TY - GEN
T1 - Go with the flow
T2 - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
AU - Sankaranarayanan, Aswin C.
AU - Hegde, Chinmay
AU - Nagaraj, Sriram
AU - Baraniuk, Richard G.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84856099676&partnerID=8YFLogxK
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U2 - 10.1109/Allerton.2011.6120390
DO - 10.1109/Allerton.2011.6120390
M3 - Conference contribution
AN - SCOPUS:84856099676
SN - 9781457718168
T3 - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
SP - 1824
EP - 1831
BT - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Y2 - 28 September 2011 through 30 September 2011
ER -