Colour image segmentation based on a convex K‐means approach

Abstract

Image segmentation is a fundamental and challenging task in image processing and computer vision. The colour image segmentation is attracting more attention as the colour image provides more information than the grey image. A variational model based on a convex K-means approach to segment colour images is proposed. The proposed variational method uses a combination of l 1 and l 2 regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our one-stage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, the colour set which can be determined by human or the K-means method is specified. Second, a variational model to obtain the most appropriate colour for each pixel from the colour set via convex relaxation and lifting is used. The Chambolle-Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of the method. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Multi-phase image segmentation by the Allen--Cahn Chan--Vese model

“…Except for the image "flowers", the SLaT model finishes the segmentation in the least time among all models. For the image of white blood cells, the segmentation shows double edges around the cell membrane of the red blood cell due to [36], SLaT [5], ICTM [30], CKA [34], and our ACCV model. the low resolution.…”

“…In view of stability, the discrete maximum bound principle holds for variables U 1 and U 2 . The energy evolution of the two temporal discretizations sketched in (ICTM) [30], and convex K-means approach (CKA) [34]. 4-phase and 6-phase image segmentations will be tested in Figure 4.5.…”

An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation

“…For these real images, we employ the dimension lifting technique to extract more information, which is first proposed in the SLaT model [7] and drawn on by many other models [7,36]. The dimension lifting in this paper is to add the color information of the CIELAB color space [21,27] to the RGB images to reflect the color information in a more comprehensive way.…”

“…The initial contour significantly affects segmentation results since most of the energy functionals in the region-based active contour models are non-convex. A feasible solution for this initialization issue is to relax the energy functional into a convex functional [3,4,5,6,8,11,29,36]. However, convex relaxation deprives all the non-convex parts of the original energy functional, and hence may entail the loss of non-convex information of the segments and reduce models' capability of preserving the sharpness and neatness of edges [10,39].…”

“…Acknowledgments. We thank Prof. Tieyong Zeng at The Chinese University of Hong Kong for providing the MATLAB codes of [8] and thank Prof. Tingting Wu at Nanjing University of Posts and Telecommunications for providing the MATLAB codes of [36].…”