Isometry-Based Shape-Adaptive Fractal Coding for Images

Fractal image coding is an effective method to eliminate the image redundancy through piecewise self-transformability. The fractal code consists of a set of contractive affine transforms. To improve the performance when a range block experiences large error, we usually partition the range block into square or nonsquare subrange blocks for two- or multilevel fractal coding. In this paper, we find an inherent property of fractal coding that can be used to decide the edge orientation of a range block. Then this property is used for shape-adaptive fractal coding (SAFC). In SAFC, the top-level range block is partitioned into square or nonsquare (rectangle or triangle) subrange blocks for multilevel fractal encoding. Here, the maximum size of the range block can be the same as that of the whole image size while the minimum size is 4×4. In SAFC, no additional computations are required to obtain the edge orientation of a range block. Instead, we propose an edge-orientation detector, where the edge orientation of a range block is obtained during the fractal encoding process. According to our simulation results, SAFC can reduce the bit rate requirement of the conventional fractal coding scheme.     

Two-Dimensional Adaptive Decimation and Interpolation Scheme for Low Bit-Rate Image Coding

A novel image compression scheme based on two-dimensional adaptive decimation is reported in this paper. In this approach, images are encoded with adaptive sampling along the horizontal and vertical directions, and decoded with an edge prediction interpolation algorithm. The method is capable of maintaining reasonable coding fidelity at low bit-rate with good visual quality. As only a small amount of computation is required in the encoding and decoding processes, the compression scheme can be implemented for real time operation with simple hardware and a small amount of memory storage. The proposed scheme had been applied in encoding images at bit-rates between 0.2 and 0.33 bpp and the results are encouraging.     

Iteration-free fractal image coding based on efficient domain pooldesign

The domain pool design is one of the dominant issues which affect the coding performance of fractal image compression. In this paper, we employ the LBG algorithm and propose a block averaging method to design the efficient domain pools based on a proposed iteration-free fractal image codec. The redundancies between the generated domain blocks are reduced by the proposed methods. Therefore, we can obtain the domain pools that are more efficient than those in the conventional fractal coding schemes and thus the coding performance is improved. On the other hand, the iteration process in the conventional fractal coding scheme not only requires a large size of memory and a high computation complexity but also prolongs the decoding process. The proposed iteration-free fractal codec can overcome the problems above. In computer simulation, both the LBG-based and block-averaging methods for the domain pool design in the proposed iteration free scheme achieve excellent performances. For example, based on the proposed block-averaging method, the decoded Lena image has at least a 0.5 dB higher PSNR (under the same bit rate) and an eight-time faster decoding speed than the conventional fractal coding schemes that require iterations.     

On Reversible Skeletonization Using Anchor-Points from Distance Transforms

In many applications thinning of objects is of great interest. We here present a skeletonization algorithm that is based on the idea of iteratively thinning the distance transform of an object layer by layer until either an anchor-point is reached or the connectivity breaks. Our algorithm is general in the sense that any metric and any connectivity can be used. Also, it is based on ideas that are not specific for 2D. The properties of the resulting skeletons are evaluated according to the “Lee–Lam–Suen properties.”     

多波段遥感图像的快速分形编码

分形图像编码用动态迭代过程的参数来表示相应的静态图像数据,可以突破熵压缩编码的理论界限,因而得到广泛的关注.将分形图像编码应用于多波段遥感图像压缩中,根据多波段遥感图像的特点,对基于四叉树分割的快速分形编码方法进行改进,令各个波段图像共享同一四叉树分割方式,同时,利用多波段遥感图像的谱间相关性,缩小仿射变换的搜索匹配空间,以此来提高压缩比和编码速度,实验表明,本方法能显著提高基于四叉树分割的分形编码方法的性能,取得了令人满意的结果.     

基于FGSE的快速分形图像编码算法及其多描述编码方案

本文在基于分形图像编码的多描述编码方案（MDFIC）的基础上,做了两处改进：一是引入提出的基于FGSE的快速分形图像编码算法,以提高编码速度;二是利用相邻值域块均值间的相关性,以减少比特率。实验结果表明,本方案与MDFIC相比,可以在保持解码图像质量几乎不变的情况下,提高编码速度和减少比特率,并具有较高的鲁棒性。     

机动目标的逆合成孔径雷达成像原理与算法

对于非合作的机动目标,由于目标相对于雷达射线的姿态和转速难以测定,而且是时变的,因而给逆合成孔径雷达(ISAR)成像造成较大困难.本文讨论了这种情况下成像的一般原理,并对机动性不太大,散射点子回波多普勒变化满足一阶近似条件时,提出了实用算法.实测数据的处理结果说明新算法是可行的.     

基于平方加权质心特征的快速分形图像压缩编码

分形图像压缩利用自身图像具有的相似性,结合压缩仿射变换减少图像数据的冗余来实现图像数据的压缩,具有压缩比高、恢复简单的特点。然而,分形图像压缩编码也具有编码时间长、计算复杂的缺点。为了解决上述的缺点,提出了基于平方加权质心特征的快速分形图像压缩编码算法,利用平方加权质心特征可以将基本分形图像压缩编码过程中的全局搜索转化为局部搜索,限定搜索范围,减少码本数量,在巨大图像信息量传输和存储过程中,在一定程度上缩短了编码时间。将平方加权质心特征快速分形图像压缩编码算法和双交叉和算法、改进叉迹算法、规范五点和算法进行比较,仿真结果表明,所提算法在恢复质量可接受情况下,编码时间具有巨大优势。     

基于分形编码的图像相似匹配研究

本文以自适应四叉树分割的分形图像编码为基础，研究了极坐极表达下分形码之间的匹配，并在此基础上提出了图像间分形码峰值信噪比的概念和算法，以达到量化图像间相似性的目的，实验证明，这种基于自适应分形编码的图像相似性匹配方法 人的主观判断非常接近，非常适合于用来构建和管理大图像数据库。     

Combining fractal image compression and vector quantization

In fractal image compression, the code is an efficient binary representation of a contractive mapping whose unique fixed point approximates the original image. The mapping is typically composed of affine transformations, each approximating a block of the image by another block (called domain block) selected from the same image. The search for a suitable domain block is time-consuming. Moreover, the rate distortion performance of most fractal image coders is not satisfactory. We show how a few fixed vectors designed from a set of training images by a clustering algorithm accelerates the search for the domain blocks and improves both the rate-distortion performance and the decoding speed of a pure fractal coder, when they are used as a supplementary vector quantization codebook. We implemented two quadtree-based schemes: a fast top-down heuristic technique and one optimized with a Lagrange multiplier method. For the 8 bits per pixel (bpp) luminance part of the 512kappa512 Lena image, our best scheme achieved a peak-signal-to-noise ratio of 32.50 dB at 0.25 bpp.     

Fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms

The objective of this research is to model the mammographic parenchymal and ductal patterns and enhance the microcalcifications using a deterministic fractal approach. According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two-dimensional (2-D) affine transformations. The iterated functions systems and the collage theorem are the mathematical foundations of fractal image modeling. Here, a methodology based on fractal image modeling is developed to analyze and model breast background structures. The authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations. Therefore, microcalcifications can be enhanced by taking the difference between the original image and the modeled image. The authors' results are compared with those of the partial wavelet reconstruction and morphological operation approaches. The results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications. It may also be able to improve the detection and classification of microcalcifications in a computer-aided diagnosis system.     

Content-based image retrieval using block-constrained fractalcoding and nona-tree decomposition

Fractal coding has been proved useful for image compression. In fractal coding, an image is represented by a number of self-transformations (fractal code) by which an approximation of the original image can be reconstructed. The authors present a block-constrained fractal coding scheme and a nona-tree decomposition based matching strategy for content-based image retrieval. In the coding scheme, an image is partitioned into non-overlapped blocks with a size close to that of a query iconic image. The fractal code is generated for each block independently. In the similarity measure of the fractal code, an improved nona-tree decomposition scheme is adopted to avoid matching the fractal code globally in order to reduce computational complexity. The experimental results show that the authors' coding scheme and matching strategy are useful for image retrieval, and compare favourably with two other methods tested in terms of storage usage and computing time     

基于Krawtchouk矩不变量和核模糊聚类的快速分形编码

针对基于分类的快速分形编码方法存在着编码速度与解码质量间的矛盾,鉴于Krawtchouk矩不变量具有在仿射变换下保持不变的特性和核模糊聚类在处理非线性问题上的突出优势,本文首次将这两者引入到分形编码中,提出了基于Krawtchouk矩不变量和核模糊聚类的自适应分类快速分形编码方法。首先根据Domain块的方差将其粗分类,再根据Domain块的Krawtchouk矩不变量利用核模糊聚类对Domain块细分类。实验结果表明,与其他基于分类的快速分形编码方法相比,在解码图像质量提高的同时,大大加快了分形编码的速度。     

A review of the fractal image coding literature

Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While certain theoretical aspects of this representation are well established, relatively little attention has been given to the construction of a coherent underlying image model that would justify its use. Most purely fractal-based schemes are not competitive with the current state of the art, but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success. This review represents a survey of the most significant advances, both practical and theoretical, since the publication of Jacquin's (1990) original fractal coding scheme.     

A nonlinear model for fractal image coding

After a very promising start, progress in fractal image coding has been relatively slow recently. Most improvements have been concentrating on better adaptive coding algorithms and on search strategies to reduce the encoding time. Very little has been-done to challenge the linear model of the fractal transformations used so far in practical applications. In this paper, we explain why effective nonlinear transformations are not easy to find and propose a model based on conformal mappings in the geometric domain that are a natural extension of the affine model. Our compression results show improvements over the linear model and support the hope that a deeper understanding of the notion of self-similarity would further advance fractal image coding.     

Image Compression Based on Multistage Vector Quantization

This paper presents a new three-stage vector quantization system for the compression of images. It uses some simple schemes including error block classifier, search order coding (SOC), and index vector coding. The error block classifier preserves the edge blocks and discards the psychovisually redundant texture blocks in the last stage. The index vector coding encodes the combination of quantization indexes of the last two stages, and the SOC is used for encoding the quantization index of the first stage. The proposed system can achieve better compression performance than the conventional multistage vector quantization systems.     

Fractal coding of subbands with an oriented partition

We propose a new image compression scheme based on fractal coding of the coefficients of a wavelet transform, in order to take into account the self-similarity observed in each subband. The original image is first decomposed into subbands containing information in different spatial directions and at different scales, using an orthogonal wavelet-generated filter bank. Subbands are encoded using local iterated function systems (LIFS), with range and domain blocks presenting horizontal or vertical directionalities. Their sizes are defined according to the correlation lengths and resolution of each subband. The edge degradation and the blocking effects encountered at low bit-rates using conventional LIFS algorithm are reduced with this approach. The computation complexity is also greatly decreased by a 12:1 factor in comparison to fractal coding of the full resolution image. The proposed method is applied to standard test images. The comparison with other fractal coding approaches and with JPEG shows an important increase in terms of PPSNR/bit-rate. Especially for images presenting a privileged directionality, the use of adaptive partitions results in about 3 dB improvement in PPSNR. We also discuss the distorsion versus rate improvement obtained on high-frequency subbands when fractal coding instead of pyramidal vector quantization is used. Our approach achieves a real gain in PPSNR for low bit-rates between 0.3 and 1.2 bpp.     

Still image coding based on vector quantization and fractalapproximation

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.     

基于视觉特性的分形图像压缩编码

介绍了分形的基本概念及分形的数学原理，并针对传统的分形图像压缩编码算法的不足之处，提出了一种基于视觉特性的分形压缩算法，该方法利用人眼对灰度变化的敏感程度与背景有关的特点，在综合考虑图像块的均值与方差的前提下，动态地改变分形压编码时定义域块仿射变换后拼贴到值域块的最小误差，从而提高了编码速度。