一种测地线活动轮廓模型的快速算法*

为了完成测地线活动轮廓模型在图像分割中的平滑预处理和图像梯度的计算，给出水平集方法以实现中符号距离函数的构造。通过对Gaussian函数以及差分运算的讨论，提出了一种基于Sobel算子图像预处理方法，并利用同心圆扩散方法计算符号距离。得出将图像平滑与梯度计算结合为Sobel算子的处理，一种计算符号距离函数的快速计算方法。通过实验比较，Sobel算子既可以完成平滑处理，又降低了差分计算梯度的时间复杂度，而同心圆扩散方法能够提高模型算法的执行效率。

Fast algorithm of geodesic active contour

To smooth the image and calculate the gradient of image in the process of using GAC Model in image segmentation,and to construct the signed distance function in level set method.By discussing the calculation process of Gaussian function and difference approximation,a new pre-process method of GAC based on Sobel operator was presented.Then by expending of circle,the paper presented a method to calculate the signed distance.The operator proposed could smooth the image and calculate the gradient simultaneously and the method could calculate the distance quickly.The results of experimental comparison show that the algorithm proposed both enhanced smooth effect and reduced the time complexity in completing the GAC.