On a realization of motion and similarity group equivalence classes of labeled points in $\mathbb R^k$ with applications to computer vision

We study a realization of motion and similarity group equivalence classes of n ≥ 1 labeled points in R, k ≥ 1 as a metric space with a computable metric. Our study is motivated by applications in computer vision.

[1]  池内 克史,et al.  Computer Vision: A Reference Guide , 2014 .

[2]  P. Olver,et al.  Affine Invariant Detection: Edge Maps, Anisotropic Diffusion, and Active Contours , 1999 .

[3]  Zuzana Kukelova,et al.  Distortion Varieties , 2016, Foundations of Computational Mathematics.

[4]  Steven B. Damelin.  A walk through energy, discrepancy, numerical integration and group invariant measures on measurable subsets of euclidean space , 2008, Numerical Algorithms.

[5]  Keaton Hamm.  Nonuniform Sampling and Recovery of Bandlimited Functions in Higher Dimensions , 2017 .

[6]  K. M. Nolan,et al.  R J , 2022 .

[7]  Joseph David Kileel,et al.  Algebraic Geometry for Computer Vision , 2017 .

[8]  Fred J. Hickernell,et al.  On Energy, Discrepancy and Group Invariant Measures on Measurable Subsets of Euclidean Space , 2010 .

[9]  Joao M. Pereira,et al.  Subspace power method for symmetric tensor decomposition and generalized PCA , 2019, ArXiv.

[10]  Guillermo Sapiro,et al.  Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing , 1997, SIAM J. Appl. Math..

[11]  Michael Werman,et al.  Affine Invariance Revisited , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[12]  Michael Werman.  Affine Invariants , 2014, Computer Vision, A Reference Guide.

[13]  Michael Werman,et al.  Similarity and Affine Invariant Distances Between 2D Point Sets , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Joe Kileel,et al.  Minimal Problems for the Calibrated Trifocal Variety , 2016, SIAM J. Appl. Algebra Geom..