Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation
International Journal of Computer Vision
Examining the Role of Scale in the Context of the Non-Local-Means Filter
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
A Simple, General Model for the Affine Self-similarity of Images
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Robust Estimation Approach for NL-Means Filter
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Support vector regression based image denoising
Image and Vision Computing
A Necessary and Sufficient Contractivity Condition for the Fractal Transform Operator
Journal of Mathematical Imaging and Vision
Study on huber fractal image compression
IEEE Transactions on Image Processing
Multifractal signature estimation for textured image segmentation
Pattern Recognition Letters
Adaptive kernel-based image denoising employing semi-parametric regularization
IEEE Transactions on Image Processing
Structural similarity-based affine approximation and self-similarity of images revisited
ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part II
Continuous evolution of fractal transforms and nonlocal PDE imaging
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Fractal image coding as projections onto convex sets
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
International Journal of Applied Mathematics and Computer Science
Solving the inverse problem of image zooming using "self-examples"
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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Over the past decade, there has been significant interest in fractal coding for the purpose of image compression. However, applications of fractal-based coding to other aspects of image processing have received little attention. We propose a fractal-based method to enhance and restore a noisy image. If the noisy image is simply fractally coded, a significant amount of the noise is suppressed. However, one can go a step further and estimate the fractal code of the original noise-free image from that of the noisy image, based upon a knowledge (or estimate) of the variance of the noise, assumed to be zero-mean, stationary and Gaussian. The resulting fractal code yields a significantly enhanced and restored representation of the original noisy image. The enhancement is consistent with the human visual system where extra smoothing is performed in flat and low activity regions and a lower degree of smoothing is performed near high frequency components, e.g., edges, of the image. We find that, for significant noise variance (σ≥20), the fractal-based scheme yields results that are generally better than those obtained by the Lee filter which uses a localized first order filtering process similar to fractal schemes. We also show that the Lee filter and the fractal method are closely related.