To solve the blurred image edge segmentation problem and the influence of a complex background on the segmentation accuracy of the clustering algorithm, this paper proposes an edge gravity mean shift (EGMS) image segmentation algorithm. Aiming at the problem of partial edge information loss when the Canny algorithm processes images, the L0 gradient minimization method is introduced to iteratively optimize the gradient map to extract more edge information, and then the L0 Canny edge detection algorithm is proposed. Aiming at the problem that the Epanechnikov mean shift algorithm will converge to the local optimum due to the non-smooth Epanechnikov kernel function, the optimal bandwidth is obtained, and the smoothness of the kernel function shape is improved by cross-validation and spline function. Then, the sleek Epanechnikov kernel function is constructed by integrating the weight function, which can reflect the richness of clustering information at the peak so that the kernel function can more accurately reflect the data characteristics of the peak. Based on the sleek Epanechnikov kernel function, the sleek Epanechnikov mean shift (SEMS) clustering algorithm is proposed. The EGMS image segmentation algorithm is constructed by fusing the L0 Canny and SEMS. The experimental results indicate that EGMS can retain more edge contour information when segmenting images, and it can generate better clustering clusters for clustered datasets. In addition, compared to other clustering segmentation algorithms, the proposed EGMS algorithm demonstrates superior clustering accuracy and convergence on the majority of image datasets. Our code is available at: https://gitee.com/zhiweilu111/edge-gravity-mean-shift.