Transcript talk
Multi-chart Geometry Images Pedro Sander Zoë Wood Harvard Caltech Steven Gortler John Snyder Hugues Hoppe Harvard Microsoft Research Microsoft Research Geometry representation irregular semi-regular completely regular Basic idea cut parametrize Basic idea cut sample Basic idea cut store simple traversal to render [r,g,b] = [x,y,z] Benefits of regularity Simplicity in rendering No vertex indirection No texture coordinate indirection Hardware potential Leverage image processing tools for geometric manipulation Limitations of single-chart long extremities high genus Unavoidable distortion and undersampling Limitations of semi-regular Base “charts” effectively constrained to be equal size equilateral triangles Multi-chart Geometry Images irregular 400x160 piecewise regular Multi-chart Geometry Images Simple reconstruction rules; for each 2-by-2 quad of MCGIM samples: 3 defined samples render 1 triangle 4 defined samples render 2 triangles (using shortest diagonal) undefined defined Multi-chart Geometry Images Simple reconstruction rules; for each 2-by-2 quad of MCGIM samples: 3 defined samples render 1 triangle 4 defined samples render 2 triangles (using shortest diagonal) Cracks in reconstruction Challenge: the discrete sampling will cause cracks in the reconstruction between charts “zippered” MCGIM Basic pipeline Break mesh into charts Parameterize charts Pack the charts Sample the charts Zipper chart seams Optimize the MCGIM Mesh chartification Goal: planar charts with compact boundaries Clustering optimization - Lloyd-Max (Shlafman 2002): Iteratively grow chart from given seed face. (metric is a product of distance and normal) Compute new seed face for each chart. (face that is farthest from chart boundary) Repeat above steps until convergence. Mesh chartification Bootstrapping Start with single seed Run chartification using increasing number of seeds each phase Until desired number reached demo Chartification Results Produces planar charts with compact boundaries Sander et. al. 2001 80% stretch efficiency Our method 99% stretch efficiency Parameterization Goal: Penalizes undersampling L2 geometric stretch of Sander et. al. 2001 Hierarchical algorithm for solving minimization Parameterization Goal: Penalizes undersampling L2 geometric stretch of Sander et. al. 2001 Hierarchical algorithm for solving minimization Angle-preserving metric (Floater) Chart packing Goal: minimize wasted space Based on Levy et al. 2002 Place a chart at a time (from largest to smallest) Pick best position and rotation (minimize wasted space) Repeat above for multiple MCGIM rectangle shapes pick best Packing Results Levy packing efficiency 58.0% Our packing efficiency 75.6% Sampling into a MCGIM Goal: discrete sampling of parameterized charts into topological discs Rasterize triangles with scan conversion Store geometry Sampling into a MCGIM Boundary rasterization Non-manifold dilation Zippering the MCGIM Goal: to form a watertight reconstruction Zippering the MCGIM Algorithm: Greedy (but robust) approach Identify cut-nodes and cut-path samples. Unify cut-nodes. Snap cut-path samples to geometric cut-path. Unify cut-path samples. Zippering: Snap Snap Snap discrete cut-path samples to geometrically closest point on cut-path Zippering: Unify Unify Greedily unify neighboring samples How unification works Unify Test the distance of the next 3 moves Pick smallest to unify then advance How unification works Unify Test the distance of the next 3 moves Pick smallest to unify then advance How unification works Unify Test the distance of the next 3 moves Pick smallest to unify then advance Geometry image optimization Goal: align discrete samples with mesh features Hoppe et. al. 1993 Reposition vertices to minimize distance to the original surface Constrain connectivity Multi-chart results genus 2; 50 charts 478x133 Rendering PSNR 79.5 Multi-chart results genus 1; 40 charts 174x369 Rendering PSNR 75.6 Multi-chart results genus 0; 25 charts 281X228 Rendering PSNR 84.6 Multi-chart results genus 0; 15 charts 466x138 Rendering PSNR 83.8 Multi-chart results irregular original single chart PSNR 68.0 multichart PSNR 79.5 demo 478x133 Comparison to semi-regular Original irregular Semi-regular MCGIM Comparison to semi-regular Original irregular mesh Semi-regular mesh PSNR 87.8 MCGIM mesh PSNR 90.2 Summary Contributions: Overall: MCGIM representation – Rendering simplicity Major: zippering and optimization Minor: packing and chartification Future work Provide: Compression Level-of-detail rendering control Exploit rendering simplicity in hardware Improve zippering