基于测地轮廓和特征函数的灰度异质图像分割

Image Segmentation with Intensity Inhomogeneity Based on Geodesic Contour and Characteristic Function

灰度异质图像的分割是图像处理中一项非常有挑战性的任务。CVB模型虽然能较好分割灰度异质图像,但是其分割结果容易出现过度分割或欠分割问题。为了精确分割灰度异质图像,该文在CVB模型的基础上,引入基于测地轮廓的长度项来捕捉目标物体的边缘信息,提出一种新的变分分割模型。同时,为了提高计算效率,该文利用特征函数来表示测地轮廓长度,并且通过基于特征函数的热核卷积形式逼近测地轮廓的周长。进一步,结合交替极小化和迭代卷积阈值法,该文设计出一种快速数值求解算法,并且给出了该算法的收敛性和稳定性分析。最后,对合成图像、核磁共振图像以及魏茨曼分割数据集上的原始自然图像等三类灰度不均匀图像进行分割实验,并且采用Dice相似系数和Hausdorff距离作为图像分割的评价指标,实验结果表明:该方法不仅提高了图像分割精度,而且明显提升了收敛速度。

Image segmentation with intensity inhomogeneity is a quite challenging task in image processing.CVB model can be used to segment images with intensity inhomogeneity well,but its segmentation results are prone to over-segmentation or under-segmentation.In order to accurately segment images with intensity inhomogeneity,based on the CVB model,a new variational segmentation model is proposed to capture the edge information of the object by introducing geodesic contour length term.At the same time,for improving the computational efficiency,we use a characteristic function to represent the geodesic contour length,where the perimeter of geodesic contour is approximated by a heat kernel convolution with the characteristic function.Furthermore,combining the alternating minimization and iterative convolution thresholding method,we design a fast numerical solution algorithm,and the convergence and stability of the algorithm are proved.Finally,segmentation experiments are performed on three kinds of images with intensity inhomogeneity,including synthetic images,magnetic resonance(MR)images and original natural images of Weizmann segmentation dataset.Dice similarity coefficient and Hausdorff distance are used as evaluation indicators of image segmentation.The experimental results show that the proposed method not only improves the segmentation accuracy,but also accelerates the convergence speed significantly.