TY - GEN
T1 - High-resolution navigation on non-differentiable image manifolds
AU - Wakin, Michael B.
AU - Donoho, David L.
AU - Choi, Hyeokho
AU - Baraniuk, Richard G.
PY - 2005
Y1 - 2005
N2 - The images generated by varying the underlying articulation parameters of an object (pose, attitude, light source position, and so on) can be viewed as points on a low-dimensional image parameter articulation manifold (IPAM) in a high-dimensional ambient space. In this paper, we develop theory and methods for the inverse problem of estimating, from a given image on or near an IPAM, the underlying parameters that produced it. Our approach is centered on the observation that, while typical image manifolds are not differentiable, they have an intrinsic multiscale geometric structure. In fact, each IPAM has a family of approximate tangent spaces, each one good at a certain resolution. Putting this structural aspect to work, we develop a new algorithm for high-accuracy parameter estimation based on a coarse-to-fine Newton iteration through the family of approximate tangent spaces. We test the algorithm in several idealized registration and pose estimation problems.
AB - The images generated by varying the underlying articulation parameters of an object (pose, attitude, light source position, and so on) can be viewed as points on a low-dimensional image parameter articulation manifold (IPAM) in a high-dimensional ambient space. In this paper, we develop theory and methods for the inverse problem of estimating, from a given image on or near an IPAM, the underlying parameters that produced it. Our approach is centered on the observation that, while typical image manifolds are not differentiable, they have an intrinsic multiscale geometric structure. In fact, each IPAM has a family of approximate tangent spaces, each one good at a certain resolution. Putting this structural aspect to work, we develop a new algorithm for high-accuracy parameter estimation based on a coarse-to-fine Newton iteration through the family of approximate tangent spaces. We test the algorithm in several idealized registration and pose estimation problems.
UR - http://www.scopus.com/inward/record.url?scp=33646014913&partnerID=8YFLogxK
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U2 - 10.1109/ICASSP.2005.1416493
DO - 10.1109/ICASSP.2005.1416493
M3 - Conference contribution
AN - SCOPUS:33646014913
SN - 0780388747
SN - 9780780388741
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - V1073-V1076
BT - 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Education, Spec. Sessions
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05
Y2 - 18 March 2005 through 23 March 2005
ER -