Shape Analysis by Computing Geodesics on a Manifold via Cubic B-splines

Abstract

When a parameterized probability density function is used to represent a landmark-based shape, the shape can be viewed as a point on the manifold that equips with a Riemannian metric corresponding to the mixture models. Hence, given two shapes parameterized by the same density model, the geodesic distance between them can be used for an appropriate shape distance measure. We provide a computational strategy, which is based on the cubic B-splines, to get geodesics and geodesic distances between plane shapes represented by the mixture of Gaussians. In contrast to the methods that discretize geodesic into a sequence of line segments, the proposed method is computationally efficient and numerically stable.

Keywords

Shapes / Riemannian metric / Manifold / Geodesic / Shape deformation

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Funding

National Natural Science Foundation of China(61772167)

Natural Science Research of Jiangsu Higher Education Institutions of China(22KJB110015)