Fast algorithms for p-elastica energy with the application to image inpainting and curve reconstruction

Authors:
Jooyoung Hahn;Ginmo J. Chung;Yu Wang;Xue-Cheng Tai
Affiliations:
Institute for Mathematics and Scientific Computing, University of Graz, Austria;Division of Mathematical Sciences, School of Physical Mathematical Sciences, Nanyang Technological University, Singapore;Division of Mathematical Sciences, School of Physical Mathematical Sciences, Nanyang Technological University, Singapore;Division of Mathematical Sciences, School of Physical Mathematical Sciences, Nanyang Technological University, Singapore
Venue:
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Year:
2011

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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.