中文摘要：

基于Tibshirani等人的间隙统计思想，构造了图像灰度间隙统计，并应用Dempster-shafet（DS）证据理论融合多尺度间隙统计信息，实现图像边缘检测，有效地解决了抑制噪声与边缘定位的两难问题。本文算法在融合过程中引入检测不确定性，根据间隙统计响应与检测阈值的关系设计基本可信度分配函数（BPAF），使得检测不确定性在阈值处达到最大值。利用DS合成规则融合各尺度间隙统计的BPAF，根据合成后的联合可信度分配函数将像素分成边缘与非边缘。通过检测结果比较及分析表明，本文算法能够有效降低边缘检测不确定性，性能优于传统边缘检测方法。

英文摘要：

To solve the conflict between image denoising and edge localization,a novel edge detection algorithm based on multiscale gap statistic information fusion through DS evidence theory was proposed. Gap statistic of gray-scale image was defined. Detection uncertainty was introduced in fusion procession. Mass functions （or basic probability assignment functions） were designed based on the relationship between Gap statistic response and detection threshold. Detection uncertainty reaches maximum value at the detection threshold. And mass functions corresponding to each Gap statistic at different scales were combined by Dempster＇s combination rule. Pixels were classified into edge or off-edge according to the joint mass function. Tex experimental results show that this proposed method is effective in reducing detection uncertainty and better than classical edge detectors.