A fast computational approach for illusory contour reconstruction

Abstract

Illusory contour reconstruction can be modeled as a minimization problem with a tractable variational level set formulation, utilizing Euler’s elastica to reconstruct the illusory boundaries. However, this kind of formulation is very difficult to solve numerically as it is hard to implement such optimization algorithms efficiently in practice. In this paper, we propose an equivalently reduced variational level set formulation by taking the level set functions as signed distance functions. Technically, an alternating direction method of multipliers (ADMM) is developed by introducing some auxiliary variables, Lagrange multipliers and applying an alternating optimization strategy. With the proposed ADMM method, the minimization problem can be transformed into a series of sub-problems, which can be solved easily via using the Gauss-Seidel iterations and Fast Fourier Transform (FFT). The corresponding level set functions are regarded as signed distance functions during computation process using a simple algebraic projection method, which avoids the traditional re-initialization process for conventional level set functions. Extensive experiments have been conducted on both synthetic and real images, which validated the proposed approach, and demonstrated the advantages of the proposed ADMM-Projection (ADMM-P) method over the existing algorithms based on traditional gradient descent method (GDM) in terms of computational efficiency.