YANG Wenting, WANG Xiaopeng, FANG Chao
（School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China）
Abstract： Classical mathematical morphology operations use a fixed size and shape structuring element to process the whole image. Due to the diversity of image content and the complexity of target structure, for processed image, its shape may be changed and part of the information may be lost. Therefore, we propose a method for constructing salience adaptive morphological structuring elements based on minimum spanning tree (MST). First, the gradient image of the input image is calculated, the edge image is obtained by non-maximum suppression (NMS) of the gradient image, and then chamfer distance transformation is performed on the edge image to obtain a salience map (SM).Second, the radius of structuring element is determined by calculating the maximum and minimum values of SM and then the minimum spanning tree is calculated on the SM. Finally, the radius is used to construct a structuring element whose shape and size adaptively change with the local features of the input image. In addition, the basic morphological operators such as erosion, dilation, opening and closing are redefined using the adaptive structuring elements and then compared with the classical morphological operators. The simulation results show that the proposed method can make full use of the local features of the image and has better processing results in image structure preservation and image filtering.
Key words： adaptive structuring element； mathematical morphology； salience map (SM)； minimum spanning tree (MST)
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基于最小生成树的显著性自适应形态学
结构元素构造方法 杨文婷， 王小鹏， 房超
（兰州交通大学 电子与信息工程学院， 甘肃 兰州 730070）
摘要：经典数学形态学运算采用固定大小和形状的结构元素处理整幅图像， 由于图像内容的多样性以及目标结构的复杂性， 容易导致处理后的图像形状发生改变且丢失部分信息。 为此， 提出了一种基于最小生成树(Minimum spanning tree, MST)的显著性自适应形态学结构元素构造方法。 首先， 计算图像梯度， 通过非极大值抑制（Non-maximum suppression, NMS）得到边缘图像， 对边缘图像进行倒角距离变换， 得到显著性图（Salience map， SM）。 然后， 通过计算SM的极大极小值确定结构元素半径， 并在SM上计算MST。 最后， 利用计算得到的半径构造出一种形状和大小随输入图像局部特征自适应变化的结构元素。 利用该自适应结构元素对腐蚀、 膨胀、 开和闭等基本形态学算子进行了重新定义， 并且与经典形态学算子做了仿真对比。 结果表明， 该方法能够充分利用图像的局部特征， 在图像结构保持以及图像滤波等方面都具有较好的处理结果。
关键词：自适应结构元素； 数学形态学； 显著性图； 最小生成树
引用格式： YANG Wenting， WANG Xiaopeng， FANG Chao. Salience adaptive morphological structure element construction method based on minimum spanning tree. Journal of Measurement Science and Instrumentation, 2021, 12（1）： 36-43. DOI： 10．3969／j．issn．1674-8042．2021．01．005
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