Estimation of priors in natural images

@article{Obuchi2014EstimationOP,
  title={Estimation of priors in natural images},
  author={Tomoyuki Obuchi and Hirokazu Koma and Muneki Yasuda},
  journal={ArXiv},
  year={2014},
  volume={abs/1412.7012}
}
We investigate prior distributions in natural images by using Boltzmann machine, to find some possible universal properties and individual characteristics of natural images. For simplicity, we specifically focus on binary pictures. We find that in most cases there emerges a structure with two sublattices, and the nearest-neighbor and next-nearest-neighbor interactions correspondingly take two discriminative values, which reflects individual characteristics of each set of pictures. On the other… Expand

References

SHOWING 1-10 OF 24 REFERENCES
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
  • S. Geman, D. Geman
  • Mathematics, Medicine
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1984
TLDR
The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation. Expand
Statistical thermodynamics of natural images.
TLDR
The distribution of pixels in small image patches is examined and how to construct the corresponding thermodynamics is shown, finding evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how "surprising" the authors find individual images. Expand
Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials
TLDR
This paper considers fully connected CRF models defined on the complete set of pixels in an image and proposes a highly efficient approximate inference algorithm in which the pairwise edge potentials are defined by a linear combination of Gaussian kernels. Expand
Statistics of Natural Images: Scaling in the Woods
TLDR
This work gathers images from the woods and finds that these scenes possess an ensemble scale invariance, and this non-Gaussian character cannot be removed through local linear filtering, meaning information is maximized at fixed channel variance. Expand
Statistical-mechanical approach to image processing
The basic frameworks and techniques of the Bayesian approach to image restoration are reviewed from the statistical-mechanical point of view. First, a few basic notions in digital image processingExpand
The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-fieldExpand
Advanced mean field methods: theory and practice
A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variablesExpand
Efficient Learning in Boltzmann Machines Using Linear Response Theory
TLDR
This work presents a new approximate learning algorithm for Boltzmann machines, based on mean-field theory and the linear response theorem, that is close to the optimal solutions and gives a significant improvement when correlations play a significant role. Expand
Deterministic Boltzmann Learning Performs Steepest Descent in Weight-Space
TLDR
By using the appropriate interpretation for the way in which a DBM represents the probability of an output vector given an input vector, it is shown that the DBM performs steepest descent in the same function as the original SBM, except at rare discontinuities. Expand
A Learning Algorithm for Boltzmann Machines
TLDR
A general parallel search method is described, based on statistical mechanics, and it is shown how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. Expand
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