TY - JOUR
T1 - Affine-invariant geodesic geometry of deformable 3D shapes
AU - Raviv, Dan
AU - Bronstein, Alexander M.
AU - Bronstein, Michael M.
AU - Kimmel, Ron
AU - Sochen, Nir
N1 - Funding Information:
This research was supported by European Community's FP7–ERC program , Grant agreement no. 267414 . MB is partly supported by the Swiss High-Performance and High-Productivity Computing (HP2C).
PY - 2011/6
Y1 - 2011/6
N2 - Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.
AB - Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.
KW - Affine
KW - Equi-affine
KW - Geodesics
UR - http://www.scopus.com/inward/record.url?scp=79957795883&partnerID=8YFLogxK
U2 - 10.1016/j.cag.2011.03.030
DO - 10.1016/j.cag.2011.03.030
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AN - SCOPUS:79957795883
SN - 0097-8493
VL - 35
SP - 692
EP - 697
JO - Computers and Graphics (Pergamon)
JF - Computers and Graphics (Pergamon)
IS - 3
ER -