A New Probabilistic Approach for Fractal Based Image Compression

Compression of images process is a step in the image processing. It is concerned with the transmission and storage of digitally created images. Fractal coding is a potential image and video compression approach with good reconstruction fidelity and relatively large compression ratios, because of its simplicity and great performance; fractal image compression (FIC) is a particularly popular approach in image compression applications. However, it has a significant disadvantage in the form of a long encoding time. This is because encoding any small bit necessitates a massive similarity search in the original data As a result; the FIC search time is reduced while the quality of the reconstructed images is maintained acceptable level in many introduced paper and other still a study topic in progress. Fractal images are images that are self-similar in that each individual part is the same as the total. This paper will discusses many attempts for more author that working on image and video compression using fractal compression technique based on various approach and with each discuss focuses on the main parameter of compression such compression ratio (CR), peak signal to noise ratio (PSNR) and encoding time, as well as the details of data set the used for testing also writing with each technique to creating fractal video and image compression. Index Terms— FIC, Video compression, parallel processing, Iteration Function System (IFS), Image processing.

An image such as the fractal fern of the previous chapter can be reproduced with a relatively simple iterated function system (IFS) because this type of image has the property of global self-similarity. That is, the entire image is made up of smaller copies of itself, or parts of itself. If one zooms in on this type of image, it will display the same level of detail, regardless of the resolution scale. Also, this type of image is a binary image, that is, each of its pixels can be represented with either a 1 or a 0. Real-world images do not exhibit the type of global self-similarity present in the IFS images of the previous chapter. Moreover, real-world images are not binary, but rather each pixel belongs to a range of values (grayscale) or a vector of values (color). If we are going to represent such an image as the attractor of an iterated system, then clearly we need a more general system than the IFS's of the previous chapter. This chapter examines the development and implementation of such a system that can be used for the fractal encoding of general grayscale images.

In this paper, the fractal function is used for the image representation and compression. By introducmg a searching strategyinto the fractal-function-based image coding, the image representation accuracy is improved by 10%. A regional adaptiveresolution-based fractal block coding is formed by combining the encoding and the decoding processes together with aquadtree structure to perform image compression. It is shown by the experiments that the image compression ratio isincreased up to 1 2 without a great loss of visual quality.Keywords: Image coding; image compression; fractal function. 1. INTRODUCTION AND THEORETICAL FOUNDATION Fractal has been stimulating great interests since John Hutchinson introduced the theory of iterated function system(IFS) [1] to model collections of contractive transformations in a metric space as dynamical systems. After the work of M.Barnsley and A. E. Jacquin [2]-[3] in using the partitioned iterated function system (PIFS) to do fractal-based imagecompression, many works have been done either to improve the compression ratio or to reduce the encoding time. F.Dudbridge[4]-[5] developed a method which is quite different from the traditional fractal (TF) image coding. He proposedusing a new fractal function (FF) for the image representation.Before the concept of fractal function is introduced the following preliminaries are needed: (1) w1 ,

Many effective methods have been proposed to solve the problem of image compression. Fractal image code can compress an image in a higher compress ratio level, the fundamental idea of fractal image compression is based on the iteration function system (IFS). In this paper, we proposed a novel method based on IFS with probabilities can be used in image compression and image retrieval, we obtain enlightenment from fractal no search methods, our method also no need to carried out searching stage when compress the image, so the consuming time with image compression is less than traditional methods. We utilized the image code as index file, and apply our method in image retrieval, experiment results indicate that our method is effective in image retrieval.

One of the main disadvantages of fractal image data compression is a loss time in the process of image compression (encoding) and conversion into a system of iterated functions (IFS). In this paper, the idea of the inverse problem of fixed point is introduced. This inverse problem is based on collage theorem which is the cornerstone of the mathematical idea of fractal image compression. Then this idea is applied by iterated function system, iterative system functions and grayscale iterated function system down to general transformation. Mathematical formulation form is also provided on the digital image space, which deals with the computer. Next, this process has been revised to reduce the time required for image compression by excluding some parts of the image that have a specific milestone. The neural network algorithms have been applied on the process of compression (encryption). The experimental results are presented and the performance of the proposed algorithm is discussed. Finally, the comparison between filtered ranges method and self-organizing method is introduced.

Fractals are geometric patterns generated by Iterated Function System theory. A popular technique known as fractal image compression is based on this theory, which assumes that redundancy in an image can be exploited by block-wise self-similarity and that the original image can be approximated by a finite iteration of fractal codes. This technique offers high compression ratio among other image compression techniques. However, it presents several drawbacks, such as the inverse proportionality between image quality and computational cost. Numerous approaches have been proposed to find a compromise between quality and cost. As an efficient optimization approach, genetic algorithm is used for this purpose. In this paper, a crowding method, an improved genetic algorithm, is used to optimize the search space in the target image by good approximation to the global optimum in a single run. The experimental results for the proposed method show good efficiency by decreasing the encoding time while retaining a high quality image compared with the classical method of fractal image compression.

In the field of Image compression and particularly for the process of image encoding, Fractal image compression (FIC) technique plays a vital role. This technique is based on fractals present in an image and also it is capable of generating the copying blocks dependent on numerical changes. The only drawback in the Fractal image compression is that the time taken during the encoding process when the data is large. Thus, it is necessary to optimize the encoding process for efficient resource utilization as optimization algorithms are generally known for converging behavior. This research work attempts to apply the Tree Seed Algorithm as a characteristic enlivened high-level algorithm to improve FIC. Output shows the improvement of such calculation under various types (encoding time, pressure proportion, top sign to clamor proportion, and mean square error. Moreover, an examination with a portion of the current techniques underlines this addition.

This paper presents a comparative analysis of three image compression methods: JPEG, JPEG2000, and fractal compression (FIC). The theoretical foundations of each method are reviewed, including the discrete cosine transform (DCT) for JPEG, the discrete wavelet transform (DWT) for JPEG2000, and the iterated function system (IFS) for FIC. The performance of the algorithms is evaluated using a set of metrics: compression ratio (CR), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and the learned fragment image similarity metric (LPIPS). The analysis shows that JPEG2000 generally provides better quality at a given bitrate than JPEG, especially at high compression ratios, and offers additional features such as scalability, but this advantage is rather small. JPEG remains popular due to its simplicity and speed, but suffers from block artifacts. Fractal compression, despite its theoretical advantages, such as potential resolution independence, has significant drawbacks, including extremely slow encoding and often uncompetitive quality on general images. The application areas, reasons for limited implementation, and the current relevance of FIC are discussed. It is concluded that it is necessary to use various metrics for comprehensive quality assessment and that the choice of the optimal compression method depends on the specific requirements of the application.

Fractal compression of digital images has attracted much attention. It is based on the mathematical theory of iterated function systems (IFS) developed by Hutchinson (1981) and Barnsley (1988). We show that the tree method may be combined with the block classification method to get a greater speed-up. In block classification the classes are stored without any additional structure, usually as a list, and searched linearly until a best match is found. We should expect an enhancement if we arrange the classes into trees, and use the pruning algorithm for the search. Another way to express this idea is that the domain pool is grown into lots of small trees rather than one big one. The experiments show that a significant speed-up is achievable provided two conditions are met. First, only reasonable size classes should be grown into a tree. Second, the feature extraction methods for the classification and for the tree construction should be distinct.

Image compression research has increased dramatically as a result of the growing demands for image transmission in computer and mobile environments. It is needed especially for reduced storage and efficient image transmission and used to reduce the bits necessary to represent a picture digitally while preserving its original quality. Fractal encoding is an advanced technique of image compression. It is based on the image's forms as well as the generation of repetitive blocks via mathematical conversions. Because of resources needed to compress large data volumes, enormous programming time is needed, therefore Fractal Image Compression's main disadvantage is a very high encoding time where decoding times are extremely fast. An artificial intelligence technique similar to a neural network is used to reduce the search space and encoding time for images by employing a neural network algorithm known as the “back propagation” neural network algorithm. Initially, the image is divided into fixed-size and domains. For each range block its most matched domain is selected, its range index is produced and best matched domains index is the expert system's input, which reduces matching domain blocks in sets of results. This leads in the training of the neural network. This trained network is now used to compress other images which give encoding a lot less time. During the decoding phase, any random original image, converging after some changes to the Fractal image, reciprocates the transformation parameters. The quality of this FIC is indeed demonstrated by the simulation findings. This paper explores a unique neural network FIC that is capable of increasing neural network speed and image quality simultaneously.

A new method of suppressing the block effect brought about by fractal image compression is proposed by means of introducing quasi-X shape template into the process of smoothing image locally on the reconstructed color image compressed by the fractal method based on iterated function system. The effects of the two different kinds of smooth templates, quasi-X shape and traditional square are compared with each other. It is found that the mosaic effect can be suppressed effectively with the help of quasi-X shape template in the process of smoothing image locally under the condition that certain objective image quality measured by the PSNR value is guaranteed. At the same time, the compression ratio is improved by means of getting rid of the position parameters of range blocks as one kind of redundancy when adopting the method of fractal image compression during the process of compressing color image, taking the fact that range blocks are stored in encoding file successively into account.

In this paper an adaptive algorithm is proposed to reduce the long time that has been taken in the Fractal Image Compression (FIC) technique. This algorithm worked on reducing the number of matching operations between range and domain blocks by reducing both of the range and domain blocks needed in the matching process, for this purpose, two techniques have been proposed; the first one is called Range Exclusion ( RE ), in this technique variance factor is used to reduce the number of range blocks by excluding ranges of the homogenous or flat regions from the matching process; the second technique is called Reducing the Domain Image Size ( RDIZ ), it is responsible for the reduction of the domain by minimizing the Domain Image Size to 1/16 th instead of 1/4 th of the original image size used in the traditional FIC. This in turn will affect the encoding time, compression ratio and the reconstructed image quality. For getting best results, the two techniques are coupled in one algorithm; the new algorithm is called ( RD-RE ). The tested (256x256) gray images are partitioned into fixed (4x4) blocks and then compressed using visual C++ 6.0 code. The results show that RE technique is faster and gets more compression ratio than the traditional FIC and keeping a high reconstructed images quality while RD-RE is faster and it gets higher compression ratio than RE but with slight loss in the reconstructed image quality.

Self-similar sets satisfying the common point property

Recently a number of researches have demonstrated performance improvement in the video fractal compression compared to the current video transmission standards (MPEG, H.263, H.264). This article describes a current problem of relatively low fractal encoding speed. Indeed, high computational complexity is a sore point of fractal compression approach. It seems almost every paper on this subject touches the problem of encoding speed. Productive ideas and algorithms can be borrowed from the pattern recognition problem. In the course of recent decades feature points approach in computer vision has been demonstrating good performance in SLAM and pattern recognition. Technology of feature detection, description and tracking is being developed successfully and has effective applications in augmented reality like Android ARCore and IOS ARKit frameworks that are real-time engines. Similarities among parts of video frames are analyzed and used for both image registration and visual scene tracking therefore it fits highly to block matching task. Statistic properties for domain/range blocks matching has been analyzed on the basis of previous investigation for fractal compression. As a result, a simple algorithm is proposed based on computer vision approach. The approach includes a visual feature points extraction, feature descriptors calculation and fast NN-search in descriptor space. The key idea of the proposed approach is as follows. Only a limited number of domain blocks around the most salient points are subject to selection. Other blocks are not essential for matching as transforms would have big Lipschitz constant and will have worse contractive properties. Salient points should be unique as well. Further the descriptors for feature point are calculated. The algorithm has O(N log N) complexity for pixel number in the frame image, however if the number of domain blocks is limited the complexity could be almost linear. Python program for the algorithm test has been developed and shows that reconstruction result is acceptable in terms of encoding speed (< 2 s on 2 GHz CPU) and quality (PSNR) ~25 dB. The result of the proposed approach could be interesting for further improvement both for image and video compression. Further steps for quality increasing are also described.

Image compression frequently supports reduced storage requirement in a computer system, as well as enhancement of effective channel bandwidth in a communication system, by decreasing the source bit rate through reduction of source redundancy. The majority of image compression techniques emphasize pixel-level operations, such as matching rectangular or elliptical sampling blocks taken from the source data stream, with exemplars stored in a database (e.g., a codebook in vector quantization or VQ). Alternatively, one can represent a source block via transformation, coefficient quantization, and selection of coefficients deemed significant for source content approximation in the decompressed image. This approach, called transform coding (TC), has predominated for several decades in the signal and image processing communities. A further technique that has been employed is the deduction of affine relationships from source properties such as local self-similarity, which supports the construction of adaptive codebooks in a self-VQ paradigm that has been called <i>iterated function systems </i>(IFS). Although VQ, TC, and IFS based compression algorithms have enjoyed varying levels of success for different types of applications, bit rate requirements, and image quality constraints, few of these algorithms examine the higher-level spatial structure of an image, and fewer still exploit this structure to enhance compression ratio. In this paper, we discuss a fourth type of compression algorithm, called <i>object-based compression</i>, which is based on research in joint segmentaton and compression, as well as previous research in the extraction of sketch-like representations from digital imagery. Here, large image regions that correspond to contiguous recognizeable objects or parts of objects are segmented from the source, then represented compactly in the compressed image. Segmentation is facilitated by source properties such as size, shape, texture, statistical properties, and spectral signature. In particular, discussion addresses issues such as efficient boundary representation, variance assessment and representation, as well as a texture classification and replacement algorithms that can decrease compression overhead and increase reconstruction fidelity in the decompressed image. Contextual extraction of motion patterns in digital video sequences, using a frequency-domain pattern recognition technique based on interframe correlation, is described in a companion paper. This technique can also be extended to multidimensional image domains, to support joint spectral, spatial, and temporal compression.