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

Department of Computer Science

3 Citations (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.

Original language	English
Title of host publication	Deep Structure, Singularities, and Computer Vision
Publisher	<Forlag uden navn>
Publication date	2005
Pages	12-23
ISBN (Print)	978-3-540-29836-6
DOIs	https://doi.org/10.1007/11577812_2
Publication status	Published - 2005
Event	First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV) - Maastricht, Netherlands Duration: 29 Nov 2010 → … Conference number: 1

Conference

Conference	First International Workshop in Deep Structure, Singularities, and Computer Vision (DSSCV)
Number	1
Country/Territory	Netherlands
City	Maastricht
Period	29/11/2010 → …

Series	Lecture notes in computer science
Volume	3753/2005
ISSN	0302-9743

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

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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.

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ER -

A scale invariant covariance structure on jet space

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