Fast segmentation using level set curves of complex wavelet surfaces

Active contour methods are a powerful approach to image segmentation. The first approaches were based on the direct evolution of a contour but recently level set methods have been found to give more robust solutions. These methods are based on the iterative deformation of a surface and their main drawback is the large number of iterations required. We propose a new energy formulation for which it is possible to obtain a good estimate for the optimum step size in a gradient descent algorithm and which therefore produces much faster convergence. This is made possible by representing the surface with the coefficients of a complex wavelet transform. The energy function has one term that is minimised for smooth contours, and one term that is minimised for contours close to edges in an image. We explain how the complex wavelet transform can efficiently represent both these terms and show experimental results on real and synthetic images confirming that the method gives good results within a few iterations.