汲取Hastie和Tibshiran i等人提出的“Gap statistic”的思想方法,利用样本灰度数据分布的差别定义多尺度的图像灰度间隙,在提出反分布函数概念的基础上,建立了图像边缘检测的多尺度灰度Gap统计模型。通过分析分布间隙和灰度间隙的一致性,优化了Gap统计模型的边缘检测算法。分析不同尺度下的检测结果,并比较了灰度Gap统计模型与Prew itt和Sobel边缘算子之间的相互关系。通过实例与分析,证明了该模型具有抗噪声、多尺度的特点。

On the basis of the gray-level distribution in the relative half-neighborhood of image pixels,refering to the method called "Gap statistic" proposed by Hastie and Tibshirani,a concept called inverse distribution function is brought forward,and a multi-scale edge detection model based on Gap of random variable was established.By analyzing consistency between a grayscale distribution Gap and random variable Gap,the edge detection algorithm for Gap statistic model is optimized.The paper analyzes the correlation between the Gap statistic model and two operators(Prewitt operator and Sobel operator),discusses the anti-noise and multi-scale properties of the edge detection model,and an investigation is made to analyze the difference of edge detection at different scales.Finally,experimental examples verify the capacity of the model.