A scale invariant covariance structure on jet space

Kim Steenstrup Pedersen; Marco Loog; Bo Markussen

doi:10.1007/11577812_2

A scale invariant covariance structure on jet space

Kim Steenstrup Pedersen, Marco Loog, Bo Markussen

Datalogisk Institut

3 Citationer (Scopus)

Abstract

This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part of the derivation, we introduce a blurring operator A_t that acts on jet space contrary to doing spatial filtering and a scaling operator S_s. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators A_t and S_s. This paper also includes empirical results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images.

Originalsprog	Engelsk
Titel	Deep Structure, Singularities, and Computer Vision
Forlag	<Forlag uden navn>
Publikationsdato	2005
Sider	12-23
ISBN (Trykt)	978-3-540-29836-6
DOI	https://doi.org/10.1007/11577812_2
Status	Udgivet - 2005
Begivenhed	First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV) - Maastricht, Holland Varighed: 29 nov. 2010 → … Konferencens nummer: 1

Konference

Konference	First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV)
Nummer	1
Land/Område	Holland
By	Maastricht
Periode	29/11/2010 → …

Navn	Lecture notes in computer science
Vol/bind	3753/2005
ISSN	0302-9743

Adgang til dokumentet

10.1007/11577812_2

http://www.springerlink.de/content/f152485768403743/fulltext.pdf

Citationsformater

Pedersen, KS, Loog, M & Markussen, B 2005, A scale invariant covariance structure on jet space. i Deep Structure, Singularities, and Computer Vision. <Forlag uden navn>, Lecture notes in computer science, bind 3753/2005, s. 12-23, First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV), Maastricht, Holland, 29/11/2010. https://doi.org/10.1007/11577812_2

@inproceedings{e7e300504f2911dd8d9f000ea68e967b,

title = "A scale invariant covariance structure on jet space",

abstract = "This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images.",

author = "Pedersen, {Kim Steenstrup} and Marco Loog and Bo Markussen",

year = "2005",

doi = "10.1007/11577812_2",

language = "English",

isbn = "978-3-540-29836-6",

series = "Lecture notes in computer science",

publisher = "<Forlag uden navn>",

pages = "12--23",

booktitle = "Deep Structure, Singularities, and Computer Vision",

note = "First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV) ; Conference date: 29-11-2010",

}

TY - GEN

T1 - A scale invariant covariance structure on jet space

AU - Pedersen, Kim Steenstrup

AU - Loog, Marco

AU - Markussen, Bo

N1 - Conference code: 1

PY - 2005

Y1 - 2005

N2 - This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images.

AB - This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images.

U2 - 10.1007/11577812_2

DO - 10.1007/11577812_2

M3 - Article in proceedings

SN - 978-3-540-29836-6

T3 - Lecture notes in computer science

SP - 12

EP - 23

BT - Deep Structure, Singularities, and Computer Vision

PB - <Forlag uden navn>

T2 - First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV)

Y2 - 29 November 2010

ER -

A scale invariant covariance structure on jet space

Abstract

Konference

Adgang til dokumentet

Fingeraftryk

Citationsformater