A scale invariant covariance structure on jet space

Authors:
Bo Markussen;Kim Steenstrup Pedersen;Marco Loog
Affiliations:
Department of Computer Science, University of Copenhagen, Denmark;Image Analysis Group, Department of Innovation, IT University of Copenhagen, Denmark;Image Analysis Group, Department of Innovation, IT University of Copenhagen, Denmark
Venue:
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Year:
2005

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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.