A scale invariant covariance structure on jet space
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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A scale invariant covariance structure on jet space. / Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo.
Deep Structure, Singularities, and Computer Vision. <Forlag uden navn>, 2005. s. 12-23 (Lecture notes in computer science, Bind 3753/2005).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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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 -
ID: 4979743