Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Non-Rigid Shape Comparison of Plane Curves in Images
Journal of Mathematical Imaging and Vision
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking Points on Deformable Objects Using Curvature Information
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Classification Using the Inner-Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Shape of Plane Elastic Curves
International Journal of Computer Vision
International Journal of Computer Vision
Shape matching by variational computation of geodesics on a manifold
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Geodesics between 3d closed curves using path-straightening
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Some new results on non-rigid correspondence and classification of curves
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A Computational Model of Multidimensional Shape
International Journal of Computer Vision
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We construct a 1-parameter family of geodesic shape metrics on a space of closed parametric curves in Euclidean space of any dimension. The curves are modeled on homogeneous elastic strings whose elasticity properties are described in terms of their tension and rigidity coefficients. As we change the elasticity properties, we obtain the various elastic models. The metrics are invariant under reparametrizations of the curves and induce metrics on shape space. Analysis of the geometry of the space of elastic strings and path spaces of elastic curves enables us to develop a computational model and algorithms for the estimation of geodesics and geodesic distances based on energy minimization. We also investigate a curve registration procedure that is employed in the estimation of shape distances and can be used as a general method for matching the geometric features of a family of curves. Several examples of geodesics are given and experiments are carried out to demonstrate the discriminative quality of the elastic metrics.