Fractal Compression Algorithm Research Articles

Image Encryption Technology Based on Fractal Image Compression Algorithm

As the most commonly used information transmission method, digital images often store a large amount of personal information. To prevent information leakage, encrypting images is essential. Common image encryption techniques suffer from certain limitations, such as overly simple encryption methods and long encryption times. In response to the above issues, this study proposes the Frobenius canonical form image encryption scheme. It calculates the fractal code through the fractal compression algorithm and to encrypt the image, it adjusts the brightness coefficient in the fractal code. To address unsatisfactory correlation coefficients in encrypted images, the Frobenius canonical form image encryption is improved by introducing the Arnold transformation encryption, which combines the two methods to reduce correlation coefficients. Finally, the knight tour algorithm is put forward. In response to the long image scrambling time in the knight tour algorithm, the Tetragonal theorem is combined with the scheme to encrypt the image. It is then re-encrypted using the Frobenius canonical form. The experimental findings illustrate that when using Frobenius canonical form, Arnold transformation combined with Frobenius canonical form, and the tetragonal algorithm combined with knight tour algorithm to encrypt Lena images, the three decryption methods correspond to image similarity of over 70%, over 80%, and over 90%, respectively. Combining the tetragonal algorithm and the knight tour algorithm can significantly increase the security of image encryption.

Comprehensive Study of Compression and Texture Integration for Digital Imaging and Communications in Medicine Data Analysis

In response to the COVID-19 pandemic and its strain on healthcare resources, this study presents a comprehensive review of various techniques that can be used to integrate image compression techniques and statistical texture analysis to optimize the storage of Digital Imaging and Communications in Medicine (DICOM) files. In evaluating four predominant image compression algorithms, i.e., discrete cosine transform (DCT), discrete wavelet transform (DWT), the fractal compression algorithm (FCA), and the vector quantization algorithm (VQA), this study focuses on their ability to compress data while preserving essential texture features such as contrast, correlation, angular second moment (ASM), and inverse difference moment (IDM). A pivotal observation concerns the direction-independent Grey Level Co-occurrence Matrix (GLCM) in DICOM analysis, which reveals intriguing variations between two intermediate scans measured with texture characteristics. Performance-wise, the DCT, DWT, FCA, and VQA algorithms achieved minimum compression ratios (CRs) of 27.87, 37.91, 33.26, and 27.39, respectively, with maximum CRs at 34.48, 68.96, 60.60, and 38.74. This study also undertook a statistical analysis of distinct CT chest scans from COVID-19 patients, highlighting evolving texture patterns. Finally, this work underscores the potential of coupling image compression and texture feature quantification for monitoring changes related to human chest conditions, offering a promising avenue for efficient storage and diagnostic assessment of critical medical imaging.

An Improved Robust Fractal Image Compression Based on M-Estimator

In this paper, a robust fractal image compression method based on M-estimator is presented. The proposed method applies the M-estimator to the parameter estimation in the fractal encoding procedure using Huber and Tukey’s robust statistics. The M-estimation reduces the influence of the outliers and makes the fractal encoding algorithm robust to the noisy image. Meanwhile, the quadtree partitioning approach has been used in the proposed methods to improve the efficiency of the encoding algorithm, and some unnecessary computations are eliminated in the parameter estimation procedures. The experimental results demonstrate that the proposed method is insensitive to the outliers in the noisy corrupted image. The comparative data shows that the proposed method is superior in both the encoding time and the quality of retrieved images over other robust fractal compression algorithms. The proposed algorithm is useful for multimedia and image archiving, low-cost consumption applications and progressive image transmission of live images, and in reducing computing time for fractal image compression.

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.

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.

计算全息三维显示的数据压缩编码技术

Holographic three-dimensional(3D) display can reconstruct the light field of a real scene, providing all depth cues and becoming one of the best solutions for true 3D display. Computer-generated holographic 3D display only needs to know the mathematical description of the object light wave, can flexibly control the wavefront, and display a virtual 3D object. However, the huge amount of data and the amount of calculations hinder the practical application of computer-generated holographic 3D display. This paper presented data compression coding techniques for multiple stages in computer-generated holographic 3D display, including sparse sampling of 3D objects, optimization and parameter optimization of holographic 3D video compression coding, holographic fractal compression algorithm, effectively reducing the amount of data. And the parallel computing capabilities of GPUs were utilized to enable fast calculation of holograms.

A Lossless hybrid wavelet-fractal compression for welding radiographic images.

In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.

Further investigation on adaptive search

Adaptive search is one of the fastest fractal compression algorithms and has gained great success in many industrial applications. By substituting the luminance offset by the range block mean, the authors create a completely new version for both the encoding and decoding algorithms. In this paper, theoretically, they prove that the proposed decoding algorithm converges at least as fast as the existing decoding algorithms using the luminance offset. In addition, they prove that the attractor of the decoding algorithm can be represented by a linear combination of range-averaged images. These theorems are very important contributions to the theory and applications of fractal image compression. As a result, the decoding image can be represented as the sum of the DC and AC component images, which is similar with discrete cosine transform or wavelet transform. To further speed up this algorithm and reduce the complexity of range and domain blocks matching, they propose two improvements in this paper, that is, employing the post-quantisation and geometric neighbouring local search to replace the currently used pre-quantisation and the global search, respectively. The corresponding experimental results show the proposed encoding and decoding algorithms can provide a better performance compared with the existing algorithms.

A novel image recovery method based on discrete cosine transform and matched blocks

In this paper, we propose a method for image recovery based on Discrete Cosine Transform (DCT) and finding the best matched blocks by using a part of the fractal compression algorithm. At the same time, we propose a new check algorithm for checking if image blocks are tampered. First, the original image is divided into small blocks. The best matched block of each small block is searched in a particular way. Then the matching information is embedded as backup into other blocks. For the ones that fail to find the best matched blocks, DCT is applied on them and then quantized to be the backup. In order to prevent the backup of the tampered blocks from damaging, we generate 3 backups for each block and embed them into different quadrants. On the receiving side, the tampering check bits are extracted to localize the tampered areas, and the backup bits are used to restore the contents of the tampered regions. The experimental results have proved a good restorability of this algorithm, and the lower the tampering rate is, the better quality of restored content can be obtained.

Speeding Up Fractal Image Compression by Genetic Algorithms

The main problem with all fractal compression implementation is execution time. Algorithms can spend hours to compress a single image. Most of the major variants of the standard algorithm for speeding up computation time have led to a bad-quality or a lower compression ratio. For example, the Fisher's [7] proposed classification pattern greatly accelerated the algorithm, but image quality was poor due to the search-space reduction imposed by the classification, which eleminates a lot of good solutions. By using genetic algorithms to address the problem, we optimize the domain blocks search. We explore all domain blocks present in the image but not in exhaustive way (like a standard algorithm) and without omitting any possible block (solution) as a classification pattern does. A genetic algorithm is the unique method for satisfying these constraints. And it is a way to do be a random search because the genetic one is directed by fitness selection, which produces optimal solutions. Our goal in this work is to use a genetic algorithm to solve the IFS inverse problem and to build a fractal compression algorithm based on the genetic optimization of a domain blocks search. we have also implemented standard Barnsley algorithm, the Y. Fisher based on classification, and the genetic compression algorithm with quadtree partitioning. A population of transformations was evolved for each range block, and the result is compared with the standard Barnsely algorithm and the Fisher algorithm = based classification. We deduced an optimal set of values for the best parameters combination, and we can also specify the best combination for each desired criteria: best compression ratio, best image quality, or quick compression process. By running many test images, we experimentally found the following set of optimal values of all the algorithm parameters that ensure compromise between execution time and solutions optimality: Population size = 100, Maximum generations = 20, Crossover rate = 0.7, Mutation rate = 0.1, RMS limit = 5, Decomposition error limit = 10, Flips and isometrics count = 8. In our proposed algorithm, results were much better than those obtained both vences and Rudomin [5] and Lankhorst [4] approaches.

Fast fractal coding of subbands using a non-iterative block clustering

We propose a new image coding scheme which uses a fast non-iterative algorithm for block clustering in fractal coding of wavelet transform coefficients. The original image is first decomposed into subbands containing information in different spatial directions and different scales, using an orthogonal wavelet filter bank. Subbands are encoded using local iterated function systems (LIFS) with range and domain blocks presenting horizontal or vertical directionalities. Their sizes are adapted to the correlation lengths and the resolution of each subband. This hybrid compression scheme allows to use the natural classification obtained by using a subband decomposition and reduce the computational complexity by a 12:1 factor. In order to increase this speedup, we propose a fast non-iterative algorithm for block clustering which classifies the directional domain and range blocks and leads to an accelerated LIFS generation in each subband. The proposed approach reduces the computational complexity of the basic fractal compression algorithm by a 50:1 factor and gives better PSNR/bit rate results, especially for images presenting directionalities.

Fast fractal compression of greyscale images

A new algorithm for fractal compression of greyscale images is presented. It uses some previous results allowing the compression process to be reduced to a nearest neighbors problem, and is essentially based on a geometrical partition of the image block feature space. Experimental comparisons with previously published methods show a significant improvement in speed with no quality loss.

Performance analysis of distributed implementations of a fractal image compression algorithm

Fractal image compression provides an innovative approach to lossy image encoding, with a potential for very high compression times, however, the procedure has proved feasible in only a limited range of commercial applications. In the paper the authors demonstrate that, due to the independent nature of fractal transform encoding of individual image segments, fractal image compression performs well in a coarse-grain distributed processing system. A sequential fractal compression algorithm is optimized and parallelized to execute across distributed workstations and an SP2 parallel processor using the parallel virtual machine (PVM) software. The system utilizes both static and dynamic load allocation to obtain substantial compression time speedup over the original, sequential encoding implementation. Considerations such as workload granularity and compression time versus number of processors and RMS tolerance values are also presented.