Minimum distance estimation methodology based on an empirical distribution function has been popular due to its desirable properties including robustness. Even though the statistical literature is awash with the research on the minimum distance estimation, the most of it is confined to the theoretical findings: only few statisticians conducted research on the application of the method to real world problems. Through this paper, we extend the domain of application of this methodology to various applied fields by providing a solution to a rather challenging and complicated computational problem. The problem this paper tackles is an image segmentation which has been used in various fields. We propose a novel method based on the classical minimum distance estimation theory to solve the image segmentation problem. The performance of the proposed method is then further elevated by integrating it with the ``segmenting-together" strategy. We demonstrate that the proposed method combined with the segmenting-together strategy successfully completes the segmentation problem when it is applied to the complex, real images such as magnetic resonance images.
翻译:根据经验分布函数的最小距离估计方法由于其良好的性质,包括强健性,因此在统计文献中非常流行。尽管统计文献中有许多关于最小距离估计的研究,但其中大部分都局限于理论发现:只有少数统计学家对该方法在实际问题中的应用进行了研究。通过本文,我们通过提供解决一个相当具有挑战性和复杂的计算问题的方法,扩展了该方法论到各种应用领域中的应用。本文所解决的问题是图像分割,这在各个领域中都有应用。我们提出了一种基于经典最小距离估计理论的新方法来解决图像分割问题。然后,通过将它与“一起分割”策略相结合,进一步提高了所提出方法的性能。我们证明了,当将该方法应用于复杂的实际图像(如磁共振图像)时,与“一起分割”策略相结合的所提出方法可以成功地完成分割问题。