A phase-field image segmentation for topological texture image

The topological texture image, as a branch of texture image, contains many serpentine curves, regular or irregular geometric shapes, symmetrical or unsymmetrical patterns. All kinds of jacquard patterns in textile CAD, tissue textures in medical images, and ancient mural images belong to the research objects of topological texture image. For a topological image consists of many complex patterns which contain detailed, intricate topological curves, most of existing image segmentation algorithms have difficulty in capturing complex structure of visual features, such as complex contours of a topological pattern. In this paper, a phase-field model for topological image segmentation, based on a generalized variational formulation of the phase-field functional is proposed, which is capable of handling changes in the topology of the evolving contour. Two Euler-Lagrange equations are firstly derived for optimizing the model and presenting their efficient implementation by using a conjugate gradient scheme. Then, considering the important role of a discrete finite element approximation for phase field model, a mesh adjustment procedure is deployed with finite elements in space and time. The proposed method has been evaluated on real topological images and the obtained results have shown the desirable segmentation performance.