3D shape representation by contours
Computer Vision, Graphics, and Image Processing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On minimal energy trajectories
Computer Vision, Graphics, and Image Processing
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiresolution curve editing with linear constraints
Proceedings of the sixth ACM symposium on Solid modeling and applications
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
Signed Area of Sectors Between Spline Curves and the Origin
IV '99 Proceedings of the 1999 International Conference on Information Visualisation
Length preserving multiresolution editing of curves
Computing - Geometric modelling dagstuhl 2002
Length Constrained Multiresolution Deformation for Surface Wrinkling
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Detail preserving deformation of B-spline surfaces with volume constraint
Computer Aided Geometric Design
Area preserving deformation of multiresolution curves
Computer Aided Geometric Design
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Modeling the deformation of shapes under constraints on both perimeter and area is a challenging task due to the highly nontrivial interaction between the need for flexible local rules for manipulating the boundary and the global constraints. We propose several methods to address this problem and generate "random walks" in the space of shapes obeying quite general possibly time varying constraints on their perimeter and area. Design of perimeter and area preserving deformations are an interesting and useful special case of this problem. The resulting deformation models are employed in annealing processes that evolve original shapes toward shapes that are optimal in terms of boundary bending-energy or other functionals. Furthermore, such models may find applications in the analysis of sequences of real images of deforming objects obeying global constraints as building blocks for registration and tracking algorithms.