Premium
Finding Surface Correspondences Using Symmetry Axis Curves
Author(s) -
Liu Tianqiang,
Kim Vladimir G.,
Funkhouser Thomas
Publication year - 2012
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2012.03166.x
Subject(s) - symmetry (geometry) , robustness (evolution) , extrapolation , polygon (computer graphics) , surface (topology) , computer graphics , computer science , geometry , mathematics , polynomial , algorithm , artificial intelligence , computer vision , mathematical analysis , telecommunications , biochemistry , chemistry , frame (networking) , gene
In this paper, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real‐world surfaces. Thus, it is possible to find a useful map between two surfaces by first extracting symmetry axis curves, aligning the extracted curves, and then extrapolating correspondences found on the curves to both surfaces. The main advantages of this approach are efficiency and robustness: the difficult problem of finding a surface map is reduced to three significantly easier problems: symmetry detection, curve alignment, and correspondence extrapolation, each of which has a robust, polynomial‐time solution (e.g., optimal alignment of 1D curves is possible with dynamic programming). We investigate of this approach on a wide range of examples, including both intrinsically symmetric surfaces and polygon soups, and find that it is superior to previous methods in cases where two surfaces have different overall shapes but similar reflective symmetry axes, a common case in computer graphics.