Modeling Natural Images Using Gated MRFs

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 35; no. 9; pp. 2206 - 2222
• Main Authors: Ranzato, M., Mnih, V., Susskind, J. M., Hinton, G. E.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.09.2013; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Applied sciences; Artificial intelligence; Belief networks; Boltzmann machine; Computational modeling; Computer science; control theory; systems; Connectionism. Neural networks; Covariance matrix; deep learning; denoising; density estimation; Economic models; energy-based model; Exact sciences and technology; facial expression recognition; factored 3-way model; Flexibility; Gated MRF; Gaussian; generative model; Image reconstruction; Information retrieval. Graph; Logic gates; Magnetorheological fluids; Mathematical models; natural images; object recognition; Pattern recognition. Digital image processing. Computational geometry; Pixels; Probabilistic logic; Studies; Tasks; Theoretical computing; unsupervised learning; Vectors; object recognition; Density estimation; Energy method; High resolution; Conditional distribution; Density measurement; Image processing; Boltzmann machine; Noise reduction; Modeling; Belief networks; Deep learning; denoising; energy-based model; Covariance; Hidden variable theory; Conditional reasoning; Natural scenes; facial expression recognition; Computer vision; Image resolution; Latent variable model; Covariance matrix; Markov model; Pattern recognition; Neural network; factored 3-way model; Unsupervised learning; Discrimination; Gaussian process; Gated MRF; Diagonal matrix; natural images; Graph method; generative model; Pixel; Signal to noise ratio
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2013.29

This paper describes a Markov Random Field for real-valued image modeling that has two sets of latent variables. One set is used to gate the interactions between all pairs of pixels, while the second set determines the mean intensities of each pixel. This is a powerful model with a conditional distribution over the input that is Gaussian, with both mean and covariance determined by the configuration of latent variables, which is unlike previous models that were restricted to using Gaussians with either a fixed mean or a diagonal covariance matrix. Thanks to the increased flexibility, this gated MRF can generate more realistic samples after training on an unconstrained distribution of high-resolution natural images. Furthermore, the latent variables of the model can be inferred efficiently and can be used as very effective descriptors in recognition tasks. Both generation and discrimination drastically improve as layers of binary latent variables are added to the model, yielding a hierarchical model called a Deep Belief Network.