Single Image Super-resolution With Detail Enhancement Based on Local Fractal Analysis of Gradient

In this paper, we propose a single image super-resolution and enhancement algorithm using local fractal analysis. If we treat the pixels of a natural image as a fractal set, the image gradient can then be regarded as a measure of the fractal set. According to the scale invariance (a special case of bi-Lipschitz invariance) feature of fractal dimension, we will be able to estimate the gradient of a high-resolution image from that of a low-resolution one. Moreover, the high-resolution image can be further enhanced by preserving the local fractal length of gradient during the up-sampling process. We show that a regularization term based on the scale invariance of fractal dimension and length can be effective in recovering details of the high-resolution image. Analysis is provided on the relation and difference among the proposed approach and some other state of the art interpolation methods. Experimental results show that the proposed method has superior super-resolution and enhancement results as compared to other competitors.

[1]  Maneesh Agrawala,et al.  Multiscale shape and detail enhancement from multi-light image collections , 2007, SIGGRAPH 2007.

[2]  Rob Fergus,et al.  Blind deconvolution using a normalized sparsity measure , 2011, CVPR 2011.

[3]  Michal Irani,et al.  Super-resolution from a single image , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[4]  Mehran Ebrahimi,et al.  Solving the Inverse Problem of Image Zooming Using "Self-Examples" , 2007, ICIAR.

[5]  Stanley Osher,et al.  Image Super-Resolution by TV-Regularization and Bregman Iteration , 2008, J. Sci. Comput..

[6]  Raanan Fattal,et al.  Image upsampling via imposed edge statistics , 2007, ACM Trans. Graph..

[7]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[8]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[9]  Kwang In Kim,et al.  Single-Image Super-Resolution Using Sparse Regression and Natural Image Prior , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Yong Xu,et al.  Viewpoint Invariant Texture Description Using Fractal Analysis , 2009, International Journal of Computer Vision.

[11]  Yong Xu,et al.  A Projective Invariant for Textures , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[12]  Stephen Lin,et al.  Super resolution using edge prior and single image detail synthesis , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  Yong Xu,et al.  A new texture descriptor using multifractal analysis in multi-orientation wavelet pyramid , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  H Stark,et al.  High-resolution image recovery from image-plane arrays, using convex projections. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[15]  Jian Sun,et al.  Guided Image Filtering , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Zeev Farbman,et al.  Edge-preserving decompositions for multi-scale tone and detail manipulation , 2008, SIGGRAPH 2008.

[17]  Jiejie Zhu,et al.  Context-constrained hallucination for image super-resolution , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Peyman Milanfar,et al.  Kernel Regression for Image Processing and Reconstruction , 2007, IEEE Transactions on Image Processing.

[19]  Yücel Altunbasak,et al.  Color plane interpolation using alternating projections , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[20]  Thomas S. Huang,et al.  Image super-resolution as sparse representation of raw image patches , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  Yong Xu,et al.  Dynamic texture classification using dynamic fractal analysis , 2011, 2011 International Conference on Computer Vision.

[22]  Hsieh Hou,et al.  Cubic splines for image interpolation and digital filtering , 1978 .

[23]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[24]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[25]  Manik Varma,et al.  Locally Invariant Fractal Features for Statistical Texture Classification , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[26]  Bobby Bodenheimer,et al.  Synthesis and evaluation of linear motion transitions , 2008, TOGS.

[27]  Michal Irani,et al.  Motion Analysis for Image Enhancement: Resolution, Occlusion, and Transparency , 1993, J. Vis. Commun. Image Represent..

[28]  Richard Szeliski,et al.  Image deblurring and denoising using color priors , 2009, CVPR.

[29]  Chi-Keung Tang,et al.  Fast image/video upsampling , 2008, SIGGRAPH 2008.

[30]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Rob Fergus,et al.  Fast Image Deconvolution using Hyper-Laplacian Priors , 2009, NIPS.

[32]  William T. Freeman,et al.  Example-Based Super-Resolution , 2002, IEEE Computer Graphics and Applications.

[33]  Xiangjun Zhang,et al.  Image Interpolation by Adaptive 2-D Autoregressive Modeling and Soft-Decision Estimation , 2008, IEEE Transactions on Image Processing.

[34]  Xuelong Li,et al.  Multi-scale dictionary for single image super-resolution , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[35]  Hua Han,et al.  Wavelet-domain HMT-based image super-resolution , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[36]  Raanan Fattal,et al.  Image upsampling via texture hallucination , 2010, 2010 IEEE International Conference on Computational Photography (ICCP).

[37]  M. Tech,et al.  Real Time Artifact-Free Image Upscaling , 2012 .

[38]  Lyman P. Hurd,et al.  Fractal image compression , 1993 .

[39]  Raanan Fattal,et al.  Image and video upscaling from local self-examples , 2011, TOGS.