The ubiquitous Kronecker product
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Shape Representation and Classification Using the Poisson Equation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Image and Vision Computing
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
International Journal of Computer Vision
Geodesic shape retrieval via optimal mass transport
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Gromov–Wasserstein Distances and the Metric Approach to Object Matching
Foundations of Computational Mathematics
SIAM Journal on Imaging Sciences
Weakly convex coupling continuous cuts and shape priors
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
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We present a novel convex shape prior functional with potential for application in variational image segmentation. Starting point is the Gromov-Wasserstein Distance which is successfully applied in shape recognition and classification tasks but involves solving a non-convex optimization problem and which is non-convex as a function of the involved shape representations. In two steps we derive a convex approximation which takes the form of a modified transport problem and inherits the ability to incorporate vast classes of geometric invariances beyond rigid isometries. We propose ways to counterbalance the loss of descriptiveness induced by the required approximations and to process additional (non-geometric) feature information. We demonstrate combination with a linear appearance term and show that the resulting functional can be minimized by standard linear programming methods and yields a bijective registration between a given template shape and the segmented foreground image region. Key aspects of the approach are illustrated by numerical experiments.