Large‐Scale Integer Linear Programming for Orientation Preserving 3<i>D</i> Shape Matching

Windheuser, Thomas; Schlickewei, Ulrich; Schmidt, Frank; Cremers, Daniel

doi:10.1111/j.1467-8659.2011.02021.x

Cited by 30 publications

(18 citation statements)

References 24 publications

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“…The main drawback of this approach is that it only finds similar parts, without providing a correspondence between them. Windheuser et al [WSSC11] formulated the shape matching problem as one of seeking minimal surfaces in the product space of two given shapes; the formulation notably allows for a linear programming discretization and provides guaranteed continuous and orientation-preserving solutions. The method was shown to work well with partial shapes, but requires watertight surfaces as input (e.g.…”

Section: Related Workmentioning

confidence: 99%

Partial Functional Correspondence

Rodolí

Cosmo

Bronstein

et al. 2016

Computer Graphics Forum

212

209

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In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings

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Section: Related Workmentioning

confidence: 99%

Partial Functional Correspondence

Rodolí

Cosmo

Bronstein

et al. 2016

Computer Graphics Forum

212

209

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show abstract

“…It arises in applications such as registration of partial or entire 3D shapes [1], [2], shape retrieval from databases [3], shape matching [4], [5], shape reconstruction [2], [6], [7], [8], and automatic shape understanding [9], [10].…”

Section: Introductionmentioning

confidence: 99%

SuperMatching: Feature Matching Using Supersymmetric Geometric Constraints

Cheng

Chao

Martin

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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Feature matching is a challenging problem at the heart of numerous computer graphics and computer vision applications. We present the SuperMatching algorithm for finding correspondences between two sets of features. It does so by considering triples or higher-order tuples of points, going beyond the pointwise and pairwise approaches typically used. SuperMatching is formulated using a supersymmetric tensor representing an affinity metric which takes into account feature similarity and geometric constraints between features: feature matching is cast as a higher-order graph matching problem. SuperMatching takes advantage of supersymmetry to devise an efficient sampling strategy to estimate the affinity tensor, as well as to store the estimated tensor compactly. Matching is performed by an efficient higher-order power iteration approach which takes advantage of this compact representation. Experiments on both synthetic and real data show that SuperMatching provides more accurate feature matching than other state-of-the-art approaches for a wide range of 2D and 3D features, with competitive computational cost.

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“…Previous works dealt with this problem by enforcing some global consistency, such as restricting the set of possible deformations to being isometric [58]. Others considered nearly isometric shapes [70,81], and elastic deformations [141,142]. Zhang et al [155] use a deformation-driven approach guided by a set of manually or automatically selected landmarks.…”

Section: Geometric Descriptorsmentioning

confidence: 98%