Abstract: For optimizing two crucial time-consuming processes in bidimensional local mean decomposition (BLMD): adaptive window-based search method and terminal criterion, this paper proposes two schemes, and then puts forward a new image edge detection algorithm based on this optimized bidimensional local mean decomposition. Delaunay triangulation is employed to get an ideal triangular mesh, then the local adjacent extrema and the moving average window size can be achieved from the mesh. Also, this paper presents a new convergence condition of iteration. Experiments on the synthetic and real images prove that these optimizations can make BLMD be much faster and have an identical or even better performance. Histogram equalization and binarization are applied to the first PF for achieving raw edge, then the disjoint or unconnected and undesired edges can be removed from binary image by a removal operation controlled by a threshold parameter, finally morphological thinning or skeleton operation is applied to get the final single-pixel width edge image. The proposed method is compared with several standard edge detection techniques, the experimental results show that the proposed method can successfully generate the desired edge map and has a better performance. In addition, benefitting from BLMD, the proposed method can relieve false edges produced by illumination and the final edge image is more consistent with the human visual inspection.

Key words: edge detection, bidimensional local mean decomposition, multiscale image analysis, Delaunay triangulation, skeleton

摘要： 针对二维局部均值分解（bidimensional local mean decomposition，BLMD）中影响算法速度的两个主要因素：自适应搜索窗口和迭代终止条件，提出了优化方法，并在其基础上提出了一种边缘检测算法。该算法采用Delaunay三角剖分得到局部极值点的理想规则化的三角网格，通过网格划分确定相邻极值点及滑动平均窗口的大小，并提出了一种新的BLMD算法迭代收敛条件，通过对人工合成图像以及自然图像的实验，证实了该优化算法与原算法结果非常接近甚至更优，且大幅度提高了计算速度。对BLMD得到的最高频分量进行直方图均衡，将其结果二值化，通过设定阈值剔除其中不连续的细小边缘，通过形态学将其骨骼化，得到最终提取的边缘。与几种典型边缘检测算子的比较实验表明，新算法可以较好地检测出图像边缘，相对于其他边缘检测算子，对于图像中的纹理等细节边缘有着更佳的检测效果；并且得益于BLMD图像多尺度分析的优势，较好地避免了因光照明暗等低频因素产生的假边缘，提取出的边缘更符合视觉上的主观检测。

关键词: 边缘检测, 二维局部均值分解, 多尺度图像分析, Delaunay三角剖分, 骨骼化