Variational models with elastica energies: a comparison, a new model and new algorithms

Abstract

This work comprises two parts. In the first part, we propose novel ALM based algorithms for the ECV-L1 and ECV-L2 segmentation models in order to compare their performance. By imposing one extra constraint, we develop novel augmented Lagrangian functionals that ensure the segmentation level set function to be signed distance func- tions, which avoids the reinitialization of segmentation function during the iterative process. With the proposed algorithm and with the same initial contours, we compare the performance of these two high-order segmentation models and numerically verify the different properties of the two models. Following our previous work, in the second part, we propose a new denoising model with L1 Elastica as the regularizer with corner preserving property. We develop a novel ADMM based algorithm with every subproblem being solved in a closed form. The numerical results on synthetic and real-life images verify the theoretical analysis and show that the model outperforms ROF in preserving contrast. They also show that the new algorithm has fast convergence rate.