Statistics of natural images using hash fractal image compression

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in CompSysTech '03 Proceedings of the 4th international conference conference on Computer systems and technologies: e-Learning, http://dx.doi.org/10.1145/973620.973661.Natural images form very small subset of all images. In spite of the fact, the direct computation of their block densities is not possible. On the other hand, the existence of various successful image compression methods, in particularly, the fractal compression, indicates that the compression somehow is able to capture and use at least part of the natural image statistics. In this work we show how hash based fractal image compression can be used to derive quite precise the entropies of 4 × 4 patches of the natural images. We state that the probability density in first order factorize to the probability densities of the contrast, the brightness and the index of the codebook blocks

Bump formation in a binary attractor neural network

This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the activity during the retrieval and learning is imposed. Analytical approximation for the order parameters is derived. The corresponding phase diagram shows a relatively large and stable region, where this effect is observed, although the critical storage and the information capacities drastically decrease inside that region. We demonstrate that the stability of the network, when starting from the bump formation, is larger than the stability when starting even from the whole pattern. Finally, we show a very good agreement between the analytical results and the simulations performed for different topologies of the network.Comment: about 14 page

Representing Where along with What Information in a Model of a Cortical Patch

Behaving in the real world requires flexibly combining and maintaining information about both continuous and discrete variables. In the visual domain, several lines of evidence show that neurons in some cortical networks can simultaneously represent information about the position and identity of objects, and maintain this combined representation when the object is no longer present. The underlying network mechanism for this combined representation is, however, unknown. In this paper, we approach this issue through a theoretical analysis of recurrent networks. We present a model of a cortical network that can retrieve information about the identity of objects from incomplete transient cues, while simultaneously representing their spatial position. Our results show that two factors are important in making this possible: A) a metric organisation of the recurrent connections, and B) a spatially localised change in the linear gain of neurons. Metric connectivity enables a localised retrieval of information about object identity, while gain modulation ensures localisation in the correct position. Importantly, we find that the amount of information that the network can retrieve and retain about identity is strongly affected by the amount of information it maintains about position. This balance can be controlled by global signals that change the neuronal gain. These results show that anatomical and physiological properties, which have long been known to characterise cortical networks, naturally endow them with the ability to maintain a conjunctive representation of the identity and location of objects