A 3-D Contextual Classifier

In this paper we will consider an extension of the Bayesian 2-D contextual class ification routine developed by Owen, Hjort \$\backslash\$& Mohn to 3 spatial dimensions. It is evident that compared to classical pixelwise classification further information can be obtained by tak ing into account the spatial structure of image data, i.e.\$\backslash\$ neighbouring pixels tend to be of the same class. The algorithm developed by Owen, Hjort \$\backslash\$& Mohn consists of basing the classifi cation of a pixel on the simultaneous distribution of the values of a pixel and its four nearest n eighbours. This includes the specification of a Gaussian distribution for the pixel values as well as a prior distribution for the configuration of class variables within the cross that is m ade of a pixel and its four nearest neighbours. We will extend this algorithm to 3-D, i.e. we will specify a simultaneous Gaussian distr ibution for a pixel and its 6 nearest 3-D neighbours, and generalise the class variable configuration distribution within the 3-D cross. The algorithm is tested on a synthetic 3-D multivariate dataset.