Surface Matching via Currents

By Marc Vaillant, Joan Alexis Glaunès. Information Processing in Medical Imaging, 2005

471 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/2dee10980baffb9ba870634b273ab7b2d7e35272

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In Computational Mechanics

Citations in the corpus

Matrix-valued kernels for shape deformation analysis (2013, methodology): “The method may be applied for performing registration and computing distances in different kinds of “shape spaces”, such as the manifolds curves [29, 45], surfaces [71], images [6, 46, 47], vector fields [15], diffusion tensor images [14], measures [27], currents [28, 66], and labeled landmark point”
Shape deformation analysis from the optimal control viewpoint (2014, methodology): “The purpose of this paper was to develop a very general framework for the analysis of shape deformations, along with practical methods to ﬁnd an optimal deformation in that framework.”
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences (2018, methodology): “With applications ranging from shape matching (Vaillant and Glaunès, 2005; Kaltenmark et al., 2017) to classiﬁcation (Frogner et al., 2015) and generative model training (Goodfellow et al., 2014), a common setting is that of measure ﬁtting : given a unit-mass, positive empirical distribution β ∈ M…”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, methodology): “Following the methodology of [17, 31, 52], we constrain the motion of the curve q(s, t) by asking that the evolution between the two curves results from the differential equation”
Deformable Medical Image Registration: A Survey (2013, background): “Among its extensions, one may cite volume registration for scalar [67], [77]–[79] vector- [80] and tensor-valued data [81], point-matching [68], point-matching on spheres [82], matching sets of unlabeled points [83]–[85], shape-matching [65], [86], curve-mapping [87]–[90], and hybrid registration [9”
Fast diffeomorphic matching to learn globally asymptotically stable nonlinear dynamical systems (2016, unknown): “Various gradient descent algorithms have been proposed to optimize v with respect to a cost that depends both on the deformation energy and on the accuracy of the mapping, whether the objective is to map curves [9], surfaces [10], or, as in our case, points [11].”
Computational Optimal Transport (2018, unknown): “2) are routinely used for shape matching (represented as measures over a lifted space, often called currents) in computational anatomy [Vaillant and Glaunès, 2005], but OT distances offer an interesting alternative [Feydy et al.”