利用Kolmogorov-Smirnov统计的区域化图像分割

目的 为了在未知或无法建立图像模型的情况下,实现统计图像分割,提出一种结合Voronoi几何划分、K-S(Kolmogorov-Smirnov)统计以及M-H(Metropolis-Hastings)算法的图像分割方法.方法 首先利用Voronoi划分将图像域划分成不同的子区域,而每个子区域为待分割同质区域的一个组成部分,并利用K-S统计定义类属异质性势能函数,然后应用非约束吉布斯表达式构建概率分布函数,最后采用M-H算法进行采样,从而实现图像分割.结果 采用本文算法,分别对模拟图像、合成图像、真实光学和SAR图像进行分割实验,针对模拟图像和合成图像,分割结果精度均达到98%以上,取得较好的分割结果.结论 提出基于区域的图像分割算法,由于该算法中图像分割模型的建立无需原先假设同质区域内像素光谱测度的概率分布,因此提出算法具有广泛的适用性.为未知或无法建立图像模型的统计图像分割提供了一种新思路.

Regionalized image segmentation using Kolmogorov-Smirnov statistics

Objective 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.Method 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.Result 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.Conclusion 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.