Shape alignment—optimal initial point and pose estimation
Pattern Recognition Letters
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesics between 3d closed curves using path-straightening
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Large Deformation Diffeomorphic Metric Curve Mapping
International Journal of Computer Vision
Shape of Elastic Strings in Euclidean Space
International Journal of Computer Vision
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates
Journal of Mathematical Imaging and Vision
Elastic Morphing of 2D and 3D Objects on a Shape Manifold
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Geodesics in Shape Space via Variational Time Discretization
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Kullback Leibler divergence based curve matching method
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
A Computational Model of Multidimensional Shape
International Journal of Computer Vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
A Continuum Mechanical Approach to Geodesics in Shape Space
International Journal of Computer Vision
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
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Klassen et al. [9] recently developed a theoretical formulation to model shape dissimilarities by means of geodesics on appropriate spaces. They used the local geometry of an infinite dimensional manifold to measure the distance dist(A,B) between two given shapes A and B. A key limitation of their approach is that the computation of distances developed in the above work is inherently unstable, the computed distances are in general not symmetric, and the computation times are typically very large. In this paper, we revisit the shooting method of Klassen et al. for their angle-oriented representation. We revisit explicit expressions for the underlying space and we propose a gradient descent algorithm to compute geodesics. In contrast to the shooting method, the proposed variational method is numerically stable, it is by definition symmetric, and it is up to 1000 times faster.