Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines

Details Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines

2010-11-17

arxiv.org/abs/1011.4058v1

Computer Science

Computer Vision and Pattern Recognition

11 pages, 6 figures

Scientific paper

We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.

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