TY - GEN

T1 - Anisotropic geodesic distance computation for parametric surfaces

AU - Seong, Joon Kyung

AU - Jeong, Won Ki

AU - Cohen, Elaine

PY - 2008

Y1 - 2008

N2 - The distribution of geometric features is anisotropic by its nature. Intrinsic properties of surfaces such as normal curvatures, for example, varies with direction. In this paper this characteristic of a shape is used to create a new anisotropic geodesic (AG) distance map on parametric surfaces. We first define local distance (LD) from a point as a function of both the surface point and a unit direction in its tangent plane and then define a total distance as an integral of that local distance. The AG distance between points on the surface is then defined as their minimum total distance. The path between the points that attains the minimum is called the anisotropic geodesic path. This differs from the usual geodesic in ways that enable it to better reveal geometric features. Minimizing total distances to attain AG distance is performed by associating the LD function with the tensor speed function that controls wave propagation of the convex Hamilton-Jacobi (H-J) equation solver. We present two different, but related metrics for the local distance function, a curvature tensor and a difference curvature tensor. Each creates a different AG distance. Some properties of both new AG distance maps are presented, including parametrization invariance. We then demonstrate the effectiveness of the proposed geodesic map as a shape discriminator in several applications, including surface segmentation and partial shape matching.

AB - The distribution of geometric features is anisotropic by its nature. Intrinsic properties of surfaces such as normal curvatures, for example, varies with direction. In this paper this characteristic of a shape is used to create a new anisotropic geodesic (AG) distance map on parametric surfaces. We first define local distance (LD) from a point as a function of both the surface point and a unit direction in its tangent plane and then define a total distance as an integral of that local distance. The AG distance between points on the surface is then defined as their minimum total distance. The path between the points that attains the minimum is called the anisotropic geodesic path. This differs from the usual geodesic in ways that enable it to better reveal geometric features. Minimizing total distances to attain AG distance is performed by associating the LD function with the tensor speed function that controls wave propagation of the convex Hamilton-Jacobi (H-J) equation solver. We present two different, but related metrics for the local distance function, a curvature tensor and a difference curvature tensor. Each creates a different AG distance. Some properties of both new AG distance maps are presented, including parametrization invariance. We then demonstrate the effectiveness of the proposed geodesic map as a shape discriminator in several applications, including surface segmentation and partial shape matching.

UR - http://www.scopus.com/inward/record.url?scp=50949117664&partnerID=8YFLogxK

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U2 - 10.1109/SMI.2008.4547968

DO - 10.1109/SMI.2008.4547968

M3 - Conference contribution

AN - SCOPUS:50949117664

SN - 9781424422609

T3 - IEEE International Conference on Shape Modeling and Applications 2008, Proceedings, SMI

SP - 179

EP - 186

BT - IEEE International Conference on Shape Modeling and Applications 2008, Proceedings, SMI

T2 - IEEE International Conference on Shape Modeling and Applications 2008, SMI

Y2 - 4 June 2008 through 6 June 2008

ER -