Go with the flow: Optical flow-based transport operators for image manifolds

Aswin C. Sankaranarayanan, Chinmay Hegde, Sriram Nagaraj, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Image articulation manifolds (IAMs) play a central conceptual role in a host of computer vision and image understanding problems. The core premise is that we can view a collection of images, each of which is indexed by a small number of degrees of freedom (3D camera pose, motion/deformation, etc.), as a low-dimensional nonlinear manifold. In order to perform parameter estimation and navigation on an IAM, we require a transport operator that traverses the manifold from image to image. The two current approaches to manifold transport suffer from major shortcomings that have limited the practical impact of manifold methods. First, algebraic methods require that the IAM possess an unrealistic algebraic structure. Second, locally linear methods based on a tangent plane approximation cannot cope with the non-differentiability of IAMs containing images with sharp edges. In this paper, we demonstrate that the optical flow between pairs of images on an IAM is a valid transport operator with a number of attractive properties. In particular, we establish that the optical flow forms a low-dimensional smooth manifold. Several experiments involving novel-view synthesis, geometric clustering, and manifold charting validate that the optical flow manifold approach both offers performance significantly superior to current approaches and is practical for real-world applications.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages1824-1831
Number of pages8
DOIs
StatePublished - Dec 1 2011
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period9/28/119/30/11

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

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