Enhanced Image Compression Using Fractal and Tree Seed-Bio Inspired Algorithm

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.

The image partitioning scheme in fractal image compression is one of the important aspect for enhancement of performance. In this paper, an adaptive quardtree partitioning scheme is proposed where the entire image is sub-divided recursively into four sub-images. The partitioning points are selected adaptively in a image context-dependent way instead of middle points of the image sides as in quardtree partitioning scheme. Biased successive differences of sum of pixel values of rows of the image are calculated to divide the image row-wise into two sub-images. Then, each sub-image is farther divided column-wise into two parts using biased successive differences of sum of pixel values of columns of the subimage. Then, a fractal image compression technique is proposed based on the proposed partitioning scheme. The comparison of the compression ratio and PSNR are done between fractal image compression with quardtree and proposed adaptive quardtree partitioning schemes. The comparison of the compression time between the same is also done. The fractal image compression with proposed partitioning scheme offers better compression rates most of the times with comparatively improved PSNR. But, the compression time of the fractal image compression with proposed partitioning scheme is much more than its counterpart.

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.

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.

Approximation of an image by the attractor evolved through iterations of a set of contractive maps is usually known as fractal image compression. The set of maps is called iterated function system (IFS). Several algorithms, with different motivations, have been suggested towards the solution of this problem. But, so far, the theory of IFS with probabilities, in the context of image compression, has not been explored much. In the present article we have proposed a new technique of fractal image compression using the theory of IFS and probabilities. In our proposed algorithm, we have used a multiscaling division of the given image up to a predetermined level or up to that level at which no further division is required. At each level, the maps and the corresponding probabilities are computed using the gray value information contained in that image level and in the image level higher to that level. A fine tuning of the algorithm is still to be done. But, the most interesting part of the proposed technique is its extreme fastness in image encoding. It can be looked upon as one of the solutions to the problem of huge computational cost for obtaining fractal code of images.

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.

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.

Images occupy the increasing part of the medical information systems. The Large volume of image contents needs to be compressed for effective storage and transmission. Fractal Image Compression (FIC) is a technique based on Quad tree decomposition. This compression represents an image by a contractive Affine transforms. In the existing literatures this technique has been analyzed mostly on natural images and found to be efficient. In this paper an attempt is made with medical images namely MRI, CT, Angiogram and Ultrasounds. The performance of FIC is compared with traditional SPIHT compression technique in terms of PSNR, compression Ratio, Encoding and Decoding time. From the simulation results, it is inferred that FIC technique outperforms SPIHT in terms of compression ratio with acceptable quality of reconstructed image which makes it suitable for medical image transmission applications.

This work presents Fixed Point Theorems (FPT) on Digital Images (DI) based on the Banach contraction concept developed. The study aims to develop the application of Banach Contraction Mapping Theory (BCMT) for DI, which was presented. The following finding generates a single Fixed Point (FP) for DI, exploring the core idea of DI and implementing the FPT in the context of Digital Image Compression (DIC). Fractal Image Compression (FIC) is a standard method for DIC. It is founded on a search for an object that is accurately in the image. However, a significant problem with DIC is its computational weight. The study proposed a method to reduce data transmission time by applying Image Compression (IC). It highlights the challenges of maximizing Image Quality (IQ) or reducing transmission time for definite IQ. The classic FIC method, which uses non-linear contractive mapping as a constant contractive factor, can attain this.

The main advantage of image compression is the rapid transmission of data. The conventional compression techniques exploit redundancy in images that can be encoded. The main idea is to remove redundancies when the image is to be stored and replace it back when the image is reconstructed. But the compression ratio of this technique is quite insignificant, and hence is not a suitable candidate for an efficient encoding technique. Other methods involve removing high frequency Fourier coefficients and retaining low frequency ones. This method uses discrete cosine transforms(DCT) and is used extensively in different flavors pertaining to the JPEG standards. Fractal compression provides resolution-independent encoding based on the contractive function concept. This concept is implemented using attractors (seed) that are encoded/copied using affine transformations of the plane. This transformation allows operations such as, skew, rotate, scale, and translate an input image which is in turn is extremely difficult or impossible to perform in JPEG images without having the problem of pixelization. Further, while decoding the fractal image, there exist no natural size, and thus the decoded image can be scaled to any output size without losing on the detail. A few years back fractal image was a purely a mathematical concept but with availability of cheap computing power like graphical processor units (GPUs) from Nvidia Corporation its realization is now possible graphically. The fractal compression is implemented using MatLab programming interface that runs on GPU clusters. The GPUs consist of many cores that together give a very high computing speed of over 24 GFLOPS. The advantage of fractal compression can have varied usage in satellite surveillance and reconnaissance, medical imaging, meteorology, oceanography, flight simulators, extra-terrestrial planets terrain mapping, aircraft body frame design and testing, film, gaming and animation media, and besides many other allied areas.

Image compression play an important role in efficient data storage and faster transmission in multimedia applications. In this paper, a hybrid compression algorithm is proposed combining Quadtree Fractal Image Compression (FIC) and Set Partitioning in Hierarchical Tress (SPIHT) techniques for better compression. First the image is decomposed using wavelet transform. Then Quadtree FIC is used on the approximation sub-band of the decomposed image and SPIHT is applied on all the detailed sub-bands. The performance of the proposed algorithm is assessed on standard images. Compared with the existing methods, it shows the superior results providing better PSNR of 37.07, low encoding time of 1.610 seconds and SSIM of 0.9805 for standard Lena image.

Sparse representation techniques have been found to provide improved results in many signaling and imaging applications. Especially in the field of image compression, this technique is able to compress the images with higher compression ratio and is also able to retrieve back the compressed image with good quality and resolution. In this paper, Wavelet and Sparse based image compression technique is presented. Using Discrete Wavelet Transform (DWT), the image to be compressed is initially decomposed into approximation and detail coefficients. The approximation coefficients are encoded directly with lossless encoding technique. In the case of detailed coefficients, their sparse representations are obtained using learned dictionary and these sparse vectors are quantized and encoded. Inverse discrete wavelet transform (IDWT) is applied with the estimated detail and approximation coefficients at the decompression stage, to retrieve back the decompressed image. They key issue of learning appropriate dictionaries for obtaining the sparse vectors is addressed in this paper. The proposed algorithm is tested on several standard test images and has been validated with popular metrics namely Peak signal to noise ratio (PSNR), Structural similarity index (SSIM) and Correlation coefficient.

The demand for images in video sequences and computer animation has increased drastically over the years. This gives attention on an important issue of compression, resulting into reduction in cost of data storage and transmission. For still image compression JPEG is used world -wide. But alternative methods are also being explored; Fractal image compression is one of them. It is based on the self-similarity property to find out the best match within the image itself. This property is used to generate a fractal code. In this paper, the new approach for fractal image compression using genetic algorithm with ranking select mechanism is proposed. This proposed algorithm is applied on fractal as well as non-fractal images and the experimental result shows that the encoding time for both types of images is greatly reduced while maintaining their quality intact.

This paper presents a quadtree partitioning fractal image compression (QPFIC) method used for the partial discharge (PD) image remote recognition system. Self-similarity in PD images is the premise of fractal image compression and is described for the typical PD images acquired from defect model experiments in laboratory. Influences of fractal image compression on a group of PD image features are discussed. Fifty PD data samples are used to qualify the QPFIC to be used in remote PD pattern recognition. Analysis results show that the QPFIC method produces errors of the computational features. Such errors could not influence the PD image recognition results under the control of the PD image compression errors.

Due to proper use of the image sparsity, CS (compressed sensing) image compression has made great achievements in the field of image compression without the constraint of Nyquist sampling law. A great deal of researches indicate that there exist obvious statistical and structural priors regularity for image information distribution, while traditional CS image compression algorithms only use the sparse characteristic of the image information. In this paper, we propose a CS image reconstruction algorithm based on the joint statistical and structural priors which can achieve efficient image reconstruction via a small amount of measurements. With the full use of inter-scale and intra-scale relations of the sparse coefficients, we optimize the iterative hard thresholding CS algorithm specifically by building a GSM model to constrain the local coefficients distribution statistically, and a tree model to constrain the global coefficients distribution structurally. Extensive simulations have been conducted and the results show that the proposed method has achieved a considerable promotion both on the speed and the PSNR gain of image reconstruction, compared with the traditional recovery algorithms under the same compression ratio.