Optoelectronic implementation of stochastic artificial retinas

¹ Institut d'Optique Théorique et Appliquée, CNRS, B.P. 147, 91403 Orsay Cedex, France
² : Silicon World, 12 rue de Châtillon, 75014 Paris
³ : Institut National d'Optique, 369 rue Franquet, Sainte-Foy (Québec), Canada G1P 4N8

Abstract

An analogy can be established between image processing and statistical mechanics. Just like the assignment of an energy function to a physical system determines its Gibbs distribution, the assignment of an energy function to an image determines its likelihood and, as a consequence, allows to model its structure. Within this framework, related to the statistical concept of a Markov Random Field, image restoration, image segmentation, motion detection and some other low level operations can be expressed as the minimization of the corresponding energy function, or by the analogy, as finding the ground state of the corresponding physical system. In practice, however, only stochastic algorithms allow to solve this optimization problem for arbitrary energy functions. These techniques simulate thermal equilibrium under the posterior Gibbs distribution. When a gradual temperature reduction (annealing) is applied, the computation yields the maximum a posteriori (MAP) estimate for the given image processing problem. This model provides excellent results but the computations required for the estimation are too heavy on sequential computers for any practical interest. We propose stochastic optoelectronic integrated circuits (stochastic artificial retinas) able to perform MAP estimates at video-rate. In our approach, thermal motion is implemented through noisy photocurrent sources created by speckle. The annealing is provided by a reduction of the average intensity of the speckle and the MAP estimation is performed by a stochastic gradient descent in the energy landscape.