TY - JOUR

T1 - Finding surface correspondences using symmetry axis curves

AU - Liu, Tianqiang

AU - Kim, Vladimir G.

AU - Funkhouser, Thomas

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85014411331&partnerID=8YFLogxK

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U2 - 10.1111/j.1467-8659.2012.03166. x

DO - 10.1111/j.1467-8659.2012.03166. x

M3 - Article

AN - SCOPUS:85014411331

VL - 31

SP - 1607

EP - 1616

JO - Eurographics Symposium on Geometry Processing

JF - Eurographics Symposium on Geometry Processing

SN - 1727-8384

IS - 5

ER -