Learning shape metrics based on deformations and transport

Charpiat, Guillaume

doi:10.1109/iccvw.2009.5457683

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…Charpiat [Cha09] uses the idea of composing maps between close shapes to improve the maps between non‐similar shapes. Similarly to our approach, he builds a graph where each shape is a vertex, and edges between shapes are weighted by the cost of the best map between them.…”

Section: Related Workmentioning

confidence: 99%

An Optimization Approach to Improving Collections of Shape Maps

Nguyễn

Ben‐Chen

Welnicka

et al. 2011

Computer Graphics Forum

103

127

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Finding an informative, structure-preserving map between two shapes has been a long-standing problem in geometry processing, involving a variety of solution approaches and applications. However, in many cases, we are given not only two related shapes, but a collection of them, and considering each pairwise map independently does not take full advantage of all existing information. For example, a notorious problem with computing shape maps is the ambiguity introduced by the symmetry problem -for two similar shapes which have reflectional symmetry there exist two maps which are equally favorable, and no intrinsic mapping algorithm can distinguish between them based on these two shapes alone. Another prominent issue with shape mapping algorithms is their relative sensitivity to how "similar" two shapes are -good maps are much easier to obtain when shapes are very similar. Given the context of additional shape maps connecting our collection, we propose to add the constraint of global map consistency, requiring that any composition of maps between two shapes should be independent of the path chosen in the network. This requirement can help us choose among the equally good symmetric alternatives, or help us replace a "bad" pairwise map with the composition of a few "good" maps between shapes that in some sense interpolate the original ones. We show how, given a collection of pairwise shape maps, to define an optimization problem whose output is a set of alternative maps, compositions of those given, which are consistent, and individually at times much better than the original. Our method is general, and can work on any collection of shapes, as long as a seed set of good pairwise maps is provided. We demonstrate the effectiveness of our method for improving maps generated by state-of-the-art mapping methods on various shape databases.

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Section: Related Workmentioning

confidence: 99%

An Optimization Approach to Improving Collections of Shape Maps

Nguyễn

Ben‐Chen

Welnicka

et al. 2011

Computer Graphics Forum

103

127

View full text Add to dashboard Cite

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“…The affinity-wise super graph G a sup by Definition ( 6) is similar to the one in [46], of which the author proposes to build a graph where each shape is a vertex, and edges between shapes are weighted by the cost of the best matching. We put it in the scenario for the problem of weighted multi-graph matching.…”

Section: Notations and Definitionsmentioning

confidence: 99%

A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting

Yan,

Cho,

Zha

et al. 2015

Preprint

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This paper addresses the problem of matching N weighted graphs referring to an identical object or category. More specifically, matching the common node correspondences among graphs. This multi-graph matching problem involves two ingredients affecting the overall accuracy: i) the local pairwise matching affinity score among graphs; ii) the global matching consistency that measures the uniqueness of the pairwise matching results by different chaining orders. Previous studies typically either enforce the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across graph pairs; or separate affinity optimizing and consistency regularization in two steps. This paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function when the function is biased due to noises or inappropriate modeling. We propose multigraph matching methods to incorporate the two aspects by boosting the affinity score, meanwhile gradually infusing the consistency as a regularizer. Furthermore, we propose a node-wise consistency/affinitydriven mechanism to elicit the common inlier nodes out of the irrelevant outliers. Extensive results on both synthetic and public image datasets demonstrate the competency of the proposed algorithms.

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“…Most of the works on multiple 3D shape correspondence strive to improve a given set of pairwise maps instead of computing them from scratch. One method from this category [Cha09] builds a complete graph connecting all shapes with edges weighted by the matching costs of the initially assumed pairwise maps. The method then computes the shortest path between each shape pair, which implies a map composition to replace the initial map with.…”

Section: Related Workmentioning

confidence: 99%

Multiple Shape Correspondence by Dynamic Programming

Sahillioğlu

Yemez

2014

Computer Graphics Forum

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We present a multiple shape correspondence method based on dynamic programming, that computes consistent bijective maps between all shape pairs in a given collection of initially unmatched shapes. As a fundamental distinction from previous work, our method aims to explicitly minimize the overall distortion, i.e., the average isometric distortion of the resulting maps over all shape pairs. We cast the problem as optimal path finding on a graph structure where vertices are maps between shape extremities. We exploit as much context information as possible using a dynamic programming based algorithm to approximate the optimal solution. Our method generates coarse multiple correspondences between shape extremities, as well as denser correspondences as byproduct. We assess the performance on various mesh sequences of (nearly) isometric shapes. Our experiments show that, for isometric shape collections with non-uniform triangulation and noise, our method can compute relatively dense correspondences reasonably fast and outperform state of the art in terms of accuracy.

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Learning shape metrics based on deformations and transport

Cited by 6 publications

References 17 publications

An Optimization Approach to Improving Collections of Shape Maps

An Optimization Approach to Improving Collections of Shape Maps

A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting

Multiple Shape Correspondence by Dynamic Programming

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