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Ali, Maaruf. "Fractal image coding techniques and their applications." Thesis, King's College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265858.
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Ebrahimpour-Komleh, Hossein. "Fractal techniques for face recognition." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16289/1/Hossein_Ebrahimpour-Komleh_Thesis.pdf.
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Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal methods for recognition, especially human face recognition.
This research introduces three new methods for using fractals for face recognition, the use of fractal codes directly as features, Fractal image-set coding and Subfractals. In the first part, the mathematical principle behind the application of fractal image codes for recognition is investigated. An image Xf can be represented as Xf = A x Xf + B which A and B are fractal parameters of image Xf . Different fractal codes can be presented for any arbitrary image. With the defnition of a fractal transformation, T(X) = A(X - Xf ) + Xf , we can define the relationship between any image produced in the fractal decoding process starting with any arbitrary image X0 as Xn = Tn(X) = An(X - Xf ) + Xf . We show that some choices for A or B lead to faster convergence to the final image.
Fractal image-set coding is based on the fact that a fractal code of an arbitrary gray-scale image can be divided in two parts - geometrical parameters and luminance parameters. Because the fractal codes for an image are not unique, we can change the set of fractal parameters without significant change in the quality of the reconstructed image. Fractal image-set coding keeps geometrical parameters
the same for all images in the database. Differences between images are captured in the non-geometrical or luminance parameters - which are faster to compute. For recognition purposes, the fractal code of a query image is applied to all the images in the training set for one iteration. The distance between an image and the result after one iteration is used to define a similarity measure between this image and the query image.
The fractal code of an image is a set of contractive mappings each of which transfer a domain block to its corresponding range block. The distribution of selected domain blocks for range blocks in an image depends on the content of image and the fractal encoding algorithm used for coding. A small variation in a part of the input image may change the contents of the range and domain blocks in the fractal encoding process, resulting in a change in the transformation parameters in the same part or even other parts of the image. A subfractal is a set of fractal codes related to range blocks of a part of the image. These codes are calculated to be independent of other codes of the other parts of the same image. In this case the domain blocks nominated for each range block must be located in the same part of the image which the range blocks come from.
The proposed fractal techniques were applied to face recognition using the MIT and XM2VTS face databases. Accuracies of 95% were obtained with up to 156 images.
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Ebrahimpour-Komleh, Hossein. "Fractal techniques for face recognition." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16289/.
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Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal methods for recognition, especially human face recognition.
This research introduces three new methods for using fractals for face recognition, the use of fractal codes directly as features, Fractal image-set coding and Subfractals. In the first part, the mathematical principle behind the application of fractal image codes for recognition is investigated. An image Xf can be represented as Xf = A x Xf + B which A and B are fractal parameters of image Xf . Different fractal codes can be presented for any arbitrary image. With the defnition of a fractal transformation, T(X) = A(X - Xf ) + Xf , we can define the relationship between any image produced in the fractal decoding process starting with any arbitrary image X0 as Xn = Tn(X) = An(X - Xf ) + Xf . We show that some choices for A or B lead to faster convergence to the final image.
Fractal image-set coding is based on the fact that a fractal code of an arbitrary gray-scale image can be divided in two parts - geometrical parameters and luminance parameters. Because the fractal codes for an image are not unique, we can change the set of fractal parameters without significant change in the quality of the reconstructed image. Fractal image-set coding keeps geometrical parameters
the same for all images in the database. Differences between images are captured in the non-geometrical or luminance parameters - which are faster to compute. For recognition purposes, the fractal code of a query image is applied to all the images in the training set for one iteration. The distance between an image and the result after one iteration is used to define a similarity measure between this image and the query image.
The fractal code of an image is a set of contractive mappings each of which transfer a domain block to its corresponding range block. The distribution of selected domain blocks for range blocks in an image depends on the content of image and the fractal encoding algorithm used for coding. A small variation in a part of the input image may change the contents of the range and domain blocks in the fractal encoding process, resulting in a change in the transformation parameters in the same part or even other parts of the image. A subfractal is a set of fractal codes related to range blocks of a part of the image. These codes are calculated to be independent of other codes of the other parts of the same image. In this case the domain blocks nominated for each range block must be located in the same part of the image which the range blocks come from.
The proposed fractal techniques were applied to face recognition using the MIT and XM2VTS face databases. Accuracies of 95% were obtained with up to 156 images.
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Cesbron, Fred́eŕique Chantal. "Multiresolution fractal coding of still images." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15508.
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USUI, Shin'ichi, Masayuki TANIMOTO, Toshiaki FUJII, Tadahiko KIMOTO, and Hiroshi OHYAMA. "Fractal Image Coding Based on Classified Range Regions." Institute of Electronics, Information and Communication Engineers, 1998. http://hdl.handle.net/2237/14996.
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Tan, Teewoon. "HUMAN FACE RECOGNITION BASED ON FRACTAL IMAGE CODING." University of Sydney. Electrical and Information Engineering, 2004. http://hdl.handle.net/2123/586.
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Human face recognition is an important area in the field of biometrics. It has been an active area of research for several decades, but still remains a challenging problem because of the complexity of the human face. In this thesis we describe fully automatic solutions that can locate faces and then perform identification and verification. We present a solution for face localisation using eye locations. We derive an efficient representation for the decision hyperplane of linear and nonlinear Support Vector Machines (SVMs). For this we introduce the novel concept of $\rho$ and $\eta$ prototypes. The standard formulation for the decision hyperplane is reformulated and expressed in terms of the two prototypes. Different kernels are treated separately to achieve further classification efficiency and to facilitate its adaptation to operate with the fast Fourier transform to achieve fast eye detection. Using the eye locations, we extract and normalise the face for size and in-plane rotations. Our method produces a more efficient representation of the SVM decision hyperplane than the well-known reduced set methods. As a result, our eye detection subsystem is faster and more accurate. The use of fractals and fractal image coding for object recognition has been proposed and used by others. Fractal codes have been used as features for recognition, but we need to take into account the distance between codes, and to ensure the continuity of the parameters of the code. We use a method based on fractal image coding for recognition, which we call the Fractal Neighbour Distance (FND). The FND relies on the Euclidean metric and the uniqueness of the attractor of a fractal code. An advantage of using the FND over fractal codes as features is that we do not have to worry about the uniqueness of, and distance between, codes. We only require the uniqueness of the attractor, which is already an implied property of a properly generated fractal code. Similar methods to the FND have been proposed by others, but what distinguishes our work from the rest is that we investigate the FND in greater detail and use our findings to improve the recognition rate. Our investigations reveal that the FND has some inherent invariance to translation, scale, rotation and changes to illumination. These invariances are image dependent and are affected by fractal encoding parameters. The parameters that have the greatest effect on recognition accuracy are the contrast scaling factor, luminance shift factor and the type of range block partitioning. The contrast scaling factor affect the convergence and eventual convergence rate of a fractal decoding process. We propose a novel method of controlling the convergence rate by altering the contrast scaling factor in a controlled manner, which has not been possible before. This helped us improve the recognition rate because under certain conditions better results are achievable from using a slower rate of convergence. We also investigate the effects of varying the luminance shift factor, and examine three different types of range block partitioning schemes. They are Quad-tree, HV and uniform partitioning. We performed experiments using various face datasets, and the results show that our method indeed performs better than many accepted methods such as eigenfaces. The experiments also show that the FND based classifier increases the separation between classes. The standard FND is further improved by incorporating the use of localised weights. A local search algorithm is introduced to find a best matching local feature using this locally weighted FND. The scores from a set of these locally weighted FND operations are then combined to obtain a global score, which is used as a measure of the similarity between two face images. Each local FND operation possesses the distortion invariant properties described above. Combined with the search procedure, the method has the potential to be invariant to a larger class of non-linear distortions. We also present a set of locally weighted FNDs that concentrate around the upper part of the face encompassing the eyes and nose. This design was motivated by the fact that the region around the eyes has more information for discrimination. Better performance is achieved by using different sets of weights for identification and verification. For facial verification, performance is further improved by using normalised scores and client specific thresholding. In this case, our results are competitive with current state-of-the-art methods, and in some cases outperform all those to which they were compared. For facial identification, under some conditions the weighted FND performs better than the standard FND. However, the weighted FND still has its short comings when some datasets are used, where its performance is not much better than the standard FND. To alleviate this problem we introduce a voting scheme that operates with normalised versions of the weighted FND. Although there are no improvements at lower matching ranks using this method, there are significant improvements for larger matching ranks. Our methods offer advantages over some well-accepted approaches such as eigenfaces, neural networks and those that use statistical learning theory. Some of the advantages are: new faces can be enrolled without re-training involving the whole database; faces can be removed from the database without the need for re-training; there are inherent invariances to face distortions; it is relatively simple to implement; and it is not model-based so there are no model parameters that need to be tweaked.
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Bal, Shamit. "Image compression with denoised reduced-search fractal block coding." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq23210.pdf.
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Piché, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.
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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.
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Pich??, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.
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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.
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Alexander, Simon. "Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1180.
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This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).
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Jacquin, Arnaud E. "A fractal theory of iterated Markov operators with applications to digital image coding." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/30050.
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Nolte, Ernst Hendrik. "Image compression quality measurement : a comparison of the performance of JPEG and fractal compression on satellite images." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51796.
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Thesis (MEng)--Stellenbosch University, 2000.ENGLISH ABSTRACT: The purpose of this thesis is to investigate the nature of digital image compression and the calculation of the quality of the compressed images. The work is focused on greyscale images in the domain of satellite images and aerial photographs. Two compression techniques are studied in detail namely the JPEG and fractal compression methods. Implementations of both these techniques are then applied to a set of test images. The rest of this thesis is dedicated to investigating the measurement of the loss of quality that was introduced by the compression. A general method for quality measurement (signal To Noise Ratio) is discussed as well as a technique that was presented in literature quite recently (Grey Block Distance). Hereafter, a new measure is presented. After this, a means of comparing the performance of these measures is presented. It was found that the new measure for image quality estimation performed marginally better than the SNR algorithm. Lastly, some possible improvements on this technique are mentioned and the validity of the method used for comparing the quality measures is discussed.
AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om ondersoek in te stel na die aard van digitale beeldsamepersing en die berekening van beeldkwaliteit na samepersing. Daar word gekonsentreer op grysvlak beelde in die spesifieke domein van satellietbeelde en lugfotos. Twee spesifieke samepersingstegnieke word in diepte ondersoek naamlik die JPEG en fraktale samepersingsmetodes. Implementasies van beide hierdie tegnieke word op 'n stel toetsbeelde aangewend. Die res van hierdie tesis word dan gewy aan die ondersoek van die meting van die kwaliteitsverlies van hierdie saamgeperste beelde. Daar word gekyk na 'n metode wat in algemene gebruik in die praktyk is asook na 'n nuwer metode wat onlangs in die literatuur veskyn het. Hierna word 'n nuwe tegniek bekendgestel. Verder word daar 'n vergelyking van hierdie mates en 'n ondersoek na die interpretasie van die 'kwaliteit' van hierdie kwaliteitsmate gedoen. Daar is gevind dat die nuwe maatstaf vir kwaliteit net so goed en selfs beter werk as die algemene maat vir beeldkwaliteit naamlik die Sein tot Ruis Verhouding. Laastens word daar moontlike verbeterings op die maatstaf genoem en daar volg 'n bespreking oor die geldigheid van die metode wat gevolg is om die kwaliteit van die kwaliteitsmate te bepaal
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Silva, Fernando Silvestre da. "Procedimentos para tratamento e compressão de imagens e video utilizando tecnologia fractal e transformadas wavelet." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260581.
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Orientador: Yuzo IanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-05T13:46:30Z (GMT). No. of bitstreams: 1 Silva_FernandoSilvestreda_D.pdf: 35017484 bytes, checksum: fb460a6a42e44fe0a50e94599ac027fc (MD5) Previous issue date: 2005
Resumo: A excelente qualidade visual e taxa de compressão dos codificadores fractais de imagem tem aplicações limitadas devido ao exaustivo tempo de codificação inerente. Esta pesquisa apresenta um novo codificador híbrido de imagens que aplica a velocidade da transformada wavelet à qualidade da compressão fractal. Neste esquema, uma codificação fractal acelerada usando a classificação de domínios de Fisher é aplicada na sub-banda passa-baixas de uma imagem transformada por wavelet e uma versão modificada do SPIHT (Set Partitioned in Hierarchical Trees) é aplicada nos coeficientes remanescentes. Os detalhes de imagem e as características de transmissão progressiva da transformada wavelet são mantidas; nenhum efeito de bloco comuns às técnicas fractais é introduzido, e o problema de fidelidade de codificação comuns aos codificadores híbridos fractal-wavelet é resolvido. O sistema proposto reduz o tempo médio de processamento das imagens em 94% comparado com o codificador fractal tradicional e um ganho de 0 a 2,4dB em PSNR sobre o algoritmo SPIHT puro. Em ambos os casos, o novo esquema proposto apresentou melhorias em temos de qualidade subjetiva das imagens para altas, médias e baixas taxas de compressão
Abstract: The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This research presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. In this scheme, a fast fractal encoding using Fisher¿s domain classification is applied to the lowpass subband of wavelet transformed image and a modified SPIHT coding (Set Partitioning in Hierarchical Trees), on the remaining coefficients. The image details and wavelet progressive transmission characteristics are maintained; no blocking effects from fractal techniques are introduced; and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme provides an average of 94% reduction in encoding-decoding time compared to the pure accelerated Fractal coding results, and a 0-2,4dB gain in PSNR over the pure SPIHT coding. In both cases, the new scheme improves the subjective quality of pictures for high, medium and low bit rates
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
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Wadströmer, Niclas. "Coding of fractal binary images with contractive set mappings composed of affine transformations /." Linköping : Univ, 2001. http://www.bibl.liu.se/liupubl/disp/disp2001/tek700s.pdf.
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Wang, Wei-Zhi, and 王偉志. "Fractal image coding for still-image." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/16354565487043672434.
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碩士逢甲大學
電機工程學系
89
Abstract Recently, due to the limitation of physical transmission capacity and bandwidth of communications, data compression has become a very important problem. Many compression methods have been developed. One usually distinguishes, between different coding schemes: transform coding, multiresolution coding, VQ, predictive method, and other more recent schemes such as fractal image coding. In recent years, many researches have been done to study of properties of fractal image coding due to its ability on generating high-resolution reconstructed images at very high compression ratios. However, it suffers from very high encoding complexity. In order to overcome this big trouble, several methods to reduce the search space have presented. In Chapter 3 of this thesis, a novel and simple idea based on range block rotation rather than domain block rotation suggested by Jacquin’s original approach is proposed. The principle of range block rotation can effectively reduce the total number of domain block rotations. In Chapter 4, a new fractal coding method, called Fractal Dimension-based Fast Fractal Coding (FDFFC), is proposed. Our method is based on the fact that two equal-sized image blocks cannot be closely matched unless their fractal dimensions are close. This implies that domain blocks whose fractal dimension differs greatly from the range block may be eliminated from the domain pool for matching. Finally, this thesis proposes an effective fractal coding scheme, called “Two-Layer Classified Fractal Coding using Isometry Prediction (2CFCIP),” to improve the rate-distortion and speed performance of fractal coding. This proposed fractal encoder includes the coding schemes proposed in Chapter 3 and Chapter 4. It can be seen as a bottom-up approach using block merging. This encoder can be used in any still-image coding.
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Chang, Hsuan Ting, and 張軒庭. "Studies on fractal image coding." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/24921211209646733232.
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Dzerdz, Branka. "Fractal block based image coding algorithms." Thesis, 1996. http://spectrum.library.concordia.ca/3308/1/MM18387.pdf.
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LI, CHENG-HAO, and 李成浩. "TWO LEVEL FRACTAL IMAGE CODING ALGORITHM." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/70988644937749986902.
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碩士大同工學院
電機工程學系
84
In the recent years, a variety of image coding algorithms based onfractal theory have been proposed in the literature. To achieve the goalof fast encoding, these algorithms devote to search the optimal or the suboptimal domain block by expoliting a self-similarity model of affinetransform.In this thesis, a new method of fractal image coding is proposed. To reduce the computational complexity of the image encoding, we adopt an efficient approach based on two level domain pools. The first leveldomain pool is the set of all available domain blocks but the search iswith eight isometric transforms conducted without isometric transform.The second layer domain pool is formed by the reduced subset of the firstlevel domain pool. The exhaustive search is conducted in the second leveldomain pool. It is shown that the proposed two lwvel method can speed upthe encoding process without noticeable loss of image quality.
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Lin, Che-li, and 林哲立. "NO SEARCH FRACTAL IMAGE CODING WITH VECTOR QUANTIZATION." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/78241359521855487866.
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碩士大同大學
通訊工程研究所
97
Conventional fractal image coding needs a long encoding time because it searches a lot of domain blocks and calculates the parameters, and it may induce annoying block artifacts. To solve this problem, no search fractal image coding is proposed by Shen Furao and Osamu Hasegawa. In the no search fractal image coding, the encoding time is faster than full search fractal image coding. Because of reducing amount of search scope, it reduces a lot of encoding time. In this thesis, we propose the method that combines no search fractal coding and vector quantization. This method could improve the image quality for complex regions and achieve fast encoding. Experimental results show that the proposed method for improving no search method is effective and efficient.
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Huang, Cheng-yi, and 黃承誼. "Fractal Image Coding Using Dithering and Neighboring-Block Reduction." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/98800359440156429788.
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碩士國立臺灣科技大學
電機工程系
89
The development of encoding and decoding techniques for digital images have being increasingly becoming an important issues in the recent years, due to the image transmission and storage problems. The main goal is to seek techniques that will maintain high image quality and low bit rate in the least possible encoding time. The AFBIC（Automatic Fractal Block Image Coding）architecture proposed by Jacquin[6] based on the concept of self-similarity and recursion of fractal is such an approach. In this research, an encoding technique called 「dithering neighboring-block reduction」is proposed to refine domain blocks in the domain pool, while improving image quality and reducing memory space. The major drawback of the AFBIC architecture is the high encoding complexity. Our method reduces the number of domain blocks in the domain pool according to the correlation between neighboring domain blocks in the image. The results indicate a nearly 20%~50% reduction in memory space. Besides, 「dithering sampling」 is also employed to understand the effect of different domain block collection. The results indicate a 0.1dB improvement in image quality and a 2.9% reducment in bit rate for the image such as the baboon without extra loss of encoding time and waste of memory space compared with neighboring-block reduction.
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Yeh, Chien-Cheng, and 葉建成. "Fast Image Compression Algorithms Based on Fractal Coding Technique." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/75894023373650014505.
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碩士國立高雄第一科技大學
電腦與通訊工程所
91
Nowadays, internet and information technology are widely spread in our life. Image transmission is an important trend in the future. And one of the important problems in such applications is the limit of transmission bandwidth and storage capacity. The smaller file size will help us to meet requirement. Thus, technique of the compression has become an important research topic. In order to speed up the internet transmission, it is useful for us to develop algorithm. Besides, an efficient image compression can reduce the size of image efficiently and decrease transmission time. In the fractal image compression, most of the time is spent on finding the best matching domain block and determine the transform function. If we want to transmit an image in the internet or store it, we would not like to spend much time on compressing it. Thus, we propose several algorithms to speed up fractal image coding under the condition that keep the image quality in this thesis.
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Wang, Chou-Chen, and 王周珍. "Low Complexity Fractal-Based Image and Video Coding Technique." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/73788334461447197389.
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博士國立成功大學
電機工程學系
87
Fractal image coding is based on the theory of iterated function system (IFS) which was originally developed for creation of a deterministically self-similar fractal in the 1980s. Using this theory, an image may be represented by a fractal transform, whose attractor is close to the image. For natural images, the parameters of the fractal transform can usually be coded very compactly, which makes this method suitable for image compression. Vector quantization (VQ) is an efficient image coding technique for low bit rate. A vector, which is a block of pixels, is approximated by a representative vector (codeword) of the codebook, which minimizes the distortion among all the vectors in the codebook. Compression is achieved by transmitting or storing the codeword address instead of the codeword itself. Fractal image coding has some similarity with VQ. In fractal coding, blocks of an original image are used, whereas in VQ, predetermined blocks obtained from a set of different images are used. Thus, fractal coding has a disadvantage in that it should satisfy the contractivity with a great number of search blocks. In this thesis, we first review the theoretical foundations and implementations of fractal image coding and vector quantization, separately. The relationship between VQ and fractal image coding techniques is investigated, and some methods are proposed to overcome the drawbacks occurred when we employ the two methods to compress still images and image sequences. The most serious problem in the VQ is edge degradation occurred in the decoded image. We present a signal processing unit to first classify image blocks into two groups including low-activity and high-activity blocks, and then further decompose the high-activity blocks into some outputs including visual and smoothed signals. These output signals are more suited to VQ such that we can achieve much better perceptual quality when compared to the conditional VQ. In fractal image coding, the major drawback is the high encoding complexity to find the best match between a range block and a large pool of domain blocks. In order to reduce the encoding complexity, we propose a hybrid coding scheme based on VQ and fractal approximation. The signal processing unit proposed in VQ system classifies image blocks into low-activity and high-activity blocks. The low-activity blocks are directly encoded by the VQ. The high-activity blocks are approximated by fractal coding, a two-stage search strategy is proposed to reduce the search space of domain pool. First, a fast and simple binary pattern matching algorithm is employed to extract a small pool of candidate domain blocks, and then the gray level matching algorithm is used to find the best match from the candidates. To further improve the computational efficiency of the fractal image coding, we exploit the correlation between range blocks to propose an efficient coding method. Four domain blocks mapped by the previous neighboring range blocks are considered as the good candidate blocks of the input range block. The proposed method can be based on any existing fast fractal coding algorithms to further reduce their coding complexity and raise their compression efficiency with insignificant loss of image quality. Similar ideas are extended to fractal video coding. Two intercubes correlation search methods, which separately consider the correlation of three-dimensional range blocks in spatial and temporal-spatial directions, are developed in fractal coding of image sequences. The methods can further speed up the encoding process. This dissertation also presents a comparative study on the performances using the different methods for fractal image and video coding.
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Chen, Po-Kang, and 陳柏綱. "A VLSI Design for High Speed Fractal Image Coding." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/g3a5zx.
Full textAbstract:
碩士南台科技大學
電子工程系
97
Fractal is a complex science, it can create nature image by regular、similar. The fractal geometry describes nature geometry in the main nature world. In long time ago, Barnsley support fractal compression by fractal concept, but he never announced his fractal compression method until his student Jacquin supported practical fractal compression method. In pass year, fractal compression has been interesting in research field. Although fractal image compression produces high quality at high compression ratio, it needs extremely long encoding time. In this paper, several algorithms are developed to attack this problem. They are four-direction approach， the control points approach, together with a history table design and we also design VLSI chip for fast fractal image. experiment results shows that our method and VLSI design are faster than the exiting algorithms.
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Kao, Jung-Yang, and 高榮揚. "A study of joint source-channel fractal image coding." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/45673008546346971942.
Full textAbstract:
碩士義守大學
電子工程學系
91
In this thesis, we propose a joint source-channel coding system (JSCC) for fractal image compression. We allocate the available total bit rate between the source code and channel code (error-correcting codes) using a measuring methodology for error sensitivity. We partition the information bits into sensitivity classes and assign one code from a range of error-correcting code to each sensitivity classes using unequal error protection strategy. The rate-compatible punctured convolution code (RCPC) is adopted for channel coding in this paper, which is a flexible error protection technique. The principle of the proposed JSCC system is to assign more channel codes to protect the important bits of fractal coding parameters, and lower codes or no protection for the less important parameters. The proposed JSCC coding system can not only improve the total coding performance but also achieve the same error protection as the other methods. In addition, the traditional fractal image compression is very time- consuming, so we also propose a fast fractal encoding method which joint variance-inter block correction search (JVICS) in this paper. Simulation results show that the total bit rates of the proposed JSCC coding system can be reduced about 34% ~ 55%, and the encoding time can be reduced 95%, as compared the full search fractal coding system.
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Wong, Chian-Tsang, and 翁健藏. "Low-Complexity Fractal Image Coding with Two-Stage Search Algorithm." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/88634309422171096847.
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Guo, Yu-Ming, and 郭育銘. "A Study of Fractal Image Coding with Subband Decomposition Techniques." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/75117990080465564005.
Full textAbstract:
碩士國立成功大學
電機工程研究所
83
Recently,it is well known that many Fractal image coding systems and Subband decomposition techniques were presented in image signal compression. In Fractal image coding, large time consuming make it impractical. But we found that there are some intra-band correlations in geometry property after decomposing an image. And this property just conforms to the spirit of the Fractal image coding system. So we use the technique of Subband decom- position in the Fractal image coding system. In this thesis, we will study various aspects on Fractal Image Coding with Subband decomposition technique. After decom- posing an image, the lower bands are encoded by Fractal coding scheme, and record the variation in gray level of the higher bands. The variation in geometry of the higher bands, we make use of the encoding results of the lower bands. In our system, the variable length coding technique is used to encode the lowest band. Experimental results are presented in terms of bit rates, computing time, and the qualities of the reconstructed images. The bit rates and computing time of our coder is compared with the tra- ditional Fractal coder. It is found that our coder achieves the better performance.
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Lin, Chung-Chuan, and 林鍾權. "Fractal Mating Coding for Mutual Multi-image Compression and Encryption." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/87520273746421798397.
Full textAbstract:
碩士國立雲林科技大學
電機工程系碩士班
92
Fractal Compressing is a high efficient technique for image compression. Conventional fractal coding techniques explore the self-similarity. The image compression standards (ex. JPEG, JPEG2000) only pay attention to encode and decode independently in an image. In this thesis, we propose the Fractal Mating Coding (FMC) algorithm that is different form general image compression techniques. It explores inter-similarity in images, and encode/decode multiple images simultaneously. Furthermore, the proposed FMC method can design efficient domain pools to improve the bit-rate and peak signal to noise ratio performance. The encryption function based on FMC method is difficult to break, because the image is coded by isometry, contrast scaling, contractive operation and affine transformation. We proposed the FMC method, in which two or more images one mutually encoded simultaneously. The propose FMC method provide high security and protect the image data for maliceous attacks.
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Liao, Wei-kai, and 廖緯凱. "WEIGHTED NO SEARCH FRACTAL IMAGE CODING BASED ON OVERLAPPED PARTITIONING." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/55905687066112053821.
Full textAbstract:
碩士大同大學
通訊工程研究所
94
Conventional fractal image coding methods utilizing blockwise partitioning need long encoding time and often induce annoying blocking artifacts. We propose a fast no search fractal image coding method based on overlapped block partitioning. The encoding time is greatly reduced by eliminating the search of domain pool and blocking artifacts are significantly reduced by using overlapped block partitioning of the image support. Besides, in order to improve the quality of the decoded image, the region of edge will be encoded by adding a weighting. Experimental results show that the proposed scheme not only achieves fast encoding but also improves the visual quality of the decoded images.
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PAI, Chuang, and 白莊. "The Improvement of the Image Data Coding Using the Fractal Geometry." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/38865861069224869287.
Full textAbstract:
碩士大同工學院
電機工程研究所
81
Since the video communication are popular in recent years, the technique about the digital image data coding becomes very important. In this thesis, much efforts are dedicated to the fractal-based (FB) yardstick method, which characterized by the simplicity in the implementation (in fact, no multiplier is required ). In the originally proposed FB yardstick method, the performance will not be enhanced without the application of the optimal trigger function (TF). But the way to use the optimal TF is just a idea and there is no feasible solution supported. In order to solve the problem that the original method depends on the optimal TF, we develop a novel algorithm which can enhance the performance without the hard searching for the optimal TF. Based on the proposed method, we also develop two improved algorithms: the first one is an restoration model in the restoration of this FB method and the second one an edge- oriented coding scheme. By applying the improved methods combined with all those proposed algorithms mentioned above, the peak signal-to- noise ratio (PSNR) can be promoted for about 2 dB, the visual effect is obviously much better, and the bit is reduced from the demonstration of the comparison between the simulation results using the original and proposed methods. Moreover, the complexity increased for the improved method is very little.
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Liang, Hau-Jie, and 梁皓傑. "THE IMPLEMENTATION OF FRACTAL IMAGE CODING BASED ON KICK-OUT CONDITION." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/88343658861979587584.
Full textAbstract:
碩士大同大學
電機工程學系(所)
92
The fractal image coding has been applied in many applications in recent years. The fractal encoding procedure needs a great search and comparison time, so it is required to implement the encoder by hardware to reduce the encoding time. This thesis is intended to design a hardware architecture for fractal image coding. The application of fractal coding has been proposed in the literature, but the research of the hardware architecture for fractal image coding is few. In this thesis, we proposed a new fractal image coding architecture based on the predetermined kick-out condition [7] to reduce the computational load. Moreover, we use the mean encoding technique to replace mean without changing the fractal image coding format.
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Her-Chang, Chao, and 趙和昌. "Fractal image coding and digital filter design based on minimax criterion." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/17959919342605129801.
Full textAbstract:
博士國立臺灣科技大學
電子工程技術研究所
86
This dissertation includes two parts of research results. One is image compression. Another is digital FIR filter design.In image compression, according to the texture attribution a testing image block is assigned to its corresponding texture class. The texture attribution is estimated by employing the technique of the computerized tomographic projection and back-projection skill. We then present the adaptive block size and shape fractal still and sequence image coding techniques. Under this approach, a better trade-off between the decoded image quality and transmitting bit rate is performed.Regarding the digital FIR filter design, we have presented three design strategies, namely, linear phase quincunx filter banks (QFB) with perfect reconstruction (PR) and low delay QFB satisfying PR.From the simulation examples demonstrated in each chapter of this dissertation, the effectiveness of the proposed design techniques for each considered design problem can be confirmed.
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Chen, Rong-Jian, and 陳榮堅. "Video coding and still image coding using adaptive techniques, mathematical morphology, subband systems and fractal theory." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/16772137322250907095.
Full textAbstract:
博士國立臺灣科技大學
工程技術研究所
83
We present four new image compression techniques in this dissertation. They are a fully adaptive DCT-based color image sequence coder, the three-dimensional morphological pyramidal color image sequence coding, the adaptive fractal image coding in subband domain, and the fast fractal image coding systems. The fully adaptive DCT-based color image sequence coder is the modified version of the MPEG-1 and MPEG-2, where the mechanism, of the motion compensation, zonal filters, and quantizers are adaptive. The 3-D morphological pyramids are constructed by using 3-D morphological filters, which support the applications of multiresolution. In subband domain, since the characteristic of each subband is different from the others, the coding stra- tegy of each subband must depend on its characteristics; hence we employ an adaptive fractal coding mechanism to do that. Be- cause of the fractal encoding is time consuming, it is important to develop fast fractal coding schemes. We therefore proposed two fast fractal coding schemes, one is based on the tree- structural classifier and the other uses the DCT classifier. Simulation results show that these coding systems perform very well in their respective applications.
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Van, der Merwe Riaan Louis. "The use of fractal theory, wavelet coding and learning automata in image compression." Thesis, 2014. http://hdl.handle.net/10210/9061.
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戴經哲. "An Image Compression Method Using Modified Fractal Coding and Discrete Cosine Transformation Algorithm." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/86645958746676435109.
Full textAbstract:
碩士國立中正大學
電機工程研究所
92
Fractal coding is an effective method to eliminate image redundancy. In the conventional fractal coding system, the image is partitioned into two kinds of different blocks, the non-overlapping range blocks, and the overlapping domain blocks. Every range block can find a domain block which when being contractive affine transformed is most similar to the specific range block. The parameters of transformations are recorded as the compressed data of the original range blocks. In the decoding scheme, each compressed data of the range blocks is made the same transformations repeatedly, and will finally result in a image similar to the original image. Although the method of fractal compression is simple, the encoding procedure needs a lot of time. Therefore, we reduce the encoding time by using a modified fractal coding combined with the discrete cosine transformation. In this thesis, we first classify the blocks partitioned into two classes by their standard deviations and encode those blocks with different techniques according to their classes. We use the discrete cosine transformation to encode the blocks with smaller standard deviations, and use the modified fractal coding to encode the blocks have the bigger standard deviations. The experimental results show that the method combined with the discrete cosine transformation and modified fractal coding can save a lot of the encoding time in the same compression ratio, and the quality of the decoded images in PSNR are similar to that of the image coded with conventional fractal coding system. This shows the feasibility of the proposed approach.
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Shy, Chewn-Jye, and 施純傑. "A Fractal Image Coding System Based on An Adaptive Side- Coupling Quadtree Structure." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/63498488794933384005.
Full textAbstract:
碩士國立中正大學
電機工程研究所
82
A new fractal-based image compression system based on a so- called Adaptive Side-Coupling Quadtree (ASCQ) structure is pro- posed. The propsoed system consists of three processes : a pre- process process, a compression process, and a decompression pr- ocess. In the preprocessing process, the original image is rep- resented by an ASCQ structure. The set of Iterated Function Sy- stem (IFS) codes, which is a powerful tool usually be derived in the encoding process, can be calculated directly from this tree structure. Using these IFS codes, an image which is similar to the original one can be reconstructed after several iterati- ons. The preprocessing process which creates an ASCQ structure be divided into two phases. In the first phase, a quadtree str- ucture is created by partitioning the original image into blocks with different sizes. As to the second phase, we propose to take the right, bottom, and diagonal side- coupling regions of each domain node to mount on their corresponding domain node based on two rules. The proposed ASCQ structure not only represnets the original image but also contains both the domain and range pools in it. The number of fractal codes in an ASCQ structure will be different when it is extracted from different original images. The computation time of the encoding procedure of the system will be decreased due the adaptive domain pool embedded in the ASCQ structure. We also proposed a First-N-Maximum function as a decision function to choose those blocks in the domain pool that are most similar to the terminal ones. The experimental results reflect that the ASCQ structure is indeed an efficient structure for the fractal- based image compression system.
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Tsai, Yih-Daw, and 蔡義道. "A Study on Fractal Image and Video Coding Using Interblock Correlation Search Strategy." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/13466973175286295267.
Full textAbstract:
碩士國立成功大學
電機工程學系
87
Abstract One serious drawback of fractal image compression is that it is a heavily unbalance technique: the computational requirement of the compression algorithm are orders of magnitude greater than those of the decompression. Moreover, the method used to find the domain block matched to a range block determines how much computation time the encoding process takes. In this thesis, by exploiting the correlation between range blocks a search strategy is proposed to speed up the encoding process. In the proposed strategy, the four domain blocks mapped by the previous causal neighboring range blocks are considered as potential matched blocks to the input range block. The proposed strategy can be based on an existing fast fractal coding algorithm to further reduce its coding complexity and raise the compression efficiency with insignificant loss of image quality. In recent years, image sequence compression is becoming more and more important in visual communication services and digital video storage. Therefore, The proposed interblock correlation search strategy was extended from 2-D still image coding to 3-D video sequences coding. Two intercubes correlation search methods which separately consider the correlation of three-dimensional range blocks in the spatial and the temproal-spatial directions, were developed in fractal coding of image sequences. The methods can be combined with existing fast fractal coding methods to further speed up the encoding process. We compared the performances of the proposed strategy with exhaustive search and other algorithms in terms of the average number of domain blocks searched by a range block, encoding time, bit rate and PSNR. In still image coding, the results indicate that the proposed strategy can further speed up the encoding process of an existing fast method over a factor of 2. It also indicates that the average bit rate reductions by the proposed strategy are 25.4% and 14.3% for 4×4 and 8×8 range block partitions respectively. The performance improvement of 4×4 range partition is greater that of 8×8 range partition due to the higher interblock correlation in 4×4 range partition. The loss of image quality is insignificant, all the values in PSNR incurred by our strategy over others are less than 0.35dB. In fractal vide coding, average compression ratios of 31 to 116, speedup factors of 8 to 4 with insignificant loss of quality, as compared to the local search method have been obtained the 4×4×4 and 8×8×4 range partitions respectively.
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Chou, Yen-Ping, and 周延平. "Wavelet Transform Applied to Fractal, Image Coding and Neural Networks to Identify Chaotic Systems." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/63911975271585478061.
Full textAbstract:
碩士國立交通大學
控制工程系
82
The wavelet transform (WT) provides an analyzing tool to decompose a signal into several components in a flexible time- frequency plane. The discrete wavelet transform (DWT), particularly combined orthonormal finite supported wavelets with multiresolution analysis, has been regarded as an efficient and easy-implemented WT. In this thesis, we first investigate the continuous WT and present its application of fractals. Then, based on the research of Daubechies, we explore another spectral factorization to establish some compactly supported wavelets for the DWT. Next, we apply the DWT to two physical cases. Using the extended version of the DWT$-$two- dimensional DWT, we convert an image into several wavelet coefficients. Then these subimages are quantized and encoded in order to perform compression. In the second application, we propose a wavelet-based neural network (WBNN) to identify chaotic systems. The WBNN structure overcomes a disadvantage of time-consuming, existing in the training process of conventional neural networks.
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Tin, Hsiao-Wen, and 丁筱雯. "Fractal approach in image coding and texture analysis: the improvement of searching and its applications." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/shgfe7.
Full textAbstract:
博士國立臺灣海洋大學
電機工程學系
101
Euclidean geometry describes the artificial shapes well since its development. Natural science also applied the Euclidean system to describe the shapes and structures of natural objects for a long time. However, chaos exhibits in nature everywhere. Chaos objects are characterized as complex, irregular and non-calculable which is hardly described by Euclidean system. An indescribable object is not able to be a research object. Chaos objects remained as indescribable until fractal geometry was presented. The main contribution of fractal geometry is that it well describes quantitatively most of the irregular, broken and complex natural objects. Self-similarity is one of the important features of fractal in both mathematics and physics. In practical, iterated function system (IFS) was adopted by the fractal coding to approximate the natural objects and images. In recent years, IFS method has become widely popular in fractal image coding research. Such fractal image coding is usually considered as an efficient image coding method primarily due to it is a lossy compression in nature. However, it requires some heavy computations due to the fractal block encoding requires much of the processing time to search the domain blocks, which is the major hurdle for performance. To overcome the performance bottleneck, this dissertation proposed three fractal coding algorithms based on reducing the number of domain blocks in the domain pool. The elaborately designed approaches improve the searching efficiency and preserve the image quality after encode. Image denoising is a difficult problem which is how to detract image texture information as little as possible while removing or reducing noise as much as possible. Fractal-wavelet coding methods were an efficient image denoising method in various areas but not in texture analysis. This dissertation proposes an elaborative approach to measure the image roughness for texture analysis and then introduces to Fractal-wavelet (FW) coding process. The experimental results indicate that the proposed algorithm is adaptable in denoising side-scan sonar images and that the images are more appealing visually. The fractal dimension (FD) is an abstract measure of fractal property and used to index the extracted feature. From analyzing the network traffics in various scales, this study observed the very complicated variances of network flows were actually fractal. Therefore, this dissertation proposes an approach to quantify the bursty traffic that degrades network performance and reliability by using fractal dimensions.
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Cheng, Chih-Jen, and 鄭智仁. "Fractal Coding for Still Images." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/94597194123120247767.
Full textAbstract:
碩士國立中正大學
資訊工程學系
84
In recent years, there are more and more data transmitted in the Internet.It is clear to know that the bandwidth of network is always not able to affordsuch a large amount of data. Since compressing data for saving storage andtransmitted time is easier than expanding the bandwidth of network, thecompression techniques are more and more important. Among the image codingtechniques, fractal coding has been considered to be an effective method forcoding image at low bit rate. In general, image compression scheme eliminatesthe redundancy between pixels to reduce the bit rate for storing the image.However, in the fractal coding scheme all we want to do is to find a similarblock for the block that we want to encode and employ transformations todescribe the relationship between the blocks. The parameters of transformationsand location of found block are stored as the code for the encoded block. The main disadvantage of fractal coding scheme is that the encoding procedurespends very long time. In order to find a similar block, the encoding proceduremust examines all the blocks in the image and computes the distortions. A largeramount of comparisons and computations are needed for this step. In this thesis,we propose a method that classifies the blocks into several classes and encodesthose blocks with different ways according to their classes. The blocks with small variances are encoded by their mean values, and notransformations are needed to be employed. The second kind of blocks with largervariances is restricted to search similar blocks in a small region instead ofsearching the whole image and some transformations are eliminated. For theblocks that have largest variances all transformations for the fractal codingare involved and a fast searching scheme in the whole image is employed to speedup the procedure. By the way, the quality of reconstructed image is acceptableand the bit rate is smaller with shorter encoding time. Comparing to severalfractal coding schemes, the proposed method has a better reconstructed imagewith nearly the same bit rate.
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Yang, Kuan-Hua, and 楊冠華. "Fast No Search Fractal Coding for Color Images." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/14825267229564404808.
Full textAbstract:
碩士大同大學
通訊工程研究所
93
The fractal image coding has been used in many image processing applications in recent years. In the fractal image coding, most of the time is spent on searching the best matching domain block and the parameters of the transform function. If we want to transmit an image in the internet or store it in some devices, it is desirable to achieve fast fractal encoding. In this thesis, fast no search fractal coding methods for color images are proposed which are able to speed up the encoding time and maintain the image fidelity. Based on iterated function system (IFS) and recurrent iterated function system (RIFS), we propose some no search factal coding methods for RGB images and YCbCr images. Extensive simulations show that our no search fractal coding methods achieve fast encoding time than conventional fractal coding method and maintain high quality of decoded images.
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Lin, Jun-Ping, and 林君屏. "NO SEARCH FRACTAL IMAGE CODINGIN WAVELET DOMAIN." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/45159990800898519631.
Full textAbstract:
碩士大同大學
通訊工程研究所
96
The no search fractal image coding method is very fast compared with the full search fractal image coding method. In this thesis, we propose no search fractal coding in wavelet domain method that can make encoding speed faster and have high compression ratio. This method uses fractal code on wavelet domain. Encoded image range blocks utilize fixed location domain blocks in different wavelet scale. We utilize the correlation of different wavelet scale to reduce encoding time. Experiment result show that the encoding time of proposed method is faster than the no search method and searchless in wavelet domain. It is show that the compression ratio and the reconstructed quality of our method are better than the method of searchless fractal coding in wavelet domain.
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徐宏昇. "Wavelet-based image compression using optimal scalar quantization, revised run-length coding and fractals." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/80898247311151593636.
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Brijmohan, Yarish. "Codec for multimedia services using wavelets and fractals." Thesis, 2004. http://hdl.handle.net/10413/3189.
Full textAbstract:
Increase in technological advancements in fields of telecommunications, computers and
television have prompted the need to exchange video, image and audio files between people.
Transmission of such files finds numerous multimedia applications such as, internet multimedia,
video conferencing, videophone, etc. However, the transmission and rece-ption of these files are
limited by the available bandwidth as well as storage capacities of systems. Thus there is a need
to develop compression systems, such that required multimedia applications can operate within
these limited capacities.
This dissertation presents two well established coding approaches that are used in modern' image
and video compression systems. These are the wavelet and fractal methods. The wavelet based
coder, which adopts the transform coding paradigm, performs the discrete wavelet transform on
an image before any compression algorithms are implemented. The wavelet transform provides
good energy compaction and decorrelating properties that make it suited for compression.
Fractal compression systems on the other hand differ from the traditional transform coders.
These algorithms are based on the theory of iterated function systems and take advantage of
local self-similarities present in images. In this dissertation, we first review the theoretical
foundations of both wavelet and fractal coders. Thereafter we evaluate different wavelet and
fractal based compression algorithms, and assess the strengths and weakness in each case.
Due to the short-comings of fractal based compression schemes, such as the tiling effect
appearing in reconstructed images, a wavelet based analysis of fractal image compression is
presented. This is the link that produces fractal coding in the wavelet domain, and presents a
hybrid coding scheme called fractal-wavelet coders. We show that by using smooth wavelet
basis in computing the wavelet transform, the tiling effect of fractal systems can be removed.
The few wavelet-fractal coders that have been proposed in literature are discussed, showing
advantages over the traditional fractal coders.
This dissertation will present a new low-bit rate video compression system that is based on
fractal coding in the wavelet domain. This coder makes use of the advantages of both the
wavelet and fractal coders discussed in their review. The self-similarity property of fractal
coders exploits the high spatial and temporal correlation between video frames. Thus the fractal
coding step gives an approximate representation of the coded frame, while the wavelet
technique adds detail to the frame. In this proposed scheme, each frame is decomposed using
the pyramidal multi-resolution wavelet transform. Thereafter a motion detection operation is used in which the subtrees are partitioned into motion and non-motion subtrees. The nonmotion
subtrees are easily coded by a binary decision, whereas the moving ones are coded using
the combination of the wavelet SPIHT and fractal variable subtree size coding scheme. All
intra-frame compression is performed using the SPIHT compression algorithm and inter-frame
using the fractal-wavelet method described above.
The proposed coder is then compared to current low bit-rate video coding standards such as the
H.263+ and MPEG-4 coders through analysis and simulations. Results show that the proposed
coder is competitive with the current standards, with a performance improvement been shown in
video sequences that do not posses large global motion. Finally, a real-time implementation of
the proposed algorithm is performed on a digital signal processor. This illustrates the suitability
of the proposed coder being applied to numerous multimedia applications.Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2004.