420 likes | 587 Vues
Discovering Structural Regularity in 3D Geometry. Speaker: JinliangWu Date: 25 / 9 /2008. Authors. Mark Pauly ETH Zurich Niloy J. Mitra IIT Delhi Johannes Wallner TU Graz Helmut Pottmann TU Vienna Leonidas Guibas Stanford University. Regular Structures. Regular Structures.
E N D
Discovering Structural Regularity in 3D Geometry Speaker: JinliangWu Date: 25 / 9 /2008
Authors • Mark Pauly ETH Zurich • Niloy J. Mitra IIT Delhi • Johannes Wallner TU Graz • Helmut Pottmann TU Vienna • Leonidas Guibas Stanford University
completion geometric edits Motivation compression geometry synthesis Text Motivation
Transform Analysis Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery spatial domain transform domain Structure Discovery
A similarity transformation T Repetitive Structures
Repetitive Structures 1-parameter patterns
Repetitive Structures 2-parameter commutative patterns
Repetitive Structures regular structure is a transformation group acting on is a collection of n patches of a given surface S
Repetitive Structures In the simplest setting, is a 1-parameter group with generating similarity transformation T . The elements of can be represented as
Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery
Transformation Analysis Algorithm for analyzing transformations
Transformations spatial domain transformation space pairwise transformations
Transformations spatial domain transformation space pairwise transformations
Model Estimation origin density plot of pair-wise transformations
Model Estimation cluster centers
Transformation Analysis Algorithm for analyzing transformations
Model Estimation Is there a Pattern?
Model Estimation Yes, there is!
Model Estimation Yes, there is!
Model Estimation Global, non-linear optimization – simultaneously detects outliers and grid structure
grid location generating vectors Model Estimation • Grid fitting – input: cluster centers – unknowns: grid generators
data confidence cluster center closest grid point grid confidence grid point closest cluster center Model Estimation • Fitting terms
Model Estimation • Fitting terms • Data and grid confidence terms • objective function
Model Estimation Global, non-linear optimization – simultaneously detects outliers and grid structure
Input Model Transform Clusters Model Estimation Aggregation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery
Aggregation • Region-growing to extract repetitive elements • Simultaneous registration
Input Model Transform Clusters Model Estimation Regular Structures Transform Generators Structure Discovery Transform Analysis Structure Discovery Aggregation
Conclusions • Algorithm is fully automatic • Requires no prior information on size, shape, or location of repetitive elements • Robust, efficient, independent of dimension general tool for scientific data analysis