Segmentation Model Of Illusion Contour Image And Its Fast Algorithm

Illusory contour capture is the challenging problem of obtaining three-dimensional information from a single two-dimensional image to reconstruct the missing boundaries or fuzzy areas and get the order of the relationship between the different regions in images. Image Segmentation with depth information can be modeled as a minimization problem with Nitzberg-Mumford-Shiota(NMS) functional, which can be transformed into a tractable variational level set formulation(VLSF). However, it leads to a series of complicated high order nonlinear partial differential equations(PDEs) which are difficult to solve computationally. In this paper, we first propose an equivalent reduced VLSF without curvatures by taking advantage of property of level set functions(LSFs) as signed distance functions(SDFs). Then an alternating direction method of multipliers(ADMM)based on this reduced VLSF is designed by introducing some auxiliary variables,Lagrange multipliers and using alternating optimization strategy. With the proposed ADMM method, the minimization of the reduced VLSF is transformed into a series of sub-problems, which can be solved easily via Gauss-Seidel iterations, Fast Fourier Transform(FFT) method, soft threshold formulas. The LSFs are kept as SDFs during computation process via simple algebraic projection method, which avoids the traditional re-initialization process for variational level set methods. Experimental results on both synthetic and real images validate the proposed reduced VLSF, and show advantages of the proposed ADMM-Projection over algorithms based on traditional gradient descent method in terms of computational efficiency.