On the Nonlinear Statistics of Optical Flow

被引：2

作者：

Adams, Henry ^{[1
]}

Bush, Johnathan ^{[1
]}

Carr, Brittany ^{[1
]}

Kassab, Lara ^{[1
]}

Mirth, Joshua ^{[1
]}

机构：

[1] Colorado State Univ, Ft Collins, CO 80523 USA

来源：

COMPUTATIONAL TOPOLOGY IN IMAGE CONTEXT, CTIC 2019 | 2019年 / 11382卷

关键词：

Optical flow; Computational topology; Persistent homology; Fiber bundle; Zigzag persistence; PERSISTENT HOMOLOGY ANALYSIS; TOPOLOGICAL PERSISTENCE;

D O I：

10.1007/978-3-030-10828-1_12

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In A naturalistic open source movie for optical flow evaluation, Butler et al. create a database of ground-truth optical flow from the computer-generated video Sintel. We study the high-contrast 3 x 3 patches from this video, and provide evidence that this dataset is well-modeled by a torus (a nonlinear 2-dimensional manifold). Our main tools are persistent homology and zigzag persistence, which are popular techniques from the field of computational topology. We show that the optical flow torus model is naturally equipped with the structure of a fiber bundle, which is furthermore related to the statistics of range images.

引用

页码：151 / 165

页数：15

共 36 条

[1] Adams H, 2017, J MACH LEARN RES, V18
[2] Adams H, 2015, TOPOL METHOD NONL AN, V45, P247
[3] On the Nonlinear Statistics of Range Image Patches
Adams, Henry
Carlsson, Gunnar
[J]. SIAM JOURNAL ON IMAGING SCIENCES, 2009, 2 (01): : 110 - 117
[4] Armstrong M.A, 2013, BASIC TOPOLOGY, DOI [10.1007/978-1-4757-1793-8, DOI 10.1007/978-1-4757-1793-8]
[5] A Database and Evaluation Methodology for Optical Flow
Baker, Simon
Scharstein, Daniel
Lewis, J. P.
Roth, Stefan
Black, Michael J.
Szeliski, Richard
[J]. INTERNATIONAL JOURNAL OF COMPUTER VISION, 2011, 92 (01) : 1 - 31
[6] Bao W, 2009, PROCEEDINGS OF 2009 INTERNATIONAL CONFERENCE ON IMAGE ANALYSIS AND SIGNAL PROCESSING, P233
[7] PERFORMANCE OF OPTICAL-FLOW TECHNIQUES
BARRON, JL
FLEET, DJ
BEAUCHEMIN, SS
[J]. INTERNATIONAL JOURNAL OF COMPUTER VISION, 1994, 12 (01) : 43 - 77
[8] TARGET ENUMERATION VIA EULER CHARACTERISTIC INTEGRALS
Baryshnikov, Yuliy
Ghrist, Robert
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2009, 70 (03) : 825 - 844
[9] Bauer U., 2017, RIPSER LEAN C CODE C
[10] The computation of optical flow
Beauchemin, SS
Barron, JL
[J]. ACM COMPUTING SURVEYS, 1995, 27 (03) : 433 - 467

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