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>

Y2 - 29 November 2010

ER -