Multiple Shape Correspondence by Dynamic Programming

Sahillioğlu, Yusuf; Yemez, Y.

doi:10.1111/cgf.12480

Cited by 17 publications

(6 citation statements)

References 37 publications

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“…Matching semantically similar shapes is a problem studied in deep depth for various scenarios including completely isometric shape pairs [OMMG10] [SY13], partially isometric shape pairs [SY14b] [LRB * 16], non-isometric shape pairs [PBDSH13] [SPKS16], and a collection of shapes [CRA * 16] [SY14a]. Compared to these studies, and many other related ones [vKZHCO11], matching shapes under noise, especially topological noise, is a problem that is yet at its infancy.…”

Section: Related Workmentioning

confidence: 99%

Topologically Robust 3D Shape Matching via Gradual Deflation and Inflation

Genctav¹,

Sahillioğlu²

2017

Preprint

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Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of different qualities or synthesized by algorithms of different stabilities. One approach for matching 3D shapes under topological noise is to replace the topology-sensitive geodesic distance with distances that are less sensitive to topological changes. We propose an alternative approach utilising gradual deflation (or inflation) of the shape volume, of which purpose is to bring the pair of shapes to be matched to a comparable topology before the search for correspondences. Illustrative experiments using different datasets demonstrate that as the level of topological noise increases, our approach outperforms the other methods in the literature.

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Section: Related Workmentioning

confidence: 99%

Topologically Robust 3D Shape Matching via Gradual Deflation and Inflation

Genctav¹,

Sahillioğlu²

2017

Preprint

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“…[RBA* 12] relaxed the regularity requirement by allowing sparse correspondences and introduced a mechanism to explicitly control the degree of sparsity of the solution [RTH* 13]. Sahillioğlu and Yemez [SY14] used a voting approach to match shape extremities, assuming them to be preserved by the partiality transformation. The common deficiencies of the above non‐rigid partial correspondence methods are their ability to provide only a sparse correspondence (typically, order of tens of points), high computational complexity, and inability to deal with extreme partiality where boundary effects play a significant role.…”

Section: Introductionmentioning

confidence: 99%

Fully Spectral Partial Shape Matching

Litany

Rodolà

Bronstein

et al. 2017

Computer Graphics Forum

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Figure 1: Examples of dense correspondence computed with our method on real 3D scans (left pair, the areas of contact are glued together), missing parts (middle) and strong topological artifacts (right, touching parts are glued together). Corresponding points are encoded with the same color. AbstractWe propose an efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain. Our technique relies on the recently introduced partial functional maps formalism and on the joint approximate diagonalization (JAD) of the Laplace-Beltrami operators previously introduced for matching non-isometric shapes. We show that a variant of the JAD problem with an appropriately modified coupling term (surprisingly) allows to construct quasi-harmonic bases localized on the latent corresponding parts. This circumvents the need to explicitly compute the unknown parts by means of the cumbersome alternating minimization used in the previous approaches, and allows performing all the calculations in the spectral domain with constant complexity independent of the number of shape vertices. We provide an extensive evaluation of the proposed technique on standard non-rigid correspondence benchmarks and show state-of-the-art performance in various settings, including partiality and the presence of topological noise.

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“…Multiple shape correspondence in the rigid settings has been addressed in numerous works, including [HFG*06, TRA11, LBB12]. In the non‐rigid setting, pointwise and functional maps for large shape collections have been explored in [HG13, HWG14, SY14a, CRA*16].…”

Section: Introductionmentioning

confidence: 99%

Non‐Rigid Puzzles

Litany

Rodolà

Bronstein

et al. 2016

Computer Graphics Forum

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Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

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Multiple Shape Correspondence by Dynamic Programming

Cited by 17 publications

References 37 publications

Topologically Robust 3D Shape Matching via Gradual Deflation and Inflation

Topologically Robust 3D Shape Matching via Gradual Deflation and Inflation

Fully Spectral Partial Shape Matching

Non‐Rigid Puzzles

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