Refereed full papers (journals, book chapters, international conferences)

1984

@article{GeG1984,
	vgclass =	{refpap},
	author =	{Stuart Geman and Donald Geman},
	title =	{Stochastic relaxation, {G}ibbs distributions, and the
	{B}ayesian restoration of images},
	journal =	{IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume =	{6},
	number =	{6},
	pages =	{721--741},
	year =	{1984},
	url =	{http://www.dam.brown.edu/people/geman/Papers/stochastic%20relaxation.pdf},
	abstract =	{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, non-linear 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 \emph{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.},
}