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Properties of Brownian Image Models in Scale-Space

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Scale Space Methods in Computer Vision (Scale-Space 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2695))

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Abstract

In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images.

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Author information

Authors and Affiliations

  1. DIKU, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen, Denmark

    Kim S. Pedersen

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  1. Kim S. Pedersen
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Editor information

Editors and Affiliations

  1. Imaging Sciences, 5th Floor Thomas Guy House, Guy’s Campus, London, SE1 9RT, UK

    Lewis D. Griffin

  2. IT University of Copenhagen, Glentevej 67-69, Copenhagen NV, Denmark

    Martin Lillholm

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© 2003 Springer-Verlag Berlin Heidelberg

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Pedersen, K.S. (2003). Properties of Brownian Image Models in Scale-Space. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_20

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  • DOI: https://doi.org/10.1007/3-540-44935-3_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40368-5

  • Online ISBN: 978-3-540-44935-5

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