Fractal Coding Technique Research Articles

Image and audio fractal compression: comprehensive review, enhancements and research directions

<p>This study aims to review the recent techniques in digital multimedia compression with respect to fractal coding techniques. It covers the proposed fractal coding methods in audio and image domain and the techniques that were used for accelerating the encoding time process which is considered the main challenge in fractal compression. This study also presents the trends of the researcher's interests in applying fractal coding in image domain in comparison to the audio domain. This review opens directions for further researches in the area of fractal coding in audio compression and removes the obstacles that face its implementation in order to compare fractal audio with the renowned audio compression techniques.</p>

Gradient based fractal image compression using Cayley table

Encoding complexity reduction is an active area of research in the field of fractal image compression. In this proposed method, affine transformation is predicted to reduce the computational complexity and score value is calculated to further minimise the number of computations in the exhaustive process of encoding. In this hybrid wavelet- fractal image compression, relative geometric transformation of range and domain blocks is determined using a reference matrix as GR and GD respectively. Then affine transformation is predicted as the geometric composition of GR and GD, using Cayley table. Score value is defined individually for domain and range blocks. It is the absolute value of maximum change in the intensity in the respective block. An important merit of this proposed method is that the encoding time is highly reduced in comparison to other recent fractal coding techniques, with a better value of PSNR. This method is 641 times faster than Standard fractal image compression method (SFIC). Cayley table is utilized for the first time in fractal image compression. This lossy compression technique can be used in multimedia applications to handle the situation of limited storage space and bandwidth and also to transmit enormous amount of data with acceptable value of PSNR. As the medical images are huge in size a good lossy compression technique is required to store them in medical archives in an economical manner. Since this proposed method provides a good trade-off between compression ratio and the quality of reconstructed image, it is a better solution for the storage of medical images in an efficient manner.

Image Super Resolution Using Fractal Coding and Residual Network

Fractal coding techniques are an effective tool for describing image textures. Considering the shortcomings of the existing image super‐resolution (SR) method, the large‐scale factor reconstruction performance is poor and the texture details are incomplete. In this paper, we propose an SR method based on error compensation and fractal coding. First, quadtree coding is performed on the image, and the similarity between the range block and the domain block is established to determine the fractal code. Then, through this similarity relationship, the attractor is reconstructed by super‐resolution fractal decoding to obtain an interpolated image. Finally, the fractal error of the fractal code is estimated by the depth residual network, and the estimated version of the error image is added as an error compensation term to the interpolation image to obtain the final reconstructed image. The network structure is jointly trained by a deep network and a shallow network. Residual learning is introduced to greatly improve the convergence speed and reconstruction accuracy of the network. Experiments with other state‐of‐the‐art methods on the benchmark datasets Set5, Set14, B100, and Urban100 show that our algorithm achieves competitive performance quantitatively and qualitatively, with subtle edges and vivid textures. Large‐scale factor images can also be reconstructed better.

A New Fractal Watermarking Method for Images of Text

A new method, using the orthogonal fractal coding is developed for fractal watermarking of high contrast, low-density images of texts. In this method, image is divided into one pixel height sub-images. Each sub-image is coded separately using the orthogonal fractal coding technique. A binary watermark is re-ordered using a chaotic sequence. The binary watermark is inserted into the range block means of fractal codes. This fractal code is further decoded to obtain the watermarked image. The watermark sequence is retrieved by comparing the original image and the watermarked code. The extracted watermark is re-ordered using the key of the chaotic sequence. The method is robust against JPEG and noise attacks and has a very low watermark visibility.

Implemented a Facial Recognition Based on Fractal Coding and Quadtree Techniques

Implemented a Facial Recognition Based on Fractal Coding and Quadtree Techniques

A New Hybrid Fractal based Color Image Compression in YCbCr Scheme and Discrete Cosine Transform with Quadtree and Isosceles Triangle Segmentation Approach

Color Image compression has become an important technology to decrease memory space and to reduce transmission time. The present study provides comparative values between RGB and YCbCr color spaces with respect to PSNR, execution time and compression ratio. Fractal coding is a valuable method which utilizes for compression of color image. This method is most suitable for irregular shape of images. Long encoding times still remain as main disadvantage of this compression technique. A hybrid fractal coding technique based on YCbCr scheme and Discrete Cosine Transform (DCT) with quadtree and isosceles triangle segmentation is proposed in the present study. The study needs six phases, first, conversion of input RGB image to YCbCr scheme; second, the resulting image (YCbCr) is partitioned separately based on quadtree approach and isosceles triangle segmentation approach; third, DCT is applied to every block of the partition, fourth, scanning of every block value and zigzag manner is applied to prevent zero co-efficient; fifth, both quad tree and isosceles triangle segmentation approaches are applied separately for having partitioned resulting image; sixth, to compress the image, Run Length Encoding (RLE) approach is utilized. Test results demonstrate that proposed strategy gives higher compression ratio, PSNR value with high processing speed without degrading the image quality.

Fractal Coding Using Gradient Direction Based Tag Matrix and Score Value

Reducing encoding complexity and improving the tradeoff between quality of image and compression ratio are active areas of research in the field of fractal image compression. In this paper two techniques are proposed to reduce the encoding complexity and to improve the PSNR of the reconstructed image. The first method is the prediction of affine transformation, based on the gradient direction of domain and range block using a Tag Matrix and the second involves calculation of score value based on the maximum value of intensity difference of range and domain block. An important merits of this new method is that encoding time is highly reduced and PSNR is also improved than the existing fractal coding techniques. This technique will be very applicable in situation where we have limited storage space and bandwidth but have to store and transmit enormous amount of data.

Quadtree partitioning and extended weighted finite automata-based fractal colour video coding

Fractal coding technique has become the most popular coding technique in the recent development of image/video compression technologies for its better performance, achieving a high compression ratio, less decoding time and good reconstruction quality of image. This paper elaborates on the approach which is a combination of a quadtree partitioning scheme and extended weighted finite automata (EWFA) coding for fractal video compression based on the concept of intra-frame coding. The quadtree partitioning scheme is used to specify the address of each sub-image. It is observed that any image can be represented by the quadtree-based EWFA; the quadtree-based EWFA coding process is similar to fractal coding process; and also the size of domain pool increases dynamically during the process of quadtree-based EWFA encoding as that of in fractal coding. Experimentations are carried on standard databases like Soccer, Suzie, Bus, Football, Xylophone, Paris, Traffic, Akiyo, Ice and mobile sequence. The developed basic fractal image compression existing mechanism is also further implemented on video/image sequences based on the concept of intra-frame coding used for comparing the results with the proposed approach. Experimental results show that the EWFA encoding/decoding process improves the quality, compression ratio, encoding and decoding time of reconstructed image sequence.

BASED ON RANGE AND DOMAIN FRACTAL IMAGE COMPRESSION OF SATELLITE IMAGERIES IMPROVED ALGORITHM FOR RESEARCH

Fractal coding is a novel method to compress images, which was proposed by Barnsley, and implemented by Jacquin. It offers many advantages. Fractal image coding has the advantage of higher compression ratio, but is a lossy compression scheme. The encoding procedure consists of dividing the image into range blocks and domain blocks and then it takes a range block and matches it with the domain block. The image is encoded by partitioning the domain block and using affine transformation to achieve fractal compression. The image is reconstructed using iterative functions and inverse transforms. However, the encoding time of traditional fractal compression technique is too long to achieve real-time image compression, so it cannot be widely used. Based on the theory of fractal image compression; this paper raised an improved algorithm form the aspect of image segmentation. In the present work the fractal coding techniques are applied for the compression of satellite imageries. The Peak Signal to Noise Ratio (PSNR) values are determined for images namely Satellite Rural image and Satellite Urban image. The Matlab simulation results for the reconstructed image shows that PSNR values achievable for Satellite Rural image ~33 and for Satellite urban image ~42.

A Combined Fractal and Wavelet Angiography Image Compression Approach

In this paper, a combined Fractal and Wavelet (CFW) compression algorithm targeting x-ray angiogram images is proposed. Initially, the image is decomposed using wavelet transform. The smoothness of the low frequency part of the image appears as an approximation image with higher self similarities, therefore, it is coded using a fractal coding technique. However, the rest of the image is coded using an adaptive wavelet thresholding technique. This model is implemented and its performance is compared with best performances of the available published algorithms. A data set containing 1000 x-ray angiograms is used to study the performance of the algorithm. A minimum compression ratio of 30 with a peak signal to noise ratio (PSNR) of 36 dB and percent diameter stenosis deviation of (<0.2%) was achieved. Results demonstrate the effectiveness of the proposed technique in obtaining a diagnostic quality of reconstructed images at very low bit rates.

A class of multiresolution stochastic models generating self-affine images

Fractal image compression is based on the rather poorly motivated assumption that images exhibit significant affine self-similarity. The accuracy of this assumption is evaluated by a comparison between the statistics of natural images and those of a multiresolution stochastic model designed to generate images exhibiting affine self-similarity as assumed by fractal coding techniques. These comparisons suggest that self-affinity does not represent a particularly accurate characterization of image statistics.

An efficient bath fractal transform-based image coding technique

A computationally efficient image compression technique is presented, which is based on visual patterns as well as least squares fractal approximation by a self-affine system (SAS). Simulation studies demonstrate that the use of visual pattern-based technique can code the shade (flat) regions of an image more efficiently than fractal techniques. Furthermore, the proposed technique not only gives an encoding speed several times faster than other SAS-based fractal coding techniques but also achieves higher compression ratios and better fidelity.

A fractal-based clustering approach in large visual database systems

Large visual database systems require effective and efficient ways of indexing and accessing visual data on the basis of content. In this process, significant features must first be extracted from image data in their pixel format. These features must then be classified and indexed to assist efficient access to image content. With the large volume of visual data stored in a visual database, image classification is a critical step to achieve efficient indexing and retrieval. In this paper, we investigate an effective approach to the clustering of image data based on the technique of fractal image coding, a method first introduced in conjunction with fractal image compression technique. A joint fractal coding technique, applicable to pairs of images, is used to determine the degree of their similarity. Images in a visual database can be categorized in clusters on the basis of their similarity to a set of iconic images. Classification metrics are proposed for the measurement of the extent of similarity among images. By experimenting on a large set of texture and natural images, we demonstrate the applicability of these metrics and the proposed clustering technique to various visual database applications.