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research [2018/09/23 15:31]
ipa [Variational Image Analysis on Manifolds and Metric Measure Spaces]
research [2019/04/25 10:44] (current)
ipa [Variational Image Analysis on Manifolds and Metric Measure Spaces]
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 The current focus is on the **//​assignment manifold//​** and image labeling, and on learning from image assignments in large-scale unsupervised scenarios, within the mathematical frameworks of information geometry and regularised optimal transport. A novel smooth dynamical system evolving on a statistical manifold, called **//​assignment flow//**, forms the basis of our work. The current focus is on the **//​assignment manifold//​** and image labeling, and on learning from image assignments in large-scale unsupervised scenarios, within the mathematical frameworks of information geometry and regularised optimal transport. A novel smooth dynamical system evolving on a statistical manifold, called **//​assignment flow//**, forms the basis of our work.
  
-**Current work.** We conduct a comprehensive study of //geometric integration//​ techniques, including automatic step size adaption, for numerically computing the assignment flow in a stable, efficient and parameter-free way. Based on this, we study how weights ​for geometric diffusion can be learned from data, by applying optimal control ​to the assignment flowThis enables to attach ​semantic meaning to such weights, a property ​that is missing in current models ​of artificial neural networks.+**Mathematical aspects.** The assignment flow evolves non-locally ​for any data given on a graph. Variational aspectsextensions ​to continuous domains and scale separation are investigatedA preliminary step concerns ​more classical //​additive//​ variational formulation ​that provides a smooth geometric version ​of the continuous cut approach. 
 +  * [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​Savarino2019aa.pdf|A Variational Perspective on the Assignment Flow, SSVM 2019]].
  
-**Recent work.** We extended ​the assignment flow to //​unsupervised//​ scenarios, where label evolution on a feature manifold is simultaneously performed together with label assignment to given data - see the  +**Parameter learning.** We study how weights for geometric diffusion that parametrize the adaptivity of the assignment flow can be learned from data. Symplectic integration ensures ​the commutativity of discretisation and optimisation operations. We currently investigate this approach in connection with more general objective functions. 
-  * [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​gcpr2018.pdf|preliminary announcement at the GCPR 2018]]+  * [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​Huhnerbein2019aa.pdf|Learning Adaptive Regularization for Image Labeling Using Geometric Assignment, SSVM 2019]].
-This paper sketches a special instance of a more general framework, the //​unsupervised assignment flow//, to be introduced in a forthcoming report.+
  
-We applied our approach to solve in a novel way the //MAP labeling problem// based on a given graphical model by smoothly combining a geometric reformulation of the local polytope relaxation with rounding to an integral solutionA key ingredient ​are local `//Wasserstein messages//' that couple local assignment measures along edges.+**Unsupervised label learning.** Our recent work concerns the emergence of labels ​in a completely unsupervised ​way by data //self//-assignmentThe resulting unsupervised assignment flow has connections to low-rank matrix factorisation and discrete optimal mass transport that are explored in our current work. 
 +  * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/​Zisler2019aa.pdf|Unsupervised Labeling by Geometric and Spatially Regularized Self-Assignment,​ SSVM 2019]].
  
-  ​* [[https://epubs.siam.org/doi/abs/10.1137/​17M1150669|SIAM J. on Imaging Science11/2 (2018) 1317--1362]]+We extended the assignment flow to //​unsupervised//​ scenarios, where label evolution on a feature manifold is simultaneously performed together with label assignment to given data. The following papers introduce the corresponding //​unsupervised assignment flow//. 
 +  ​* [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zern2019aa.pdf|Unsupervised Assignment Flow: Label Learning ​on Feature Manifolds by Spatially Regularized Geometric Assignmentpreprint: arXiv:​1904.10863]] 
 +  * [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​gcpr2018.pdf|Unsupervised Label Learning on Manifolds by Spatially Regularized Geometric Assignment, GCPR 2018]].
  
-Kick-off paper that introduces ​the basic approach:+**Geometric numerical integration.** We conducted a comprehensive study of //geometric integration//​ techniques, including automatic step size adaption, for numerically computing the assignment flow in a stable, efficient and parameter-free way.  
 +  * [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​Zeilmann2018aa.pdf|Geometric Numerical Integration of the Assignment Flow, preprint: arXiv:1810.06970]]
  
-  ​* [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​Astroem2017.pdf|J. Math. Imag. Vision 58/2 (2017) 211--238]]+**Evaluation of discrete graphical models.** We applied our approach to solve in a novel way the //MAP labeling problem// based on a given graphical model by smoothly combining a geometric reformulation of the local polytope relaxation with rounding to an integral solution. A key ingredient are local `//​Wasserstein messages//'​ that couple local assignment measures along edges. 
 + 
 +  * [[https://​epubs.siam.org/​doi/​abs/​10.1137/​17M1150669|Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment, SIAM J. on Imaging Science, 11/2 (2018) 1317--1362]] 
 + 
 +**Kick-off paper** that introduces the basic approach: 
 + 
 +  ​* [[https://​ipa.math.uni-heidelberg.de/​dokuwiki/​Papers/​Astroem2017.pdf|Image Labeling by Assignment., ​J. Math. Imag. Vision 58/2 (2017) 211--238]]
   * [[http://​www-rech.telecom-lille.fr/​diff-cv2016/​|Proceedings DIFF-CVML'​16;​ Grenander best paper award]]   * [[http://​www-rech.telecom-lille.fr/​diff-cv2016/​|Proceedings DIFF-CVML'​16;​ Grenander best paper award]]
   * [[https://​ipa.iwr.uni-heidelberg.de/​dokuwiki/​Papers/​Astroem2016d.pdf|Proceedings ECCV'​16]]   * [[https://​ipa.iwr.uni-heidelberg.de/​dokuwiki/​Papers/​Astroem2016d.pdf|Proceedings ECCV'​16]]