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Domains for Computation in Mathematics, Physics and Exact Real Arithmetic
 Bulletin of Symbolic Logic
, 1997
"... We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability dist ..."
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Cited by 59 (13 self)
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We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chao...
Accelerating Fractal Image Compression by MultiDimensional Nearest Neighbor Search”, CC’95 Data Compression Conference
, 1995
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Power domains and iterated function systems
 Information and Computation
, 1996
"... We introduce the notion of weakly hyperbolic iterated function system (IFS) on a compact metric space, which generalises that of hyperbolic IFS. Based on a domaintheoretic model, which uses the Plotkin power domain and the probabilistic power domain respectively, we prove the existence and uniquene ..."
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Cited by 37 (11 self)
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We introduce the notion of weakly hyperbolic iterated function system (IFS) on a compact metric space, which generalises that of hyperbolic IFS. Based on a domaintheoretic model, which uses the Plotkin power domain and the probabilistic power domain respectively, we prove the existence and uniqueness of the attractor of a weakly hyperbolic IFS and the invariant measure of a weakly hyperbolic IFS with probabilities, extending the classic results of Hutchinson for hyperbolic IFSs in this more general setting. We also present finite algorithms to obtain discrete and digitised approximations to the attractor and the invariant measure, extending the corresponding algorithms for hyperbolic IFSs. We then prove the existence and uniqueness of the invariant distribution of a weakly hyperbolic recurrent IFS and obtain an algorithm to generate the invariant distribution on the digitised screen. The generalised Riemann integral is used to provide a formula for the expected value of almost everywhere continuous functions with respect to this distribution. For hyperbolic recurrent IFSs and Lipschitz maps, one can estimate the integral up to any threshold of accuracy.] 1996 Academic Press, Inc. 1.
NextGeneration Content Representation, Creation and Searching for New Media Applications in Education
, 1998
"... Content creation, editing, and searching are extremely time consuming tasks that often require substantial training and experience, especially when highquality audio and video are involved. "New media" represents a new paradigm for multimedia information representation and processing, in ..."
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Cited by 27 (1 self)
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Content creation, editing, and searching are extremely time consuming tasks that often require substantial training and experience, especially when highquality audio and video are involved. "New media" represents a new paradigm for multimedia information representation and processing, in which the emphasis is placed on the actual content. It thus brings the tasks of content creation and searching much closer to actual users and enables them to be active producers of audiovisual information rather than passive recipients. We discuss the stateoftheart and present nextgeneration techniques for content representation, searching, creation, and editing. We discuss our experiences in developing a Webbased distributed compressed video editing and searching system (WebClip), a media representation language (Flavor) and an objectbased video authoring system (Zest) based on it, and large image/video search engines for the WorldWide Web (WebSEEk and VideoQ). We also present a case study of new media applications based on specific planned multimedia education experiments with the above systems in several K12 schools in Manhattan.
Breaking the Time Complexity of Fractal Image Compression
, 1994
"... : In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find a best match for another image portion. We show that this step can be replaced by multidimensio ..."
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Cited by 23 (5 self)
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: In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find a best match for another image portion. We show that this step can be replaced by multidimensional nearest neighbor search which runs in logarithmic time instead of linear time required for the common sequential search. Keywords: Image compression, multidimensional search, nearest neighbors, fractals. 1 Introduction With the ever increasing demand for images, sound, video sequences, computer animations and volume visualization, data compression remains a critical issue regarding the cost of data storage and transmission times. While JPEG currently provides the industry standard for still image compression there is ongoing research in alternative methods. Fractal image compression is one of them. JPEG can be termed symmetric in the sense that the encoding and decoding phases require ...
Fractal Image Compression via Nearest Neighbor Search
 Conf. Proc. NATO ASI Fractal Image Encoding and Analysis
, 1996
"... In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find best matches for other image portions called ranges. Our theory developed here shows that this bas ..."
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Cited by 22 (7 self)
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In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find best matches for other image portions called ranges. Our theory developed here shows that this basic procedure of fractal image compression is equivalent to multidimensional nearest neighbor search in a space of feature vectors. This result is useful for accelerating the encoding procedure in fractal image compression. The traditional sequential search takes linear time whereas the nearest neighbor search can be organized to require only logarithmic time. The fast search has been integrated into an existing stateoftheart classification method thereby accelerating the searches carried out in the individual domain classes. In this case we record acceleration factors up to about 50 depending on image and domain pool size with negligible or minor degradation in both image quality and com...
Performance Analysis of Distributed Implementations of a Fractal Image Compression Algorithm
, 1996
"... Fractal image compression provides an innovative approach to lossy image encoding, with a potential for very high compression ratios. Because of prohibitive compression times, however, the procedure has proved feasible in only a limited range of commercial applications. In this paper we demonstrate ..."
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Cited by 19 (2 self)
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Fractal image compression provides an innovative approach to lossy image encoding, with a potential for very high compression ratios. Because of prohibitive compression times, however, the procedure has proved feasible in only a limited range of commercial applications. In this paper we demonstrate that, due to the independent nature of fractal transform encoding of individual image segments, fractal image compression performs well in a coarsegrain distributed processing system. A sequential fractal compression algorithm is optimized and parallelized to execute across distributed workstations and an SP2 parallel processor using the Parallel Virtual Machine (PVM) software. The system utilizes both static and dynamic load allocation to obtain substantial compression time speedup over the original, sequential encoding implementation. Considerations such as workload granularity and compression time versus number of processors and RMS tolerance values are also presented. Keywords: Image com...
P.J.: Fractal Volume Compression
 IEEE Trans. Visualization and Computer Graphics
, 1996
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A guided tour of the fractal image compression literature
 Institut fur Informatik, Universitaet Freiburg, http://www.informatik.unifreiburg.de/TechReports
, 1994
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Partitioning Complexity Issue for Iterated Functions Systems based Image Coding
 in: Proceedings of the VIIth European Signal Processing Conference EUSIPCO'94
, 1994
"... . This paper copes with the issue of adaptive partitioning in the context of Iterated Functions Systems (IFS) image coding. The main concern is to provide some insights on the optimum degree of partition adaptivity. The key point is to point out the proper balance of information between the partitio ..."
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Cited by 15 (0 self)
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. This paper copes with the issue of adaptive partitioning in the context of Iterated Functions Systems (IFS) image coding. The main concern is to provide some insights on the optimum degree of partition adaptivity. The key point is to point out the proper balance of information between the partition representation and the transformation parameters of the system. Several systems involving different degrees of adaptivity will be compared. To that end a polygonalbased segmentation will be presented. This will allow to compare performances of partitioning using respectively square, rectangular and polygonal segments. 1. Introduction The concept of fractal has been introduced by Mandelbrot in the 1960's as an alternative to the classical Euclidean geometry mainly for describing shapes generated by Nature. Since then, this theory attracts the interest of many researchers in fields ranging from biology to physics through computer imaging and image processing. Iterated contractive function...