Fast Algorithms for p-elastica Energy with the Application to Image Inpainting and Curve Reconstruction

Jooyoung Hahn, Ginmo Jason Chung, Yu Wang, Xue-Cheng Tai

Abstract: In this paper, we propose fast and efficient algorithms for p-elastica energy (p = 1 or 2). Inspired by the recent algorithm for Euler’s elastica models in [16], the algorithm is extended to solve the problem related to p-elastica energy based on augmented Lagrangian method. The proposed algorithms are as efficient as the previous method in terms of low computational cost per iteration. We provide an algorithm which replaces fast Fourier transform (FFT) by a cheap arithmetic operation at each grid point. Numerical tests on image inpainting are provided to demonstrate the efficiency of the proposed algorithms. We also show examples of using the proposed algorithms in curve reconstruction from unorganized data set.