TY - JOUR
T1 - Matched Manifold Detection for Group-Invariant Registration and Classification of Images
AU - Yavo, Ziv
AU - Haitman, Yuval
AU - Francos, Joseph M.
AU - Scharf, Louis L.
N1 - Funding Information:
Manuscript received July 9, 2020; revised March 12, 2021 and June 4, 2021; accepted June 25, 2021. Date of publication July 8, 2021; date of current version August 3, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Elias Aboutanios. This work was supported by NSF-BSF Computing and by Communication Foundations (CCF) under Grants CCF-2016667, CCF-1712788 and BSF-2016667 . (Corresponding author: Joseph M. Francos.) Ziv Yavo, Yuval Haitman, and Joseph M. Francos are with the Department of Electrical and Computer Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel (e-mail: zivyavo@gmail.com; yuvalhaitman@gmail.com; francos@ee.bgu.ac.il).
Publisher Copyright:
© 1991-2012 IEEE.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - Consider the set of possible observations turned out by geometric and radiometric transformations of an object. This set is generally a manifold in the ambient space of observations. It has been shown [1] that in those cases where the geometric deformations are affine and the radiometric deformations are monotonic, the radiometry invariant universal manifold embedding (RIUME) provides a mapping from the orbit of deformed observations to a single low dimensional linear subspace of Euclidean space. This linear subspace is invariant to the geometric and radiometric transformations and hence is a representative of the orbit. It thus naturally serves as an invariant statistic for solving problems of joint transformation estimation and detection or classification. In the unsupervised detection problem, subspaces evaluated from two observations are tested for the similarity of the observed object and their relative transformation is estimated from the RIUME matrix representation. In the classification set-up the RIUME subspace extracted from an experimental observation is tested against a set of subspaces representing the different object manifolds, in search for the nearest class. We show how to extract a set of mutually orthogonal subspaces, where each subspace represents a different object manifold. In the presence of observation noise, the observations do not lie strictly on the manifold and the resulting RIUME subspaces are noisy. We derive a method for estimating the mean subspace representation of a manifold of deformed observations. To optimize the performance of the matched manifold detector in the presence of observation noise, an analytic solution for choosing the RIUME nonlinear operators is derived, achieving the effect of simultaneous denoising of the object manifolds. The invariant representation of the object is the basis of a matched manifold detection and tracking framework for objects that undergo complex geometric and radiometric deformations. The experimental results on natural scenes demonstrate the generality and applicability of the RIUME framework for classification, detection, and dense registration.
AB - Consider the set of possible observations turned out by geometric and radiometric transformations of an object. This set is generally a manifold in the ambient space of observations. It has been shown [1] that in those cases where the geometric deformations are affine and the radiometric deformations are monotonic, the radiometry invariant universal manifold embedding (RIUME) provides a mapping from the orbit of deformed observations to a single low dimensional linear subspace of Euclidean space. This linear subspace is invariant to the geometric and radiometric transformations and hence is a representative of the orbit. It thus naturally serves as an invariant statistic for solving problems of joint transformation estimation and detection or classification. In the unsupervised detection problem, subspaces evaluated from two observations are tested for the similarity of the observed object and their relative transformation is estimated from the RIUME matrix representation. In the classification set-up the RIUME subspace extracted from an experimental observation is tested against a set of subspaces representing the different object manifolds, in search for the nearest class. We show how to extract a set of mutually orthogonal subspaces, where each subspace represents a different object manifold. In the presence of observation noise, the observations do not lie strictly on the manifold and the resulting RIUME subspaces are noisy. We derive a method for estimating the mean subspace representation of a manifold of deformed observations. To optimize the performance of the matched manifold detector in the presence of observation noise, an analytic solution for choosing the RIUME nonlinear operators is derived, achieving the effect of simultaneous denoising of the object manifolds. The invariant representation of the object is the basis of a matched manifold detection and tracking framework for objects that undergo complex geometric and radiometric deformations. The experimental results on natural scenes demonstrate the generality and applicability of the RIUME framework for classification, detection, and dense registration.
KW - Object detection
KW - affine coordinate transformation
KW - dense registration
KW - invariant classification
KW - matched manifold detection
KW - subspace averaging
UR - http://www.scopus.com/inward/record.url?scp=85112744992&partnerID=8YFLogxK
U2 - 10.1109/TSP.2021.3095723
DO - 10.1109/TSP.2021.3095723
M3 - Article
AN - SCOPUS:85112744992
VL - 69
SP - 4162
EP - 4176
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
M1 - 9478272
ER -