1 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
In this paper we will consider extensions of a series of Bayesian 2-D contextual classification pocedures proposed by Owen (1984) Hjort & Mohn (1984) and Welch & Salter (1971) and Haslett (1985) to 3 spatial dimensions. It is evident that compared to classical pixelwise classification further information can be obtained by taking into account the spatial structure of image data. The 2-D algorithms mentioned above consist of basing the classification of a pixel on the simultaneous distribution of the values of a pixel and its four nearest neighbours. 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 made of a pixel and its four nearest neighbours. We will extend these algorithms to 3-D, i.e. we will specify a simultaneous Gaussian distribution for a pixel and its 6 nearest 3-D neighbours, and generalise the class variable configuration distributions within the 3-D cross given in 2-D algorithms. The new 3-D algorithms are tested on a synthetic 3-D multivariate dataset.