Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.

We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

Computer simulation of brainstem respiratory activity.

A mathematical model of the medullary respiratory oscillator, composed of two mutually inhibiting populations (inspiratory and expiratory) of computer-simulated neurons, is presented. Each population consists of randomly interconnected subpopulations of excitatory and inhibitory neurons, is presented. Each population consists of randomly interconnected subpopulations of excitatory and inhibitory neurons. Neuronal coupling is such that either the inspiratory or expiratory population alone is capable of cyclic activity. Weak inhibitory connections between inspiratory and expiratory populations provide satisfactory reciprocating activity independent of the natural frequency of either population alone. Initiation and persistence of rhythmic activity is dependent on a diffused noncyclic excitatory input. Vagal discharge, simulated by phasic inhibition of inspiratory neurons, results in increased respiratory frequency with decreased inspiratory activity. In the absence of simulated vagal discharge, uniform facilitation of synaptic connections increases averaged activities of inspiratory and expiratory populations, with minor effect on frequency. In the presence of simulated vagal discharge, facilitation of synaptic connections increases both frequency and amplitude. The simulated effects of synaptic facilitation, with and without vagal discharge, mimic the physiological response to CO2 in the intact and vagotimized animal.