Fractal Coding Algorithm Research Articles

Orthogonal sparse fractal coding algorithm based on image texture feature

Fractal image compression coding algorithm is a novel image compression technology; however, the long encoding time and unacceptable image reconstruction quality remain the primary obstacles in practical application. The purpose of this study is to improve the coding quality from the perspective of grey level transform and feature extraction. In this study, a novel orthogonal sparse fractal coding algorithm based on image texture feature is proposed. The authors define a normalised version as the new grey description feature of the image block so that two improved methods are scientifically combined in theory and algorithm. First, orthogonal sparse grey level transform based on sparse decomposition improves image reconstruction quality and decoding speed. Then, the similarity measure matrix, which stores the variance feature between range blocks and domain blocks, is used to reduce redundancies and encoding time. Simulation results show that the proposed algorithm in this study can obtain better image reconstruction quality and speed up encoding time significantly as compared to the conventional fractal coding schemes.

Underwater Acoustic Image Encoding Based on Interest Region and Correlation Coefficient

It is difficult for the conventional image compression method to achieve good compression effect in the underwater acoustic image (UWAI), because the UWAI has large amount of noise and low correlation between pixel points. In this paper, fractal coding is introduced into UWAI compression, and a fractal coding algorithm based on interest region is proposed according to the importance of different regions in the image. The application problems of traditional quadtree segmentation in UWAIs was solved by the range block segmentation method in the coding process which segmented the interest region into small size and the noninterest region into large size and balanced the compression ratio and the decoded image quality. This paper applies the classification, reduction codebook, and correlation coefficient matching strategy to narrow the search range of the range block in order to solve the problem of the long encoding time and the calculation amount of encoding process is greatly reduced. The experimental results show that the proposed algorithm improves the compression ratio and encoding speed while ensuring the image quality of important regions in the UWAI.

Fractal Depth Map Sequence Coding Algorithm with Motion-vector-field-based Motion Estimation

Three-dimensional video coding is one of the main challenges restricting the widespread applications of 3D video and free viewpoint video. In this paper, a novel fractal coding algorithm with motion-vector-field-based motion estimation for depth map sequence is proposed. We firstly add pre-search restriction to rule the improper domain blocks out of the matching search process so that the number of blocks involved in the search process can be restricted to a smaller size. Some improvements for motion estimation including initial search point prediction, threshold transition condition and early termination condition are made based on the feature of fractal coding. The motion-vector-field-based adaptive hexagon search algorithm on the basis of center-biased distribution characteristics of depth motion vector is proposed to accelerate the search. Experimental results show that the proposed algorithm can reach optimum levels of quality and save the coding time. The PSNR of synthesized view is increased by 0.56 dB with 36.97% bit rate decrease on average compared with H.264 Full Search. And the depth encoding time is saved by up to 66.47%. Moreover, the proposed fractal depth map sequence codec outperforms the recent alternative codecs by improving the H.264/AVC, especially in much bitrate saving and encoding time reduction.

Hybrid Prediction and Fractal Hyperspectral Image Compression

The data size of hyperspectral image is too large for storage and transmission, and it has become a bottleneck restricting its applications. So it is necessary to study a high efficiency compression method for hyperspectral image. Prediction encoding is easy to realize and has been studied widely in the hyperspectral image compression field. Fractal coding has the advantages of high compression ratio, resolution independence, and a fast decoding speed, but its application in the hyperspectral image compression field is not popular. In this paper, we propose a novel algorithm for hyperspectral image compression based on hybrid prediction and fractal. Intraband prediction is implemented to the first band and all the remaining bands are encoded by modified fractal coding algorithm. The proposed algorithm can effectively exploit the spectral correlation in hyperspectral image, since each range block is approximated by the domain block in the adjacent band, which is of the same size as the range block. Experimental results indicate that the proposed algorithm provides very promising performance at low bitrate. Compared to other algorithms, the encoding complexity is lower, the decoding quality has a great enhancement, and the PSNR can be increased by about 5 dB to 10 dB.

A novel fractal coding method based on M-J sets.

In this paper, we present a novel fractal coding method with the block classification scheme based on a shared domain block pool. In our method, the domain block pool is called dictionary and is constructed from fractal Julia sets. The image is encoded by searching the best matching domain block with the same BTC (Block Truncation Coding) value in the dictionary. The experimental results show that the scheme is competent both in encoding speed and in reconstruction quality. Particularly for large images, the proposed method can avoid excessive growth of the computational complexity compared with the traditional fractal coding algorithm.

Comparison of fractal coding methods for medical image compression

In this study, the performance of fractal-based coding algorithms such as standard fractal coding, quasi-lossless fractal coding and improved quasi-lossless fractal coding are evaluated by investigating their ability to compress magnetic resonance images (MRIs) based on compression ratio, peak signal-to-noise ratio and encoding time. For this purpose, MRI head scan test sets of 512 × 512 pixels have been used. A novel quasi-lossless fractal coding scheme, which preserves important feature-rich portions of the medical image, such as domain blocks and generates the remaining part of the image from it, has been proposed using fractal transformations. One of the biggest tasks in fractal image compression is reduction of encoding computation time. A machine learning-based model is used for reducing the encoding time and also for improving the performance of the quasi-lossless fractal coding scheme. The results show a better performance of improved quasi-lossless fractal compression method. The quasi-lossless and improved quasi-lossless fractal coding algorithms are found to outperform standard fractal coding thereby proving the possibility of using fractal-based image compression algorithms for medical image compression. The proposed algorithm allows significant reduction of encoding time and also improvement in the compression ratio.

Research and Implementation of Fast Image Fractal Coding Algorithm

Image is one of the most important carriers for communication in our life, and it’s the utmost medium containing information. As all we known, the data quantity of digital image is so large that it should be compressed for high-speed transmission and store. So image encoding has become one of the key technologies on which the digital society depends.

Real time fractal image coder based on characteristic vector matching

Fractal coding algorithm has many applications including image compression. In this paper a classification scheme is presented which allows the hardware implementation of the fractal coder. High speed and low power consumption are the goal of the suggested design. The introduced method is based on binary classification of domain and range blocks. The proposed technique increases the processing speed and reduces the power consumption while the qualities of the reconstructed images are comparable with those of the available software techniques. In order to show the functionality of the proposed algorithm, the architecture was implemented on a FPGA chip. The application of the proposed hardware is shown in image compression. The resulted compression ratios, PSNR error, gate count, compression speed and power consumption are compared with the existing designs. Other applications of the proposed design are feasible in certain fields such as mass–volume database coding and also in video coder’s block matching schemes.

An efficient fractal image coding algorithm using unified feature and DCT

Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.

A Classification Algorithm Based on Regions' Luminance Distribution Applying to Fractal Image Compression

This paper present three characteristic functions which can express the luminance distribute characteristic much better. Based on these functions a region classification algorithm is presented. The algorithm can offer more information on regions' similarity and greatly improve the efficiency and performance of match seeking in fractal coding. It can be widely applied to many kinds of fractal coding algorithms. Analysis and experimental results proved that it can offer more information on luminance distribute characteristics among regions and greatly improve the decoding quality and compression ratio with holding the running speed.

An efficient fractal image-coding method using interblock correlation search

An efficient fractal image-coding method that exploits the correlation between range blocks is proposed. Four domain blocks mapped by the precious neighboring range blocks are considered as the good candidate blocks of the input range block. Experimental results show that when the proposed method is implemented with a fast fractal coding algorithm, it can further reduce the encoding time and bit rate with insignificant loss of image quality.

Variable tree size fractal compression for wavelet pyramid image coding

Abstract Pyramidal wavelet decomposition provides a hierarchical data structure for image representation which is suitable for further quantization and compression. Through discrete wavelet transform, image signals are decomposed into multiresolution and multi-frequency subbands with a set of tree-structured coefficients. The coefficients which have the same spatial location but with different resolution and different orientation can be organized into wavelet subtree. This efficient representation of image signals has achieved superior coding performance in wavelet-based image compression. In this paper, a novel variable tree partition algorithm is introduced which can efficiently split the wavelet subtrees according to the local details. Then a new variable size wavelet-subtree-based fractal coding algorithm is proposed to obtain a good trade-off between image quality and compression ratio. The self-similarities among wavelet subtrees are successfully exploited in the fractal coding method by predicting the coefficients at finer scales from those at coarser scales through proper affine transformation. Experimental results show a gain over JPEG of 5–6 dB in PSNR with even a slightly higher compression ratio (around 60 : 1 to 70 : 1). A slight gain in terms of coding efficiency is also achieved when compared to a method proposed by Davis, which also applies variable tree size wavelet fractal coding, but the complexity has been significantly reduced by avoiding iterative optimization procedures.

Fractal block coding in residue domain

A new block-based fractal image coding algorithm called Fractal Block Coding in Residue Domain (FBCRD) is proposed. In basic Fractal Block Coding (FBC) algorithm, each block (called range block) is encoded by an affine mapping from a domain block within the same image to itself. The decoder uses the parameters of these mappings to synthesize the reconstructed image through an iterative procedure. FBCRD is a modification of basic FBC. In FBCRD, range blocks and domain blocks are all residue blocks subtracted from their block means and both the parameters of affine mappings and block means are coded. This modification leads to fewer iterations at the decoder. An optimized decoding strategy is also introduced which reduces total decoding time by more than half of that of basic FBC. This improvement is favorable for real time implementation of fractal image compression.

A Fractal Image Coding Scheme Based on Norm

In this paper we discuss the metric used for the search of self-similarity at different scales in fractal coding of images. It is well known that the quality of decoded images depends directly on the efficiency of the measurement of the self-similarity between objects of the original image. We present two coding schemes based on L_2 and L_{infinite} metrics. The L_2 metric, widely used in fractal coding algorithms, measures a global distortion. On the contrary, L_{infinite} gives the maximum grey level error between the pixels of two objects and enables this local error to be controlled. The performance of these schemes is compared with various standard images in terms of PSNR and maximum local distortion. L_{infinite} metric speeds up the coding process and avoids local distortion peaks. L_2 provides a better perceptual quality of the decoded images.

Still image coding based on vector quantization and fractal approximation

In this paper, we propose a coding algorithm for still images using vector quantization (VQ) and fractal approximation, in which low-frequency components of an input image are approximated by VQ, and its residual is coded by fractal mapping. The conventional fractal coding algorithms indirectly used the gray patterns of an original image with contraction mapping, whereas the proposed fractal coding method employs an approximated and then decimated image as a domain pool and uses its gray patterns. Thus, the proposed algorithm utilizes fractal approximation without the constraint of contraction mapping. For approximation of an original image, we employ the discrete cosine transform (DCT) rather than conventional polynomial-based transforms. In addition, for variable blocksize segmentation, we use the fractal dimension of a block that represents the roughness of the gray surface of a region. Computer simulations with several test images show that the proposed method shows better performance than the conventional fractal coding methods for encoding still pictures.

Fractal-based image coding with fast decoder convergence

In this paper, a new class of fractal image coders is described. As in previously published fractal coding algorithms, the encoder models each image to be coded as an attractor of a simple affine mapping, and finds the parameters in such a mapping by a blockwise image analysis. The image code consists of the parametric description of the mapping, which is selected to provide the best affine fit to the image in the l 2 sense. The decoder uses the parametric description it receives to synthesize the attractor of the mapping through a simple iterative procedure. Although the resulting coders are strongly related to previously published fractal coders, they are modified in a way that gives exact decoder convergence towards the attractor in the lowest possible number of iterations — typically three or less. In contrast to what has been the case with previous fractal coding algorithms, this number of iterations is image independent. The resulting decoder can be implemented in a computationally very efficient pyramid structure. Also, a coder offering non-iterative decoding is included as a special case. The paper describes the modifications of previously known fractal coders that are necessary to obtain the fast convergence. It is shown that the image quality remains unimpaired by these modifications. The computational complexity of the decoding algorithm in the new coder class is analyzed, and an efficient pyramid structure for the decoder is outlined. Finally, a coding example is given.