Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

A novel fast fractal image compression method based on distance clustering in high dimensional sphere surface

Fractal encoding method becomes an effective image compression method because of its high compression ratio and short decompressing time. But one problem of known fractal compression method is its high computational complexity and consequent long compressing time. To address this issue, in this paper, distance clustering in high dimensional sphere surface is applied to speed up the fractal compression method. Firstly, as a preprocessing strategy, an image is divided into blocks, which are mapped on high dimensional sphere surface. Secondly, a novel image matching method is presented based on distance clustering on high dimensional sphere surface. Then, the correctness and effectiveness properties of the mentioned method are analyzed. Finally, experimental results validate the positive performance gain of the method

An investigation into the requirements for an efficient image transmission system over an ATM network

This thesis looks into the problems arising in an image transmission system when transmitting over an A TM network. Two main areas were investigated: (i) an alternative coding technique to reduce the bit rate required; and (ii) concealment of errors due to cell loss, with emphasis on processing in the transform domain of DCT-based images. [Continues.

Data comparison schemes for Pattern Recognition in Digital Images using Fractals

Pattern recognition in digital images is a common problem with application in remote sensing, electron microscopy, medical imaging, seismic imaging and astrophysics for example. Although this subject has been researched for over twenty years there is still no general solution which can be compared with the human cognitive system in which a pattern can be recognised subject to arbitrary orientation and scale. The application of Artificial Neural Networks can in principle provide a very general solution providing suitable training schemes are implemented. However, this approach raises some major issues in practice. First, the CPU time required to train an ANN for a grey level or colour image can be very large especially if the object has a complex structure with no clear geometrical features such as those that arise in remote sensing applications. Secondly, both the core and file space memory required to represent large images and their associated data tasks leads to a number of problems in which the use of virtual memory is paramount. The primary goal of this research has been to assess methods of image data compression for pattern recognition using a range of different compression methods. In particular, this research has resulted in the design and implementation of a new algorithm for general pattern recognition based on the use of fractal image compression. This approach has for the first time allowed the pattern recognition problem to be solved in a way that is invariant of rotation and scale. It allows both ANNs and correlation to be used subject to appropriate pre-and post-processing techniques for digital image processing on aspect for which a dedicated programmer's work bench has been developed using X-Designer

Investigation of the effects of image compression on the geometric quality of digital protogrammetric imagery

We are living in a decade, where the use of digital images is becoming increasingly important. Photographs are now converted into digital form, and direct acquisition of digital images is becoming increasing important as sensors and associated electronics. Unlike images in analogue form, digital representation of images allows visual information to· be easily manipulated in useful ways. One practical problem of the digital image representation is that, it requires a very large number of bits and hence one encounters a fairly large volume of data in a digital production environment if they are stored uncompressed on the disk. With the rapid advances in sensor technology and digital electronics, the number of bits grow larger in softcopy photogrammetry, remote sensing and multimedia GIS. As a result, it is desirable to find efficient representation for digital images in order to reduce the memory required for storage, improve the data access rate from storage devices, and reduce the time required for transfer across communication channels. The component of digital image processing that deals with this problem is called image compression. Image compression is a necessity for the utilisation of large digital images in softcopy photogrammetry, remote sensing, and multimedia GIS. Numerous image Compression standards exist today with the common goal of reducing the number of bits needed to store images, and to facilitate the interchange of compressed image data between various devices and applications. JPEG image compression standard is one alternative for carrying out the image compression task. This standard was formed under the auspices ISO and CCITT for the purpose of developing an international standard for the compression and decompression of continuous-tone, still-frame, monochrome and colour images. The JPEG standard algorithm &Us into three general categories: the baseline sequential process that provides a simple and efficient algorithm for most image coding applications, the extended DCT-based process that allows the baseline system to satisfy a broader range of applications, and an independent lossless process for application demanding that type of compression. This thesis experimentally investigates the geometric degradations resulting from lossy JPEG compression on photogrammetric imagery at various levels of quality factors. The effects and the suitability of JPEG lossy image compression on industrial photogrammetric imagery are investigated. Examples are drawn from the extraction of targets in close-range photogrammetric imagery. In the experiments, the JPEG was used to compress and decompress a set of test images. The algorithm has been tested on digital images containing various levels of entropy (a measure of information content of an image) with different image capture capabilities. Residual data was obtained by taking the pixel-by-pixel difference between the original data and the reconstructed data. The image quality measure, root mean square (rms) error of the residual was used as a quality measure to judge the quality of images produced by JPEG(DCT-based) image compression technique. Two techniques, TIFF (IZW) compression and JPEG(DCT-based) compression are compared with respect to compression ratios achieved. JPEG(DCT-based) yields better compression ratios, and it seems to be a good choice for image compression. Further in the investigation, it is found out that, for grey-scale images, the best compression ratios were obtained when the quality factors between 60 and 90 were used (i.e., at a compression ratio of 1:10 to 1:20). At these quality factors the reconstructed data has virtually no degradation in the visual and geometric quality for the application at hand. Recently, many fast and efficient image file formats have also been developed to store, organise and display images in an efficient way. Almost every image file format incorporates some kind of compression method to manage data within common place networks and storage devices. The current major file formats used in softcopy photogrammetry, remote sensing and · multimedia GIS. were also investigated. It was also found out that the choice of a particular image file format for a given application generally involves several interdependent considerations including quality; flexibility; computation; storage, or transmission. The suitability of a file format for a given purpose is · best determined by knowing its original purpose. Some of these are widely used (e.g., TIFF, JPEG) and serve as exchange formats. Others are adapted to the needs of particular applications or particular operating systems

Distributed video through telecommunication networks using fractal image compression techniques

The research presented in this thesis investigates the use of fractal compression techniques for a real time video distribution system. The motivation for this work was that the method has some useful properties which satisfy many requirements for video compression. In addition, as a novel technique, the fractal compression method has a great potential. In this thesis, we initially develop an understanding of the state of the art in image and video compression and describe the mathematical concepts and basic terminology of the fractal compression algorithm. Several schemes which aim to the improve of the algorithm, for still images are then examined. Amongst these, two novel contributions are described. The first is the partitioning of the image into sections which resulted insignificant reduction of the compression time. In the second, the use of the median metric as alternative to the RMS was considered but was not finally adopted, since the RMS proved to be a more efficient measure. The extension of the fractal compression algorithm from still images to image sequences is then examined and three different schemes to reduce the temporal redundancy of the video compression algorithm are described. The reduction in the execution time of the compression algorithm that can be obtained by the techniques described is significant although real time execution has not yet been achieved. Finally, the basic concepts of distributed programming and networks, as basic elements of a video distribution system, are presented and the hardware and software components of a fractal video distribution system are described. The implementation of the fractal compression algorithm on a TMS320C40 is also considered for speed benefits and it is found that a relatively large number of processors are needed for real time execution

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: SHARPs -- Space-weather HMI Active Region Patches

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches (SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at http://jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters.Comment: 27 pages, 7 figures. Accepted to Solar Physic