Abstract: Mathematical morphological operations for binary images are of broad application areas. Unfortunately, when large binary images and large structural elements are involved, the computational speed of the morphological operations decreases. An improved morphological dilation algorithm is proposed for large structural elements consisting of a single connected component and whose reference point being a member of the structural element. The contours of the binary image to be dilated are extracted, and are dilated using the structural element. The dilated contours are then combined with the original binary image through binary OR operation to give the final dilation result. The equivalence of the standard dilation and the improved algorithm is proved. Morphological erosion operation is improved to utilize the duality between erosion and dilation, and morphological opening and closing are accelerated using the improved erosion and dilation. Standard operations and improved ones are compared on an image base consisting of 80 high resolution binary images of plant leaves. The experimental results show that the improved algorithms can significantly promote the execution speed of the morphological operations.

Key words: mathematical morphology, binary images, large structural element, MATLAB

摘要： 二值图像的数学形态学方法应用广泛，但当涉及的图像和结构元素较大时，操作速度变慢。针对结构元素参考点包括在结构元素中且为单一连通区域的大结构元素，提出了二值形态学膨胀操作的改进算法，首先提取待膨胀二值区域的轮廓，然后对轮廓进行膨胀，再将膨胀结果与原二值区域取并集得到总的膨胀结果；证明了改进膨胀算法与标准膨胀操作的等价性；基于膨胀与腐蚀操作的对偶关系给出了改进的腐蚀算法；给出了改进的开、闭运算算法。在80张高分辨率植物叶片二值图像上进行了腐蚀、膨胀、开运算和闭运算标准方法和改进算法的对比实验，结果表明改进算法可显著提高二值形态学处理的速度。

关键词: 数学形态学, 二值图像, 大结构元素, MATLAB