General Deformations of Point Configurations Viewed By a Pinhole Model Camera

Yirmeyahu Kaminski; Michael Werman

doi:https://doi.org/10.1007/s10851-023-01142-1

General Deformations of Point Configurations Viewed By a Pinhole Model Camera

Yirmeyahu Kaminski, Michael Werman

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is a theoretical study of the non-rigid structure from motion problem: what can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for 3D affine and general smooth deformations (under some mild technical restrictions) with either a calibrated or an uncalibrated camera. We show that in general at least three images related by quasi-identical deformations are needed to have a finite set of solutions to the points’ structure.

Original language	English
Pages (from-to)	631-643
Number of pages	13
Journal	Journal of Mathematical Imaging and Vision
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s10851-023-01142-1
State	Published - Aug 2023

Keywords

Deformation
Dynamic scenes
Multiple-view geometry
Structure from motion

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Condensed Matter Physics
Computer Vision and Pattern Recognition
Geometry and Topology
Applied Mathematics

Access to Document

https://doi.org/10.1007/s10851-023-01142-1

Cite this

@article{90e8c0c07e43496cbbe9c529fd478b9b,

title = "General Deformations of Point Configurations Viewed By a Pinhole Model Camera",

abstract = "This paper is a theoretical study of the non-rigid structure from motion problem: what can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for 3D affine and general smooth deformations (under some mild technical restrictions) with either a calibrated or an uncalibrated camera. We show that in general at least three images related by quasi-identical deformations are needed to have a finite set of solutions to the points{\textquoteright} structure.",

keywords = "Deformation, Dynamic scenes, Multiple-view geometry, Structure from motion",

author = "Yirmeyahu Kaminski and Michael Werman",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2023",

month = aug,

doi = "https://doi.org/10.1007/s10851-023-01142-1",

language = "الإنجليزيّة",

volume = "65",

pages = "631--643",

journal = "Journal of Mathematical Imaging and Vision",

issn = "0924-9907",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - General Deformations of Point Configurations Viewed By a Pinhole Model Camera

AU - Kaminski, Yirmeyahu

AU - Werman, Michael

PY - 2023/8

Y1 - 2023/8

N2 - This paper is a theoretical study of the non-rigid structure from motion problem: what can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for 3D affine and general smooth deformations (under some mild technical restrictions) with either a calibrated or an uncalibrated camera. We show that in general at least three images related by quasi-identical deformations are needed to have a finite set of solutions to the points’ structure.

AB - This paper is a theoretical study of the non-rigid structure from motion problem: what can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for 3D affine and general smooth deformations (under some mild technical restrictions) with either a calibrated or an uncalibrated camera. We show that in general at least three images related by quasi-identical deformations are needed to have a finite set of solutions to the points’ structure.

KW - Deformation

KW - Dynamic scenes

KW - Multiple-view geometry

KW - Structure from motion

UR - http://www.scopus.com/inward/record.url?scp=85150601057&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s10851-023-01142-1

DO - https://doi.org/10.1007/s10851-023-01142-1

M3 - مقالة

SN - 0924-9907

VL - 65

SP - 631

EP - 643

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

IS - 4

ER -

General Deformations of Point Configurations Viewed By a Pinhole Model Camera

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this