Displacement interpolation using Lagrangian mass transport

By Nicolas Bonneel, Michiel van de Panne, Sylvain Paris, Wolfgang Heidrich. ACM Transactions on Graphics, 2011

438 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/7ac0a2cd0cc0ebf26474b88e1b0a38498ab1df3d

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Scaling Algorithms for Unbalanced Transport Problems (2016, methodology): “…by theoreticians, OT is now becoming popular in applied ﬁelds, and we refer for instance to application for color manipulation in image processing [61], reﬂectance interpolation in computer graphics [12], image retrieval in computer vision [66] and statistical inference in machine learning [74].”
Primal Wasserstein Imitation Learning (2020, methodology): “The Wasserstein distance is evaluated at the end of an episode using a transportation simplex (Bonneel et al., 2011); we used the implementation from Flamary & Courty (2017).”
Iterative Bregman Projections for Regularized Transportation Problems (2014, background): “OT has recently found a ﬂurry of applications in various ﬁelds such as computer vision [50], economy [22] [19], computer graphics [11], image processing [60], astrophysics [34].”
Entropic Approximation of Wasserstein Gradient Flows (2015, background): “However, one can now find many relevant uses of OT in very diverse fields such as astrophysics [43], computer vision [59], computer graphics [17], image processing [73], statistics [14], and machine learning [33], to name a few.”
Computational Optimal Transport (2018, background): “McCann’s interpolation finds many applications, for instance, color, shape, and illumination interpolations in computer graphics [Bonneel et al., 2011].”
POT: Python Optimal Transport (2021, methodology): “For solving the problem of non regularized OT, we have used a state-of-the-art solver provided in C++ by Bonneel et al. (2011).”
Zero-shot Image Recognition Using Relational Matching, Adaptation and Calibration (2019, background): “The linear program of finding the intermediate variable Cd in Algorithm 1 can be easily solved using a network simplex formulation of the earth-mover’s distance problem [28].”
Sliced and Radon Wasserstein Barycenters of Measures (2014, positive): “Displacement interpolation has been employed for image warping and registration [18,24], to remove flickering in old movies [12] and in computer graphics to perform manipulations on textures [22] and to interpolate reflectance for 3-D rendering [8].”
Domain Adaptation with Regularized Optimal Transport (2014, methodology): “In every experiment, the original optimal transport (OT-ori) is computed with a network simplex approach [17].”
Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration (2017, background): “Computing distances between probability measures on metric spaces, or more generally between point clouds, plays an increasingly preponderant role in machine learning [SL11, MJ15, LG15, JSCG16, ACB17], statistics [FCCR16, PZ16, SR04, BGKL17] and computer vision [RTG00, BvdPPH11, SdGP + 15].”
Fast geometric learning with symbolic matrices (2020, positive): “…y j ) = k x i y j k or 12 k x i y j k 2 and stand to beneﬁt greatly from our library. benchmark an exact linear � � To demonstrate this, we solver [13, 42] against several variants and implementations of the Sinkhorn algorithm: a vanilla Sinkhorn loop [27, 29, 34, 41, 44, 94, 98, 112, 117]; an…”