Suppress results dependency to K-Means clusters number. • General algorithm: • Region adjacency graph construction. • Nodes: connected regions. • Edges: adjacency between two regions. • Calculation of similarity distances between regions. • Valuation of the graph edges. • Graph reduction. • At each iteration the smallest adjacency edge is eliminated. • Stopping criteria. • A number of queried final regions. • A maximum distance threshold. WorkShop Télégéo 6/11/03

  13. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Ri Rj Rj Ri Region merging • Region distance measurement. • The distance Dij between ith and jth regionsis: • The curvature distance DCij : • Two situations between two regions: Chosen curvature distance No significant boundary but a curvature difference With: Ci , Cj, the curvature values of the ith and jth regions. Cij, the curvature value of their boundary. No curvature difference but a significant boundary WorkShop Télégéo 6/11/03

  14. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Region merging • The nesting coefficient Nij : Introduced in image processing by Schettini in Segmentation Algorithm For Color Images (Pattern Recognition Letters 1993). • The filtering coefficient Sij : The fusion of smallest regions is accelerated. With: Pi , Pj, the perimeters of the ith and jth regions. Pij, the common perimeter of the ith and jth regions. With: Ai , Aj, the areas of the ith and jth regions. Aij, a minimum fixed area. , a positive number ~ 0. WorkShop Télégéo 6/11/03

  15. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Samples Region merging Threshold = 50 Vertex classification Region growing Segmented Fandisk 68 regions Fandisk 6475 vertices Segmented Fandisk 16 regions Classified vertices 14 clusters WorkShop Télégéo 6/11/03

  16. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Samples Region merging Threshold = 50 Region growing Vertex classification Segmented Shark 343 regions Shark 10234 vertices Segmented Shark 16 regions Classified vertices 10 clusters WorkShop Télégéo 6/11/03

  17. Curvature classification results dependency • Tests conducted with different K-Means clusters number. WorkShop Télégéo 6/11/03

  18. Plan • Context. • Method overview. • The region segmentation process. • Vertex classification. • Region growing. • Region merging. • The boundary rectification process. • Purpose. • The Boundary Score definition. • General algorithm. • Correct boundary marking. • Contour tracking. • Perspectives. WorkShop Télégéo 6/11/03

  19. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Purpose ? The subdivision surface fitting needs clean boundaries without discontinuities. • Method: • Extraction of the boundary edges from the segmented object. • Marking of the “correct” boundary edges with a boundary score calculation. • Contour tracking to complete boundaries according to the correct ones. WorkShop Télégéo 6/11/03

  20. Context - Method Overview - Region segmentation - boundary rectification -Perspectives dmin dmax The Boundary Score definition. • Principal curvature directions are used. • The curvature varies according to dmax and tend to be constant following dmin. boundaries are parallel to dmin. • Boundary Score processing. WorkShop Télégéo 6/11/03

  21. Context - Method Overview - Region segmentation - boundary rectification -Perspectives General algorithm. • Boundary edges extraction. • Correct boundary edges marking. A threshold S is fixed to determine Correct Boundary Edges (CBE), among the boundary edges which come from the region segmentation step. WorkShop Télégéo 6/11/03

  22. Context - Method Overview - Region segmentation - boundary rectification -Perspectives CBE Potential edge General algorithm. • Contour tracking. • Correct boundary edges form pieces of boundary contours. • For each not closed boundary, we extract the edges potentially being able to complete it (edges adjacent to one extremity CBE). • Each potential edge e is associated with a weight function Pi depending of its score and its angle with its CBE. Sorted list WorkShop Télégéo 6/11/03

  23. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Lowest weight edge integration Only closed boundaries? Yes Sorted list construction List update No CBE CBE CBE Potential edge Potential edge Potential edge Contour tracking End WorkShop Télégéo 6/11/03

  24. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Sample 3D-object Vertex Classification Region growing Region merging Correct boundary edges marking Contour tracking WorkShop Télégéo 6/11/03

  25. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Plan • Context. • Method overview. • The region segmentation process. • Vertex classification. • Region growing. • Region merging. • The boundary rectification process. • Purpose. • The Boundary Score definition. • General algorithm. • Correct boundary marking. • Contour tracking. • Perspectives. WorkShop Télégéo 6/11/03

  26. Context - Method Overview - Region segmentation - boundary rectification -Perspectives Conclusion and perspectives • Our method: • The segmentation algorithm. • Curvature classification. Curvature transition detection, not only hard edges cutting. Constant curvature region extraction. • Mixed Vertex-Triangle approach. Regions boundaries are clearly distinguishable edges. • The boundary rectification method: • Original method based on principal curvature directions. • Perspectives: • Considering curvature variance or distribution histogram analysis. Improve classification. Automatically process the merging threshold. • Subdivision surface fitting in our adaptive multi-resolution compression objective. WorkShop Télégéo 6/11/03

More Related