Fractal Block Coding Research Articles

Colour Image Compression Method Based On Fractal Block Coding Technique

Colour Image Compression Method Based On Fractal Block Coding Technique

A Novel Fractal Block Coding Method by Using New Shape-based Descriptor

The basic theory of Jacquin's fractal block coding is to approximate a na tural image by its partial subdivided parts, given that the parts resemble the whole at either the same scale or different scales. The fact that self-similarity most commonly exists within an entire natural image leads to the development of the proposed method that uses arc as the fractal descriptor, in which an arc commonly exists within the entire natural image, named as Arc-Descriptor Fractal Coding (ADFC) method. In the ADFC, each range block is approximated by using the selected arc-descriptor from an optimal pool. This paper experimentally demonstrates the ADFC method on Java and the ADFC system is verified with 5 medical images. The experim ental results indicate the ADFC method can encode and decode the experimental images effectively. The PSNR of the images after encoding can reach 30 dB at limited cost while the CR is less than 17%. The ADFC outperforms Jacquin's method under the comparison of the number of search in matching process. We conclude that the ADFC successfully encodes and decodes image in an efficient s earch during encoding phase without noticeable loss of image quality.

Self-embedding fragile watermarking based on DCT and fast fractal coding

A self-embedding fragile watermarking scheme is proposed in this paper, which is based on Discrete Cosine Transform and fractal compression coding. To overcome the high computational complexity of fractal coding, a fast coding method is also presented that improves the efficiency of fractal block coding in the watermarking procedure. In our algorithm, three kinds of watermarks are generated for image authentication and recovery, which is based on an interleaved and overlapped 8 ×8 image block structure. This makes our method obtain an authentication granularity of 4 ×4 approximately. At the same time, we take advantage of two levels of mapping to select mapping block for every image block. Three versions of recovery watermarks for each block are embedded in different quadrants, which provides another two chances for block recovery in case one is destroyed. Experimental results demonstrate that the proposed scheme not only outperforms conventional self-embedding fragile watermarking algorithms in tamper recovery, but also improves the security against the various counterfeiting attacks.

A multi-purpose digital image watermarking using fractal block coding

In this paper, a new multi-purpose watermarking technique is presented which satisfies both verification and authentication purposes simultaneously by embedding a binary watermark into the image. The proposed method uses a special type of fractal block coding with a local search region with contrast scaling and mean of range block as its parameters. It also utilizes Fuzzy C-Mean clustering to specify the watermark bits. To overcome the high computational complexity of fractal coding, a new simple coding method is also presented which improves the robustness of the watermarking and decreases the run time of fractal block coding in the watermarking procedure. To measure the fragility and robustness of the method to signal distortions such as JPEG compression, median filter, and additive noise, some experiments were employed. The experimental results showed that the proposed method has provided a sensitive authentication and a reliable verification.

A novel fractal image watermarking

A novel watermarking method is proposed to hide a binary watermark into image files compressed by fractal block coding. This watermarking method utilizes a special type of orthogonalization fractal coding method where the fractal affine transform is determined by the range block mean and contrast scaling. Such orthogonalization fractal decoding is a mean-invariant iteration. In contrast, the fractal parameters of classical fractal compression are very sensitive to any change of domain block pool and to common signal and geometric distortion. Hence, it is impossible to directly place a watermark in fractal parameters. The proposed watermark embedding procedure inserts a permutated pseudo-random binary sequence into the quantized range block means. The watermark is detected by computing the correlation coefficient between the original and the extracted watermark. Experimental results show that the proposed fractal watermarking scheme is robust against common signal and geometric distortion such as JPEG compression, low-pass filtering, rescaling, and clipping.

A low-complexity index for fractal image indexing

Fractal signatures are an important statistical property of texture images. Most existing fractal signatures are extracted by computing an image multiscale fractal dimension. Recently, it has been very interesting to see fractal block coding being investigated for image indexing. A second kind of fractal signature is extracted from image fractal codes. This paper investigates how to reduce the complexity of fractal-code signatures based on independence between the fractal parameters of orthogonalization fractal block coding. This independence is used to construct a low-complexity index. The proposed index is compared with existing fractal-dimension signatures using a database of texture images. The results indicate that the proposed index outperforms the fractal-dimension signatures.

Gradient match and side match fractal vector quantizers for images

In this paper, we propose gradient match fractal vector quantizers (GMFVQs) and side match fractal vector quantizers (SMFVQs), which are two classes of finite state fractal vector quantizers (FSFVQs), for the image coding framework. In our previous work, we proposed the noniterative fractal block coding (FBC) technique to improve the decoding speed and the coding performance for conventional FBC techniques. To reduce the number of bits for denoting the fractal code of the range block, the concepts of the gradient match vector quantizers (GMVQs) and the side match vector quantizers (SMVQs) are employed to the noniterative FBC technique. Unlike ordinary vector quantizers, the super codebooks in the proposed GMFVQs and SMFVQs are generated from the affine-transformed domain blocks in the noniterative FBC technique. The codewords in the state codebook are dynamically extracted from the super codebook with the side-match and gradient-match criteria. The redundancy in the affine-transformed domain blocks is greatly reduced and the compression ratio can be significantly increased. Our simulation results show that 15%-20% of the bit rates in the noniterative FBC technique are saved by using the proposed GMFVQs.

A fast fractal image compression coding method

Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block’s neighbours is presented. Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley’s fractal block coding .

Adaptive Schemes for Improving Fractal Block Coding of Images

In this paper, we propose several adaptive methods to improve the fractal block coding (FBC) of still images. First of all, the range of the contrast scaling is adaptively selected according to its statistical property: then, we search for the best quantized value in the selected range. Then, the domain pool of the current range block is predicted using a finite-state method, which uses the information of previous best-match domain blocks and domain pools. The size of the domain pool is automatically adjusted; however, conventional studies can only determine a fixed-size domain pool. Therefore, the search process for finding the best-match domain block in our approach is more flexible. In addition, we propose a finite-state method to estimate the mean (average pixel value) of the current range block by using the means of the previous blocks. From the simulation, we achieve 0.35 dB improvement in peak signal-to-noise ratio and 10.5% reduction in bit rate on average compared with the basic FBC scheme. Finally, the encoding and decoding time of different FBC schemes is also evaluated for completeness.

Merged quadtree fractal image compression

The quadtree method is usually used in fractal block coding, but its efficiency is very low. We propose a new scheme, merged quadtree partitioning (MQP), for efficient image compression. It is an improved quadtree method, and can merge the quadtree nodes on the same level and on the different levels to share one transformation. As the merged nodes describe irregular regions with boundaries approximating the image edges, which need only one transformation, the total number of transformations required by MQP is much less than by the quadtree method. Thus, we obtain a greater compression ratio. In addition, we speed up MQP method by using the relationship between the search of the merged range and that of its parent range, and obtain a shorter encoding time than with other partitioning schemes.

Fast fractal image block coding based on local variances

In fractal image block coding, most of the time is spent on finding a close match between a range block and a large pool of domain blocks. For a large image, this effect becomes aggravated as the domain pool increases exponentially. We propose using the local variances of domain blocks to reduce the search space. By sorting the contracted domain pool according to their local variances and defining an acceptance criterion for a close match, we can confine all the potential close matches to a relatively small sized window to limit the search space. The encoding time can hence be shortened with the decoded image quality as good as that using the full search method. The speedup can be over ten times depending on the complexity of encoded images.

A wavelet-based analysis of fractal image compression

Why does fractal image compression work? What is the implicit image model underlying fractal block coding? How can we characterize the types of images for which fractal block coders will work well? These are the central issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression schemes. Within this framework we are able to draw upon insights from the well-established transform coder paradigm in order to address the issue of why fractal block coders work. We show that fractal block coders of the form introduced by Jacquin (1992) are Haar wavelet subtree quantization schemes. We examine a generalization of the schemes to smooth wavelets with additional vanishing moments. The performance of our generalized coder is comparable to the best results in the literature for a Jacquin-style coding scheme. Our wavelet framework gives new insight into the convergence properties of fractal block coders, and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm. Our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees. Finally, our framework reveals some of the fundamental limitations of current fractal compression schemes.

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.

Fractal block coding: A new method

Fractal image compression[1] is a completely new method to compress images by searching and exploiting the self-similarity of the whole image[2]. Fractal Block Coding (FBC) is a practicable fractal coding scheme with annoying slow encoding speed[3]. In this paper, we classify the image blocks by Classified Vector Quantization (CVQ) technique and present an Adaptive Block Truncation Coding (ABTC) scheme to process the midrange blocks in the image. By this method, we reduce the encoding time to one forty-fifth comparing to ordinary FBC method with little change in compression ratio and a little decreased coded image quality.

Image coding by block prediction of multiresolution subimages

The redundancy of the multiresolution representation has been clearly demonstrated in the case of fractal images, but it has not been fully recognized and exploited for general images. Fractal block coders have exploited the self-similarity among blocks in images. We devise an image coder in which the causal similarity among blocks of different subbands in a multiresolution decomposition of the image is exploited. In a pyramid subband decomposition, the image is decomposed into a set of subbands that are localized in scale, orientation, and space. The proposed coding scheme consists of predicting blocks in one subimage from blocks in lower resolution subbands with the same orientation. Although our prediction maps are of the same kind of those used in fractal block coders, which are based on an iterative mapping scheme, our coding technique does not impose any contractivity constraint on the block maps. This makes the decoding procedure very simple and allows a direct evaluation of the mean squared error (MSE) between the original and the reconstructed image at coding time. More importantly, we show that the subband pyramid acts as an automatic block classifier, thus making the block search simpler and the block matching more effective. These advantages are confirmed by the experimental results, which show that the performance of our scheme is superior for both visual quality and MSE to that obtainable with standard fractal block coders and also to that of other popular image coders such as JPEG.

フラクタルブロック符号化における画像圧縮の高速化

フラクタルブロック符号化における画像圧縮の高速化

Fractal block coding of digital video

A video coding method is proposed which is based upon fractal block coding. The method utilizes a novel three-dimensional partitioning of input frames for which a number of efficient block-matching search methods can be used, and permits spatio-temporal splitting of the input blocks to improve overall-encoding quality. After describing the basic fractal block coding algorithm, the details of the proposed three-dimensional algorithm are presented along with encoding and decoding results from two standard video test sequences, representative of video-conferencing data. These results indicate that average compression rates ranging from 40 to 77 can be obtained with subjective reconstruction quality of video-conferencing quality. The results also indicate that, in order to meet the compression rates required for very low bit rate coding, it is necessary to employ additional techniques such as entropy encoding of the fractal transformation coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fractal image coding: a review

An approach to image coding based on a fractal theory of iterated contractive transformations defined piecewise is described. The main characteristics of this approach are that it relies on the assumption that image redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis, and it approximates an original image by a fractal image, obtained from a finite number of iterations of an image transformation called a fractal code. This approach is referred to as fractal block coding. The general coding-decoding system is based on the construction, for an image to be encoded, of a fractal code-a contractive image transformation for which the original image is an approximate fixed point-which, when applied iteratively on any initial image of the decoder, produces a sequence of images which converges to a fractal approximation of the original. The design of a system for the encoding of monochrome digital images at rates below 1 b/pixel is described. Ideas and extensions from the work of other researchers are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fractal block coding of images

An original method is presented for the efficient fractal approximation of rectangular grey-scale image blocks. Its application to the block coding of images is applied to standard test images, and compared to ADCT coding. Fractal coding by this method is relatively efficient and holds promise for applications in which low computational cost is a priority.

Image coding based on a fractal theory of iterated contractive image transformations

The author proposes an independent and novel approach to image coding, based on a fractal theory of iterated transformations. The main characteristics of this approach are that (i) it relies on the assumption that image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and (ii) it approximates an original image by a fractal image. The author refers to the approach as fractal block coding. The coding-decoding system is based on the construction, for an original image to encode, of a specific image transformation-a fractal code-which, when iterated on any initial image, produces a sequence of images that converges to a fractal approximation of the original. It is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0.5-1.0 b/pixel. The fractal block coder has performance comparable to state-of-the-art vector quantizers.