Fractal Image Compression Scheme Research Articles

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.

Low-Delay Parallel Architecture for Fractal Image Compression

This paper presents an efficient hardware architecture for implementing fractal image compression (FIC) algorithm aimed toward image compression with improved encoding speed. The proposed architecture follows the full-search-based FIC scheme. Parallel processing has been effectively used in the present work to achieve the goal of reducing the time complexity of the encoder. This architecture requires a total of $$2n+2$$2n+2 clock cycles for executing the set of operations consisting of fetching the pixels, calculating the mean of range and domain blocks and doing their mapping, computing the error, and storing the fractal parameter in a memory with n number of pixels in the range block. Further, this architecture does not make use of any preprocessing operations as specified in literature and utilizes the benefits of isometric transformation without requiring additional cycles for every single matching operation. Effective application of isometric transformation has also led to memory reduction of nearly 67 %. Again, in the present work, the use of multipliers has been avoided to save the chip area, to reduce hardware complexity, and to enhance the encoding speed. The operation of transforming contracted domain block with a zero-mean domain block has facilitated relatively fast convergence at the decoder. PSNR above 30dB for a range block of size $$4\times 4$$4×4 has been achieved by the proposed architecture, which is comparable to that realizable by other architectures. The proposed design has been coded in Verilog HDL, has been implemented in Xilinx Virtex-5 FPGA, and operates at a clock frequency of 75.52 MHz.

A Novel Fractal Image Compression Scheme With Block Classification and Sorting Based on Pearson's Correlation Coefficient

Fractal image compression (FIC) is an image coding technology based on the local similarity of image structure. It is widely used in many fields such as image retrieval, image denoising, image authentication, and encryption. FIC, however, suffers from the high computational complexity in encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. In this paper, a new FIC scheme is proposed based on the fact that the affine similarity between two blocks in FIC is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them. First, all blocks in the range and domain pools are chosen and classified using an APCC-based block classification method to increase the matching probability. Second, by sorting the domain blocks with respect to APCCs between these domain blocks and a preset block in each class, the matching domain block for a range block can be searched in the selected domain set in which these APCCs are closer to APCC between the range block and the preset block. Experimental results show that the proposed scheme can significantly speed up the encoding process in FIC while preserving the reconstructed image quality well.

Fractal image compression based on spatial correlation and hybrid genetic algorithm

In order to solve the high complexity of the conventional encoding scheme for fractal image compression, a spatial correlation hybrid genetic algorithm based on the characteristics of fractal and partitioned iterated function system (PIFS) is proposed in this paper. There are two stages for the algorithm: (1) Make use of spatial correlation in images for both range and domain pool to exploit local optima. (2) Adopt simulated annealing genetic algorithm (SAGA) to explore the global optima if the local optima are not satisfied. In order to avoid premature convergence, the algorithm adopt dyadic mutation operator to take place of the traditional one. Experiment results show that the algorithm convergent rapidly. At the premise of good quality of the reconstructed image, the algorithm saved the encoding time and obtained high compression ratio.

Study on Huber Fractal Image Compression

In this paper, a new similarity measure for fractal image compression (FIC) is introduced. In the proposed Huber fractal image compression (HFIC), the linear Huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. When the original image is corrupted by noises, we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression. The proposed HFIC is one of our attempts toward the design of robust fractal image compression. The main disadvantage of HFIC is the high computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed HFIC is robust against outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.

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.

DCT based simple classification scheme for fractal image compression

In this paper, a fast fractal encoding algorithm using simple classification scheme is proposed. During the encoding process, the range blocks and domain blocks are classified first. Then, each range block is limited to search in the corresponding domain class to find the best match. Since the searching space is reduced, the encoding speed is improved. Three classes of image blocks are defined, which are smooth class, diagonal/sub-diagonal edge class and horizontal/vertical edge class. The classification operation is performed using only the lowest horizontal and vertical DCT coefficients of the given block. Thus the classification scheme is simple and computationally efficient. Moreover, since the classification mechanism is designed according to the edge properties and the intrinsic idea of fractal coding, the quality of the decoded image can be preserved. The thresholds for the classifier are also adaptively determined from the range pool so as to reduce the overhead and to guarantee a stable speedup ratio of 3. Simulation results show that the stable speedup ratio of the proposed algorithm can be achieved and is independent of images while the quality of the decoded image is almost the same as that of the full search method.

Detecting and restoring the tampered images based on iteration-free fractal compression

In current research, fractal image compression scheme has been used to compress images. In this paper, we apply this technique to refine characteristic values of a specific image and embed the characteristic values into the least significant bits of pixels in the image. Once the picture is damaged by an intruder, the system can detect the tampered blocks and restore them using characteristic values without requiring the original image. From experimental results, we see that the proposed scheme can precisely achieve the detection of a damaged image and improve the performance of image restoration.

Low-complexity fractal-based image compression using two-stage search strategy

A fractal image compression scheme is presented which incorporates the vector quantizer (VQ) to reduce the computational complexity in the encoding phase. The high-detail blocks of an input image are approximated by a fast fractal coding, and the low-detail blocks are encoded by the VQ technique. In fractal image coding, most of the time is spent on finding a close match between a range block and a large pool of domain blocks. We propose a two-stage search algorithm to reduce the search space of the domain pool. First, a fast and simple binary pattern matching algorithm is proposed to extract a small pool of candidate domains, and then the gray-level-matching algorithm is used to find the best match from the candidates. In addition, a variable block-size segmentation method is used in our coding system to further improve the image quality. It is shown that the average encoding time is short, and the average speedup factor of 45 is achieved, as compared to the full search fractal coding. Simulation results also show that the proposed scheme can achieve better image quality and higher compression ratio than other fast fractal-based coding schemes.

Speed-up fractal image compression with a fuzzy classifier

Abstract This paper presents a fractal image compression scheme incorporated with a fuzzy classifier that is optimized by a genetic algorithm. The fractal image compression scheme requires to find matching range blocks to domain blocks from all the possible division of an image into subblocks. With suitable classification of the subblocks by a fuzzy classifier we can reduce the search time for this matching process so as to speedup the encoding process in the scheme. Implementation results show that by introducing three image classes and using fuzzy classifier optimized by a genetic algorithm the encoding process can be speedup by about 40% of an unclassified encoding system.

An Adaptive Partition for Fractal Image Coding

In this paper we present a flexible partitioning scheme for fractal image compression, based on the Delaunay triangles. The aim is to have the advantage of triangular blocks over squares, in terms of adaptivity to the image content. In a first step, the triangulation is computed so that the triangles are more densely distributed in regions containing interesting features such as corners and edges, or so that they tend to run along the strong edges in the image. In a second step we merge adjacent triangles into quadrilaterals, in order to decrease the number of blocks. Quadrilaterals permit a reduction of the number of local contractive affine transformations composing the fractal transform, and thus to increase the compression ratio, while preserving the visual quality of the decoded image.

Codebook Clustering by Self-Organizing Maps for Fractal Image Compression

A fast encoding scheme for fractal image compression is presented. The method uses a clustering algorithm based on Kohonen's self-organizing maps. Domain blocks are clustered, yielding a classification with a notion of distance which is not given in traditional classification schemes.

Fractal image compression based on Delaunay triangulation and vector quantization

Presents a new scheme for fractal image compression based on adaptive Delaunay triangulation. Such a partition is computed on an initial set of points obtained with a split and merge algorithm in a grey level dependent way. The triangulation is thus fully flexible and returns a limited number of blocks allowing good compression ratios. Moreover, a second original approach is the integration of a classification step based on a modified version of the Lloyd algorithm (vector quantization) in order to reduce the encoding complexity. The vector quantization algorithm is implemented on pixel histograms directly generated from the triangulation. The aim is to reduce the number of comparisons between the two sets of blocks involved in fractal image compression by keeping only the best representative triangles in the domain blocks set. Quality coding results are achieved at rates between 0.25-0.5 b/pixel depending on the nature of the original image and on the number of triangles retained.

Parallel Pipelined Fractal Image Compression using Quadtree Recomposition

In this paper we present a model and experimental results for performing parallel fractal image compression using circulating pipeline computation and employing a new quadtree recomposition approach. A circular linear array of processors is employed and utilized in a pipelined fashion. In this approach, a modification of the scheme given by Jackson and Blom, quadtree sub-blocks of an image are iteratively recombined into larger blocks for fractal coding. For complex images, this approach exhibits superior parallel runtime performance when compared to a classical quadtree decomposition scheme for fractal image compression, while maintaining high fidelity for reconstructured images. Quantitative results include parallel runtime comparisons with the decomposition approach for several images of varying complexity, an evaluation of attained compression ratios and SNR for reconstructed images. Experimental results using an nCUBE-2 supercomputer are presented.

A neural network to compute the Hutchinson metric in fractal image processing

The Hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing. A neural network is described which can quickly calculate this metric. By combining this with the architecture previously described by the author for implementing the Markov operator of an iterated function system (IFS) on a neural network, a fast method is obtained for determining the distance between a target image and the invariant measure of a trial IFS. This has obvious applications to Barnsley's fractal image compression scheme.