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Aiming at content-based image retrieval (CBIR) in fractal domain, this paper puts forward a fast fractal encoding method to extract image features, which is based on a novel non-searching and adaptive quadtree division. As a result, it enhances fractal coding speed sharply, only needs 0.0485 seconds on average for a 256 × 256 image and is approximately 70 times faster than algorithm in addition to good reconstructed image quality. Furthermore, this paper improves image matching algorithm, consequently enhancing the accuracy of query results. In addition, we present a method to further accelerate image retrieval based on the analysis to fractal codes distance and number. Experimental results show that our proposed method is performs highly in retrieval speed and feasible in retrieval accuracy.

Most information retrieval systems make indirect use of human knowledge in their retrieval process. The new method we present here aims to efficiently use human knowledge directly in combination with fractal coding and support vector machine (SVM) for clustering. As illustrated in this paper, this approach is particularly applicable to soccer concept retrieval from video databases. The first phase consists of extracting suitable features and key frames from video shots. Then, using a fractal coding, soccer shots are retrieved, and using a fuzzy rule base containing the experiences of experts, shots that do not include significant soccer events are removed. Finally, the last phase uses SVM to classify results coming from the fuzzy system. The results of the classification phase are accompanied by a textual description and enables retrieval through text based query. Experimental results show proper classification and satisfying retrieval process.

In recent years, sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, this paper investigates incorporating a dictionary learning approach into fractal image coding, which leads to a new model containing three terms: a patch-based sparse representation prior over a learned dictionary, a quadratic term measuring the closeness of the underlying image to a fractal image, and a data-fidelity term capturing the statistics of Gaussian noise. After the dictionary is learned, the resulting optimization problem with fractal coding can be solved effectively. The new method can not only efficiently recover noisy images, but also admirably achieve fractal image noiseless coding/compression. Experimental results suggest that in terms of visual quality, peak-signal-to-noise ratio, structural similarity index and mean absolute error, the proposed method significantly outperforms the state-of-the-art methods.

Fractal coding has been widely used as an image compression technique in many image processing problems in the past few decades. On the other hand side, most of the natural images have the characteristic of nonlocal self-similarity that motivates low-rank representations of them. We would employ both the fractal image coding and the nonlocal self-similarity priors to achieve image compression in image denoising problems. Specifically, we propose a new image denoising model consisting of three terms: a patch-based nonlocal low-rank prior, a data-fidelity term describing the closeness of the underlying image to the given noisy image, and a quadratic term measuring the closeness of the underlying image to a fractal image. Numerical results demonstrate the superior performance of the proposed model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.

Image denoising has been a fundamental problem in the field of image processing. In this paper, we tackle removing impulse noise by combining the fractal image coding and the nonlocal self-similarity priors to recover image. The model undergoes a two-stage process. In the first phase, the identification and labeling of pixels likely to be corrupted by salt-and-pepper noise are carried out. In the second phase, image denoising is performed by solving a constrained convex optimization problem that involves an objective functional composed of three terms: a data fidelity term to measure the similarity between the underlying and observed images, a regularization term to represent the low-rank property of a matrix formed by nonlocal patches of the underlying image, and a quadratic term to measure the closeness of the underlying image to a fractal image. To solve the resulting problem, a combination of proximity algorithms and the weighted singular value thresholding operator is utilized. The numerical results demonstrate an improvement in the structural similarity (SSIM) index and peak signal-to-noise ratio.