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.
| Original language | English |
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| Title of host publication | Scale Space Methods in Computer Vision : 4th International Conference, Scale Space 2003 Isle of Skye, UK, June 10–12, 2003 Proceedings |
| Publisher | <Forlag uden navn> |
| Publication date | 2003 |
| Pages | 281-296 |
| ISBN (Print) | 978-3-540-40368-5 |
| DOIs | |
| Publication status | Published - 2003 |
| Event | 4th International Conference in Scale Space - Isle of Skye, United Kingdom Duration: 29 Nov 2010 → … Conference number: 4 |
Conference
| Conference | 4th International Conference in Scale Space |
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| Number | 4 |
| Country/Territory | United Kingdom |
| City | Isle of Skye |
| Period | 29/11/2010 → … |
| Series | Lecture notes in computer science |
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| Volume | 2695/2003 |
| ISSN | 0302-9743 |