Optimal Mass Transport for Registration and Warping

By Steven Haker, Lei Zhu, Allen R. Tannenbaum, Sigurd B. Angenent. International Journal of Computer Vision, 2004

430 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/e0de2f11f37ec9ca06fd3d738ae3998d99363c26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Characterization of barycenters in the Wasserstein space by averaging optimal transport maps (2012, neutral): “[28, 29] and references therein.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “The algorithm that we see in this section comes from an interesting minimizing flow proposed and studied in [19] (see also [191]).”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, neutral): “On the applied side these include applications to vision (image registration and morphing [64]), economics (equilibration of supply with demand [42] [27], structure of cities [23], maximization of profits [118] [22] [49] or social welfare [49]), physics [40] [129] [95] [51], engineering (optimal sha”
Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation (2019, background): “Wasserstein metric, the natural geometry for probability measures induced by the optimal transport theory, has been investigated in several fields such as image retrieval [55], color-based style transfer [51], and image warping [21].”
Sliced Wasserstein Kernels for Probability Distributions (2015, background): “Recent advances utilizing variational minimization [14, 7], particle approximation [38], and entropy regularization [9, 33], have enabled transport metrics to be efﬁciently applied to machine learning and computer vision problems.”
Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits (2022, background): “Currently, this problem has several theoretical and practical applications in a variety of scientific fields, including statistics and machine learning [70], computer vision [71], linguistics [72], classical mechanics [73], and molecular biology [74].”
Structure-preserving discretization of incompressible fluids (2009, methodology): “of medical datasets as studied by Tannenbaum et al. [ 21 ].”
Computational Optimal Transport (2018, background): “Note also that related solvers based on fixed-point iterations have been applied to image registration [Haker et al., 2004].”
Displacement interpolation using Lagrangian mass transport (2011, methodology): “In the special case where the cost function is quadratic and the space is Euclidean, the Kantorovich formulation can be solved with linear partial differential equations [Benamou and Brenier 2000; Haker et al. 2004; Rehman et al. 2009; Zhu et al. 2007].”
Optimal Mass Transport: Signal processing and machine-learning applications (2017, methodology): “The method was used in several imageregistration applications [22], pattern recognition [27], [50], and computer vision [26].”
Application of the Wasserstein metric to seismic signals (2013, methodology): “This information is useful for problems in image registration [13], meteorology [7], mesh generation [6], reflector design [12], and astrophysics [8].”
Consistent estimation of a population barycenter in the Wasserstein space (2013, neutral): “[25, 26] and references therein.”
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].”