Abstract
As a fundamental tool, L 0 gradient smoothing has found a flurry of applications. Inspired by the progress of research on hyper-Laplacian prior, we propose a novel model, corresponding to L p-norm of gradients, for image smoothing, which can better maintain the general structure, whereas diminishing insignificant texture and impulse noise-like highlights. Algorithmically, we use augmented Lagrangian method (ALM) to efficiently solve the optimization problem. Thanks to the fast convergence rate of ALM, the speed of the proposed method is much faster than the L 0 gradient method. We apply the proposed method to natural image smoothing, cartoon artifacts removal, and tongue image segmentation, and the experimental results validate the performance of the proposed algorithm.
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References
Park, J.M., Murphey, Y.L.: Edge detection in grayscale, color, and range images. Wiley Encyclopedia of Computer Science and Engineering (2008)
Carreira, J., Sminchisescu, C.: Constrained parametric min-cuts for automatic objects egmentation. In: IEEE Conference on Computer Vision and Pattern Recognition(CVPR), pp. 3241–3248 (2010)
Durand, F., Dorsey, J.: Fast bilateral filtering for the display of high-dynamic-rangeimages. ACM Transactions on Graphics (TOG) 21, 257–266 (2002)
Farbman, Z., Fattal, R., Lischinski, D., Szeliski, R.: Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Transactions on Graphics (TOG)Â 27, 67 (2008)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1), 259–268 (1992)
Xu, L., Lu, C., Xu, Y., Jia, J.: Image smoothing via L0 gradient minimization. ACM Transactions on Graphics (TOG)Â 30(6), 174 (2011)
Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-laplacian priors. NIPS 22, 1–9 (2009)
Field, D.J.: What is the goal of sensory coding? Neural Computation 6(4), 559–601 (1994)
Levin, A., Fergus, R., Durand, F., Freeman, W.T.: Image and depth from a conventionalcamera with a coded aperture. ACM Transactions on Graphics (TOG)Â 26(3), 70 (2007)
Simoncelli, E.P., Adelson, E.H.: Noise removal via bayesian wavelet coring. In: International Conference on Image Processing, vol. 1, pp. 379–382 (1996)
Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: IEEE international conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3869–3872 (2008)
Cho, T.S., Joshi, N., Zitnick, C.L., Kang, S.B., Szeliski, R., Freeman, W.T.: A content-aware image prior. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 169–176 (2010)
Candes, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted l1 minimization. Journal of Fourier Analysis and Applications 14(5-6), 877–905 (2008)
Zuo, W., Meng, D., Zhang, L., Feng, X., Zhang, D.: A generalized iterated shrinkage algorithm for non-convex sparse coding. In: IEEE International Conference on Computer Vision (ICCV) (2013)
She, Y.: An iterative algorithm for fitting non-convex penalized generalized linear models with grouped predictors. Computational Statistics & Data Analysis 56(10), 2976–2990 (2012)
Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low-rank representation. NIPSÂ 2, 6 (2011)
Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. Image Processing 7(3), 359–369 (1998)
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Chen, L., Zhang, H., Ren, D., Zhang, D., Zuo, W. (2014). Fast Augmented Lagrangian Method for Image Smoothing with Hyper-Laplacian Gradient Prior. In: Li, S., Liu, C., Wang, Y. (eds) Pattern Recognition. CCPR 2014. Communications in Computer and Information Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45643-9_2
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DOI: https://doi.org/10.1007/978-3-662-45643-9_2
Publisher Name: Springer, Berlin, Heidelberg
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