A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Curvature minimization for surface reconstruction with features
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Image Segmentation Using Euler's Elastica as the Regularization
Journal of Scientific Computing
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Minimization of total variation (TV) is a well-known method for image denoising. Recently, the relationship between TV minimization problems and binary MRF models has been much explored. This has resulted in some very efficient combinatorial optimization algorithms for the TV minimization problem in the discrete setting via graph cuts. To overcome limitations, such as staircasing effects, of the relatively simple TV model, variational models based upon higher order derivatives have been proposed. The Euler's elastica model is one such higher order model of central importance, which minimizes the curvature of all level lines in the image. Traditional numerical methods for minimizing the energy in such higher order models are complicated and computationally complex. In this paper, we will present an efficient minimization algorithm based upon graph cuts for minimizing the energy in the Euler's elastica model, by simplifying the problem to that of solving a sequence of easy graph representable problems. This sequence has connections to the gradient flow of the energy function, and converges to a minimum point. The numerical experiments show that our new approach is more effective in maintaining smooth visual results while preserving sharp features better than TV models.