Autocorrelation-Driven Diffusion Filtering

In this paper, we present a novel scheme for anisotropic diffusion driven by the image autocorrelation function. We show the equivalence of this scheme to a special case of iterated adaptive filtering. By determining the diffusion tensor field from an autocorrelation estimate, we obtain an evolution equation that is computed from a scalar product of diffusion tensor and the image Hessian. We propose further a set of filters to approximate the Hessian on a minimized spatial support. On standard benchmarks, the resulting method performs favorable in many cases, in particular at low noise levels. In a GPU implementation, video real-time performance is easily achieved.

[1]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[2]  J. Bigun,et al.  Optimal Orientation Detection of Linear Symmetry , 1987, ICCV 1987.

[3]  Michael J. Black,et al.  Fields of Experts: a framework for learning image priors , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[4]  Johan Wiklund,et al.  Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Joachim Weickert,et al.  Theoretical Foundations of Anisotropic Diffusion in Image Processing , 1994, Theoretical Foundations of Computer Vision.

[6]  Joachim Weickert,et al.  Parallel implementations of AOS schemes: a fast way of nonlinear diffusion filtering , 1997, Proceedings of International Conference on Image Processing.

[7]  Joachim Weickert,et al.  From Tensor-Driven Diffusion to Anisotropic Wavelet Shrinkage , 2006, ECCV.

[8]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..

[9]  Hans Knutsson,et al.  A New Approach to Image Enhancement Using Tensor Fields , 1990 .

[10]  Michael Felsberg.  On the Relation between Anisotropic Diffusion and Iterated Adaptive Filtering , 2008, DAGM-Symposium.

[11]  Björn Johansson,et al.  Low Level Operations and Learning in Computer Vision , 2004 .

[12]  Alan C. Bovik,et al.  Image information and visual quality , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Guillermo Sapiro,et al.  Non-local sparse models for image restoration , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[14]  Edward H. Adelson,et al.  The Design and Use of Steerable Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Song-Chun Zhu,et al.  Prior Learning and Gibbs Reaction-Diffusion , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Rachid Deriche,et al.  Vector-valued image regularization with PDE's: a common framework for different applications , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[17]  Chandrika Kamath,et al.  Comparison of PDE-based non-linear anistropic diffusion techniques for image denoising , 2003, IS&T/SPIE Electronic Imaging.

[18]  Hanno Scharr,et al.  Numerische Isotropieoptimierung von FIR-Filtern mittels Querglättung , 1997, DAGM-Symposium.

[19]  Rachid Deriche,et al.  Vector-valued image regularization with PDEs: a common framework for different applications , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Hans Knutsson,et al.  Signal processing for computer vision , 1994 .

[21]  Michael Felsberg,et al.  Channel smoothing: efficient robust smoothing of low-level signal features , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Yizong Cheng,et al.  Mean Shift, Mode Seeking, and Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[24]  Michael Felsberg,et al.  Anisotropic Channel Filtering , 2003, SCIA.

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

[26]  R. Wilson,et al.  Anisotropic Nonstationary Image Estimation and Its Applications: Part I - Restoration of Noisy Images , 1983, IEEE Transactions on Communications.

[27]  Joachim Weickert,et al.  Recursive Separable Schemes for Nonlinear Diffusion Filters , 1997, Scale-Space.

[28]  Joachim Weickert,et al.  A Review of Nonlinear Diffusion Filtering , 1997, Scale-Space.

[29]  Michael J. Black,et al.  On the unification of line processes, outlier rejection, and robust statistics with applications in early vision , 1996, International Journal of Computer Vision.

[30]  Jian Bai,et al.  Fractional-Order Anisotropic Diffusion for Image Denoising , 2007, IEEE Transactions on Image Processing.

[31]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[32]  Pierre Baylou,et al.  Mixed anisotropic diffusion , 2002, Object recognition supported by user interaction for service robots.

[33]  René A. Carmona,et al.  Adaptive smoothing respecting feature directions , 1998, IEEE Trans. Image Process..

[34]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

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

[37]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  Michael Felsberg,et al.  Continuous dimensionality characterization of image structures , 2009, Image Vis. Comput..

[39]  Andrew R. Mitchell,et al.  Alternating Direction Methods for Parabolic Equations in Two Space Dimensions with a Mixed Derivative , 1970, Comput. J..

[40]  R D Richtmyek,et al.  Survey of the Stability of Linear Finite Difference Equations , 2022 .

[41]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[42]  Wolfgang Förstner,et al.  Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range Images , 2000 .

[43]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.