Fractal Compression Research Articles

Fast Fractal Technique using Modified Moment Features on Domain Blocks

In this research, a new technique is suggested to reduce the long time required by the encoding process by using modified moment features on domain blocks. The modified moment features were used in accelerating the matching step of the Iterated Function System (IFS). The main disadvantage facing the fractal image compression (FIC) method is the over-long encoding time needed for checking all domain blocks and choosing the least error to get the best matched domain for each block of ranges. In this paper, we develop a method that can reduce the encoding time of FIC by reducing the size of the domain pool based on the moment features of domain blocks, followed by a comparison with threshold (the selected threshold based on experience is 0.0001). The experiment was conducted on three images with size of 512x512 pixel, resolution of 8 bits/pixel, and different block size (4x4, 8x8 and, 16x16 pixels). The resulted encoding time (ET) values achieved by the proposed method were 41.53, 39.06, and 38.16 sec, respectively, for boat , butterfly, and house images of block size 4x4 pixel. These values were compared with those obtained by the traditional algorithm for the same images with the same block size, which were 1073.85, 1102.66, and 1084.92 sec, respectively. The results imply that the proposed algorithm could remarkably reduce the ET of the images in comparison with the traditional algorithm.

Ways to Increase the Efficiency of Steganographic Use of Fractal Image Compression Algorithm

The state of the art in fractal picture compression algorithms is investigated. The primary directions for improving compression algorithms are discussed. In terms of classification efficiency and picture processing speed, the methods are among the most effective. The concept of steganographic use of the fractal algorithm is discussed. The differences between the advanced compression algorithm and the classic compression algorithm are evaluated to accomplish so. The differences discovered are used to define ways to improve the efficiency of the stego algorithm. The development of digital image compression technology was spurred by the necessity for speedy communication and "live" digital image information over the internet. Time has passed, and many tactics exist now to reduce the compression ratio and increase the usability of speedy computation, but because we are limited by certain constraints, there are many inventive ways to overcome these limitations. Today's environment is heavily reliant on digital media storage, necessitating the creation of more effective image or data compression algorithms. Images must be compressed and soft-encoded before being used in the transmission phase due to limited bandwidth and power. This paper discusses the differences between Lossy and Lossless compression methods as they apply to image processing.

Semi-lossless Fractal MRI Image Compression Based on Fixed length Technique

Medical image compression plays an essential role to handle large amounts of data for communication and storage purposes. Fractal image compression is a potential lossy compression models with a resulting image that loses some of its information. However, health data communication usually cannot afford any lose for patients visual information. This paper proposes a new high efficiency semi-lossless fractal image compression method (SLFIC) based on fractal theory and fixed length technique. Technically, the resultant lossy fractals compressed image is analyzed and error in comparison with the original image is detected. Then, Fixed-length is developed to compress the detected errors and attached to the compressed image. In practice, a potential performance by the new developed model has been obtained in comparison with two other lossless models: ( Lion optimization algorithm (LOA) and Lempel Ziv Markov chain Algorithm (LZMA) with Linde–Buzo–Gray (LBG) (L2-LBG)) and(Neural Network Radial Basis Function (NNRBF)). Moreover, a high quality that has been obtained by the proposed system based on Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).

Partitioned iterated function systems by regression models for head pose estimation

Head pose estimation represents an important computer vision technique in different contexts where image acquisition cannot be controlled by an operator, making face recognition of unknown subjects more accurate and efficient. In this work, starting from partitioned iterated function systems to identify the pose, different regression models are adopted to predict the angular value errors (yaw, pitch and roll axes, respectively). This method combines the fractal image compression characteristics, such as self-similar structures in order to identify similar head rotation, with regression analysis prediction. The experimental evaluation is performed on widely used benchmark datasets, i.e., Biwi and AFLW2000, and the results are compared with many existing state-of-the-art methods, demonstrating the robustness of the proposed fusion approach and excellent performance.

Image compression methods for efficient storage and transmission

This paper presents a detailed and comprehensive review of image compression methods, emphasizing their role in optimizing both storage and transmission efficiency across various domains, from everyday use in social media to specialized applications like medical imaging and satellite data processing. We systematically explore both traditional and contemporary image compression techniques, categorizing them into lossless and lossy methods, transform-based approaches, and the latest advancements in machine learning-based compression. Lossless compression techniques, including Run-Length Encoding (RLE), Huffman Coding, Lempel-Ziv-Welch (LZW), and the Portable Network Graphics (PNG) format, are discussed for their ability to preserve image quality perfectly, albeit at the cost of relatively lower compression ratios. Conversely, lossy compression methods, such as JPEG and fractal compression, offer significant file size reduction by discarding non-essential data, while still maintaining acceptable visual quality for many practical applications. We further delve into transform-based approaches like Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT), which form the backbone of popular standards such as JPEG and JPEG 2000, enabling more efficient data representation in the frequency domain. Additionally, the study highlights emerging machine learning and deep learning techniques, such as autoencoders and Generative Adversarial Networks (GANs), that are pushing the boundaries of image compression by achieving unprecedented compression ratios while minimizing perceptual loss in image quality. Through a comparative analysis, we evaluate these methods based on multiple performance metrics, including compression ratio, computational complexity, image fidelity (measured via Peak Signal-to-Noise Ratio, PSNR, and Structural Similarity Index, SSIM), and their practical applications across different industries. Our findings suggest that while traditional methods such as JPEG, PNG, and JPEG 2000 remain widely adopted due to their simplicity and efficiency, emerging techniques driven by deep learning show great potential in adapting to specific image characteristics, achieving higher compression ratios, and better preserving image quality under extreme compression. Finally, this paper identifies key challenges and trends in the field, such as the increasing computational demands of advanced techniques, the need for adaptive compression strategies, and the importance of standardization for broad industry adoption. We conclude that while traditional methods will continue to play a significant role, the future of image compression lies in the integration of machine learning and content-aware technologies that dynamically optimize compression performance across diverse image types and application contexts.

A Fast Image Compression Algorithm Based on Wavelet Transform

With multimedia becoming widely popular, the conflict between mass data and finite memory devices has been continuously intensified; so, it requires more convenient, efficient and high-quality transmission and storage technology and meanwhile, this is also the researchers’ pursuit for highly efficient compression technology and it is the fast image transmission that is what people really seek. This paper mainly further studies wavelet analysis and fractal compression coding, proposes a fast image compression coding method based on wavelet transform and fractal theory, and provides the theoretical basis and specific operational approaches for the algorithm. It makes use of the smoothness of wavelet, the high compression ratio of fractal compression coding and the high quality of reconstructed image. It firstly processes the image through wavelet transform. Then it introduces fractal features and classifies the image according to the features of image sub-blocks. Each class selects the proper features. In this way, for any sub-block, it only needs to search the best-matched block in a certain class according to the corresponding features. With this method, it can effectively narrow the search in order to speed up coding and build the relation of inequality between the sub-block and the matching mean square error. So, it can effectively combine wavelet transform with fractal theory and further improves the quality of reconstructed image. By comparing the simulation experiment, it objectively analyzes the performance of algorithm and proves that the proposed algorithm has higher efficiency.

Image Compression Technique Based on Fractal Image Compression Using Neural Network – A Review

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.

Fractal image compression using a fast affine transform and hierarchical classification scheme

Fractal image compression using a fast affine transform and hierarchical classification scheme

IMPROVEMENT OF METHODS AND ALGORITHM OF FRACTAL COMPRESSION OF A GRAPHIC IMAGE

During the intensive development of information systems, the volumes of data necessary for storing and processing information, in particular graphic images, grow. One of the reasons for this phenomenon is the desire to continually improve the quality of the content we receive. The ever-growing demand for image quality requires the development of new and improvement of existing approaches to information compression. Compression algorithms use the presence of so-called surplus in the data, which can be eliminated during data storage and restored during playback. Currently in demand methods are based on storing only low-frequency components. Such methods are used in JPEG, MPEG compression algorithms. The disadvantage of such algorithms is not a large compression ratio. In this regard, methods have emerged based on fractal data compression. The main idea of ​​the method is to store the image as affine transformations, which leads to its compression.
 The paper proposes preliminary processing of graphic data for storing them in the form of a file with the * .json extension. The application of a further fractal compression algorithm to the already obtained file allows to reduce the processing time of data, computational calculations. The resulting file will have the advantages of fractal compression such as decompression speed, better compression ratio and higher resolution compared to * .jpeg and * .bmp.
 Despite all the advantages, fractal compression of graphic information is used quite rarely. This is due to the complexity of the algorithm, the lack of a sufficient number of specialists on this issue and the estimate of the licensed software. The improvement is aimed at simplifying the algorithm and its implementation will avoid these drawbacks and expand the scope of fractal compression.

Medical image processing using fractal functions

In this paper, a comparison was made between a modified methods for repeated engineering modeling in order to increase the accuracy of medical images. A comparison was made between different types in terms of classification accuracy. The lacuinartiy feature has also been used to reduce the noise ratio in the received images. The results showed the importance of fractal IFS in medical pulse compression, where a ratio of (98%) was obtained in reducing noise and a ratio of (0.421) in the gap coefficient was obtained. It separated the diseased tissues from the healthy tissues by applying several multi-fractal factors. Fractal image compression is dependent on subjective similarity, with one part of the image being the same as the other part of a similar image. The partial coding is constantly linked to the grayscale images by dividing a color RGB image into three channels - red, green and blue, and is compressed independently by considering each color segment as a specific gray scale image. Based on the smart neural network, the patterns are distinguished for the medical images used by a few learning time and positive error 0.22%.

Medical image processing using fractal functions

In this paper, a comparison was made between a modified methods for repeated engineering modeling in order to increase the accuracy of medical images. A comparison was made between different types in terms of classification accuracy. The lacuinartiy feature has also been used to reduce the noise ratio in the received images. The results showed the importance of fractal IFS in medical pulse compression, where a ratio of (98%) was obtained in reducing noise and a ratio of (0.421) in the gap coefficient was obtained. It separated the diseased tissues from the healthy tissues by applying several multi-fractal factors. Fractal image compression is dependent on subjective similarity, with one part of the image being the same as the other part of a similar image. The partial coding is constantly linked to the grayscale images by dividing a color RGB image into three channels - red, green and blue, and is compressed independently by considering each color segment as a specific gray scale image. Based on the smart neural network, the patterns are distinguished for the medical images used by a few learning time and positive error 0.22%.

Image Compression Using Fractal Functions

The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

THE PARALLEL-PIPELINED IMPLEMENTATION OF THE FRACTAL IMAGE COMPRESSION FOR RECONFIGURABLE COMPUTING SYSTEMS

The developed fractal image compression method, implemented for reconfigurable computing systems is described. The main idea parallel fractal image compression based on parallel execution pairwise comparison of domain and rank blocks. Achievement high performance occurs at the expense of simultaneously comparing maximum number of pairs. Implementation fractal image compression for reconfigurable computing systems has two critical resources, as number of input channels and FPGA Look-up Table (LUT). The main critical resource for fractal image compression is data channels, and implementation this task for reconfigurable computing systems requires parallel-pipeline computations organization replace parallel, preliminarily produced performance reduction parallel computational structure. The main critical resource for fractal image compression is data channels, and implementation this task for reconfigurable computing systems requires parallel-pipeline computations organization replace parallel computations organiation. For using parallel-pipeline computations organization, preliminarily have produce performance reduction parallel computational structure. Each operator has routed to computational structure sequentially (bit by bit) to save computational resources and reduces equipment downtime. Storing iterated functions system coefficients for image encoding has been introduced in data structure, which correlates between corresponding parameters the numbers of rank and domain blocks. Applying this approach for parallel-pipeline programs allows scaling computing structure to plurality programmable logic arrays (FPGAs). Task implementation on the reconfigurable computer system Tertius-2 containing eight FPGAs 15 000 times provides performed acceleration relatively with universal multi-core processor, and 18 – 25 times whit to existing solutions for FPGAs.

Improving Fractal Image Compression Scheme through Quantization Operation

We explore the transform coefficients of fractal and exploit new method to improve the compression capabilities of these schemes. In most of the standard encoder/ decoder systems the quantization/ de-quantization managed as a separate step, here we introduce new way (method) to work (managed) simultaneously. Additional compression is achieved by this method with high image quality as you will see later.

Performance analysis of a new fractal compression method for medical images based on fixed partition

Applications of image compression have been gaining importance over the years in medical fields. The medical imaging modalities produced a large amount of information on all levels of hospital care. This information, in the form of images, needs to be stored for future references. While compressing the medical images, it is necessary to maintain high diagnostic quality with a high compression rate. Several image compression approaches have been developed towards the direction of the storage space problem in such a way that the doctors accurately and reliably diagnose the patient’s diseases from the reconstructed image after decompression. A high compression ratio is required to reduce the storage space due to the large size of medical images. Fractal image compression is a lossy technique to compress the image in a coded form instead of pixels and is differentiated by its long encoding time with a high compression ratio, resolution-independent, fast decoding, and self-similarity. The main purpose of this paper is to present a comparative performance study of the three coding schemes of fractal compression for grayscale medical images based on fixed partition. The first two coding schemes are based on the pixel-pattern measure and the third scheme is a proposed method based on the fractal dimension for complexity measure of range and domain blocks. The comparative study included encoding time, peak signal to noise ratio, and compression ratio, as a result, has been accomplished.

Modified OFS-RDS bat algorithm for IFS encoding of bitmap fractal binary images

This work is an extension of a previous paper (presented at the Cyberworlds 2019 conference) introducing a new method for fractal compression of bitmap binary images. That work is now extended and enhanced through three new valuable features: (1) the bat algorithm is replaced by an improved version based on optimal forage strategy (OFS) and random disturbance strategy (RDS); (2) the inclusion of new similarity metrics; and (3) the consideration of a variable number of contractive maps, whose value can change dynamically over the population and over the iterations. The first feature improves the search capability of the method, the second one improves the reconstruction accuracy, and the third one computes the optimal number of contractive maps automatically. This new scheme is applied to a benchmark of two binary fractal images exhibiting a complex and irregular fractal shape. The graphical and numerical results show that the method performs very well, being able to reconstruct the input images with high accuracy. It also computes the optimal number of contractive maps in a fully automatic way. A comparative work with other alternative methods described in the literature is also carried out. It shows that the presented method outperforms the previous approaches significantly.

Computational complexity of fractal image compression algorithm

This study presents insights into the computational complexity of fractal image compression (FIC) algorithms. Unlike JPEG, a fractal encoder necessitates more CPU time in contrast to the decoder. The study examines various factors that impact the encoder and its computational cost. Many researchers have dedicated themselves to the field of fractal encoding to overcome the computational cost of the FIC algorithm. Here, this study offers a look over the approaches in the aspect of time complexity. The automated baseline fractal compression algorithm is studied to demonstrate the understanding of delay in the encoder. The study establishes how various approaches trade-off between the quality of decoder, compression ratio, and CPU time. The experiment section shows the bargain between fidelity criteria of the baseline algorithm.

Development and analysis of IWT-SVD and DWT-SVD steganography using fractal cover

The assurance of secret data transmitted over the Internet and confining its access to explicit grouped information has become a significant security and protection issue. To hide the presence of such information, a robust and blind color image steganography algorithm, using fractal cover images, Singular Value Decomposition (SVD), Integer Wavelet Transform (IWT), and Discrete Wavelet Transform (DWT) is proposed in this paper. The proposed algorithm conceals the color secret image intelligently inside a fractal cover image thus creating a unique stego-image that is virtually a replica of the original cover image. The novelty of this proposed blind image hiding method lies in the fact that a small file size of a unique fractal image can be used to conceal a large amount of information payload. The fractal cover images can be implemented without debasing its quality to make the shrouded information sufficiently strong against image processing attacks. The algorithm possesses features like robustness, imperceptibility, security, and greater hiding capacity due to the application of fractal compression, DWT-SVD, and IWT-SVD hybrid transform schemes. The secret image is inserted in U and V components of the fractal cover with a scaling factor based on the HVS model and a stego-image with sufficiently large keyspace is created. Furthermore, the proposed work compares the performance analysis and security offered by IWT- SVD and DWT- SVD hybrid combinations for different fractal covers using certain metrics like PSNR (Peak Signal to Noise Ratio), MSE (Mean Square Error), SSIM (Structural Similarity Index), BRISQUE (Blind/ Reference less Image Spatial Quality Evaluator) score and Bits per pixel (BPP). The results prove that image degradation is very less (less than 0.6%) in the proposed algorithm even when the secret image file size is more than double the file size of the fractal cover image which also saves the bandwidth and storage requirements.

Survey on Fractal image compression

The need for multimedia applications has increased over the years. Due to this issue, image and video compression becoming an essential problem in reducing time and data storage. Fractal Image Compression (FIC) is a compression technique which results in loss, and we can have large amounts of compression. This scheme works by classifying an image into blocks and uses Contractive Mapping. Some of FICs advantages can be expressed as follows: comparing with other standard compression techniques, it has a good interchange between PNSR and compression ratio and it zooms the image without reducing the quality due to its resolution independent nature. The main FICs drawback, is its complexity in encoding and lack of speed.

Optimal Management of the Multimedia Application

The need for multimedia applications has increased over the years. Due to this issue, image and video compression becoming an essential problem in reducing time and data storage. Fractal Image Compression (FIC) is a compression technique which results in loss, and we can have large amounts of compression. This scheme works by classifying an image into blocks and uses Contractive Mapping. Some of FICs advantages can be expressed as follows: comparing with other standard compression techniques, it has a good interchange between PNSR and compression ratio and it zooms the image without reducing the quality due to its resolution independent nature. The main FICs drawback, is its complexity in encoding and lack of speed.