reconstruct {bayess}

Image reconstruction for the Potts model with six classes

Description

This function adresses the reconstruction of an image distributed from a Potts model based on a noisy version of this image. The purpose of image segmentation (Chapter 8) is to cluster pixels into homogeneous classes without supervision or preliminary definition of those classes, based only on the spatial coherence of the structure. The underlying algorithm is an hybrid Gibbs sampler.

Usage

reconstruct(niter, y)

Arguments

niter

number of Gibbs iterations

y

blurred image defined as a matrix

Details

Using a Potts model on the true image, and uniform priors on the genuine parameters of the model, the hybrid Gibbs sampler generates the image pixels and the other parameters one at a time, the hybrid stage being due to the Potts model parameter, since it implies using a numerical integration via integrate. The code includes (or rather excludes!) the numerical integration via the vector dali, which contains the values of the integration over a 21 point grid, since this numerical integration is extremely time-consuming.

Value

beta

MCMC chain for the parameter \beta of the Potts model

mu

MCMC chain for the mean parameter of the blurring model

sigma

MCMC chain for the variance parameter of the blurring model

xcum

frequencies of simulated colours at every pixel of the image

See Also

Menteith

Examples

## Not run: data(Menteith)
lm3=as.matrix(Menteith)
#warning, this step is a bit lengthy
titus=reconstruct(20,lm3)
#allocation function
affect=function(u) order(u)[6]
#
aff=apply(titus$xcum,1,affect)
aff=t(matrix(aff,100,100))
par(mfrow=c(2,1))
image(1:100,1:100,lm3,col=gray(256:1/256),xlab="",ylab="")
image(1:100,1:100,aff,col=gray(6:1/6),xlab="",ylab="")

## End(Not run)