Image segmentation is a critical step in image processing. Several algorithms based on statistics have been proposed

in which the statistical image model must be built under a certain assumption on the image. For example

the commonly used statistical model on pixel intensities includes normal distribution and gamma distribution (especially for SAR intensities image). Although optimal segmentation results could be obtained through most algorithms

statistical models are an approximation of pixel intensities and could not accurately describe the characteristics. Moreover

building an accurate image model

especially for remote sensing images

is difficult because of the complexity and uncertainty of spectral characteristics of objects on the earth's surface. Kolmogorov-Smimov statistic (K-S distance) defines the similarity by measuring the maximum distance of two statistical distributions. In this case

building a statistical model for an image is not necessary. By contrast

grayscale histogram could be used to describe the distribution of two classes for image segmentation tasks. K-S distance solves the difficulty in building an accurate statistic distribution model for an image. To date

K-S distance image processing is based only on pixel scale. Given that histogram is not sensitive when only a pixel changes its class

K-S distance based segmentation could not be used. In this paper

region and K-S distance based image segmentation was proposed. Voronoi tessellation was used to partition image domain into sub-regions (Voronoi polygons) corresponding to the components of homogenous regions. Each Voronoi polygon was assigned a random variable as label to indicate the homogenous region to which it belongs. All labels for the Voronoi polygons formed a label field. The intensity histogram of each homogenous region was then calculated

and the dissimilarity between two homogenous regions was determined by the K-S distance on the two histograms corresponding to the two regions. Thereafter

the potential energy function of the dissimilarity was constructed. Employing Bayesian inference

a posterior distribution was obtained using the likelihood constructed by non-constrained Gibbs expression. Finally

Metropolis-Hastings (M-H) scheme included updating labels

moving generation points

and birth and death generation points operations designed to simulate the posterior. The optimal segmentation was obtained by Maximum A Posterior (MAP) estimation. Using the proposed algorithm

segmentation was performed on simulated and synthesized images

as well as real optical and SAR images. Qualitative and quantitative accuracy evaluations were carried out to assess the effectiveness of the proposed algorithm. In addition

results from both proposed algorithm and pixel and statistic based segmentation algorithm are compared and show that the proposed algorithm performed significantly better. The analysis on the regionalized image segmentation algorithm based on K-S statistics does not need to build an image model and could be viewed as regional based algorithm to avoid the effect of image noise during segmentation. To improve the accuracy of fitting homogeneous regions with partitioned sub-regions

different geometry tessellation methods must be considered to partition the image domain. Furthermore

the proposed methodology will be developed for image segmentation with variable classes.