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WAVELETS IN REAL-TIME RENDERING
Title
WAVELETS IN REAL-TIME RENDERING.
Creator
sun, weifeng, Mukherjee, Amar, University of Central Florida
Abstract / Description
Interactively simulating visual appearance of natural objects under natural illumination is a fundamental problem in computer graphics. 3D computer games, geometry modeling, training and simulation, electronic commerce, visualization, lighting design, digital libraries, geographical information systems, economic and medical image processing are typical candidate applications. Recent advances in graphics hardware have enabled real-time rasterization of complex scenes under artificial lighting...
Show moreInteractively simulating visual appearance of natural objects under natural illumination is a fundamental problem in computer graphics. 3D computer games, geometry modeling, training and simulation, electronic commerce, visualization, lighting design, digital libraries, geographical information systems, economic and medical image processing are typical candidate applications. Recent advances in graphics hardware have enabled real-time rasterization of complex scenes under artificial lighting environment. Meanwhile, pre-computation based soft shadow algorithms are proven effective under low-frequency lighting environment. Under the most practical yet popular all-frequency natural lighting environment, however, real-time rendering of dynamic scenes still remains a challenging problem. In this dissertation, we propose a systematic approach to render dynamic glossy objects under the general all-frequency lighting environment. In our framework, lighting integration is reduced to two rather basic mathematical operations, efficiently computing multi-function product and product integral. The main contribution of our work is a novel mathematical representation and analysis of multi-function product and product integral in the wavelet domain. We show that, multi-function product integral in the primal is equivalent to summation of the product of basis coefficients and integral coefficients. In the dissertation, we give a novel Generalized Haar Integral Coefficient Theorem. We also present a set of efficient algorithms to compute multi-function product and product integral. In the dissertation, we demonstrate practical applications of these algorithms in the interactive rendering of dynamic glossy objects under distant time-variant all-frequency environment lighting with arbitrary view conditions. At each vertex, the shading integral is formulated as the product integral of multiple operand functions. By approximating operand functions in the wavelet domain, we demonstrate rendering dynamic glossy scenes interactively, which is orders of magnitude faster than previous work. As an important enhancement to the popular Pre-computation Based Radiance Transfer (PRT) approach, we present a novel Just-in-time Radiance Transfer (JRT) technique, and demonstrate its application in real-time realistic rendering of dynamic all-frequency shadows under general lighting environment. Our work is a significant step towards real-time rendering of arbitrary scenes under general lighting environment. It is also of great importance to general numerical analysis and signal processing.
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Date Issued
2006
Identifier
CFE0001495, ucf:47079
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001495
TRANSFORM BASED AND SEARCH AWARE TEXT COMPRESSION SCHEMES AND COMPRESSED DOMAIN TEXT RETRIEVAL
Title
TRANSFORM BASED AND SEARCH AWARE TEXT COMPRESSION SCHEMES AND COMPRESSED DOMAIN TEXT RETRIEVAL.
Creator
Zhang, Nan, Mukherjee, Amar, University of Central Florida
Abstract / Description
In recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need...
Show moreIn recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need from this huge mass of data. Sometimes, a single site may also contain large collections of data such as a library database, thereby requiring an efficient search mechanism even to search within the local data. To facilitate the information retrieval, an emerging ad hoc standard for uncompressed text is XML which preprocesses the text by putting additional user defined metadata such as DTD or hyperlinks to enable searching with better efficiency and effectiveness. This increases the file size considerably, underscoring the importance of applying text compression. On account of efficiency (in terms of both space and time), there is a need to keep the data in compressed form for as much as possible. (2) Exact and approximate pattern matching in Burrows-Wheeler transformed (BWT) files: We proposed a method to extract the useful context information in linear time from the BWT transformed text. The auxiliary arrays obtained from BWT inverse transform brings logarithm search time. Meanwhile, approximate pattern matching can be performed based on the results of exact pattern matching to extract the possible candidate for the approximate pattern matching. Then fast verifying algorithm can be applied to those candidates which could be just small parts of the original text. We present algorithms for both k-mismatch and k-approximate pattern matching in BWT compressed text. A typical compression system based on BWT has Move-to-Front and Huffman coding stages after the transformation. We propose a novel approach to replace the Move-to-Front stage in order to extend compressed domain search capability all the way to the entropy coding stage. A modification to the Move-to-Front makes it possible to randomly access any part of the compressed text without referring to the part before the access point. . Modified LZW algorithm that allows random access and partial decoding for the compressed text retrieval: Although many compression algorithms provide good compression ratio and/or time complexity, LZW is the first one studied for the compressed pattern matching because of its simplicity and efficiency. Modifications on LZW algorithm provide the extra advantage for fast random access and partial decoding ability that is especially useful for text retrieval systems. Based on this algorithm, we can provide a dynamic hierarchical semantic structure for the text, so that the text search can be performed on the expected level of granularity. For example, user can choose to retrieve a single line, a paragraph, or a file, etc. that contains the keywords. More importantly, we will show that parallel encoding and decoding algorithm is trivial with the modified LZW. Both encoding and decoding can be performed with multiple processors easily and encoding and decoding process are independent with respect to the number of processors. Text compression is concerned with techniques for representing the digital text data in alternate representations that takes less space. Not only does it help conserve the storage space for archival and online data, it also helps system performance by requiring less number of secondary storage (disk or CD Rom) accesses and improves the network transmission bandwidth utilization by reducing the transmission time. Unlike static images or video, there is no international standard for text compression, although compressed formats like .zip, .gz, .Z files are increasingly being used. In general, data compression methods are classified as lossless or lossy. Lossless compression allows the original data to be recovered exactly. Although used primarily for text data, lossless compression algorithms are useful in special classes of images such as medical imaging, finger print data, astronomical images and data bases containing mostly vital numerical data, tables and text information. Many lossy algorithms use lossless methods at the final stage of the encoding stage underscoring the importance of lossless methods for both lossy and lossless compression applications. In order to be able to effectively utilize the full potential of compression techniques for the future retrieval systems, we need efficient information retrieval in the compressed domain. This means that techniques must be developed to search the compressed text without decompression or only with partial decompression independent of whether the search is done on the text or on some inversion table corresponding to a set of key words for the text. In this dissertation, we make the following contributions: (1) Star family compression algorithms: We have proposed an approach to develop a reversible transformation that can be applied to a source text that improves existing algorithm's ability to compress. We use a static dictionary to convert the English words into predefined symbol sequences. These transformed sequences create additional context information that is superior to the original text. Thus we achieve some compression at the preprocessing stage. We have a series of transforms which improve the performance. Star transform requires a static dictionary for a certain size. To avoid the considerable complexity of conversion, we employ the ternary tree data structure that efficiently converts the words in the text to the words in the star dictionary in linear time. (2) Exact and approximate pattern matching in Burrows-Wheeler transformed (BWT) files: We proposed a method to extract the useful context information in linear time from the BWT transformed text. The auxiliary arrays obtained from BWT inverse transform brings logarithm search time. Meanwhile, approximate pattern matching can be performed based on the results of exact pattern matching to extract the possible candidate for the approximate pattern matching. Then fast verifying algorithm can be applied to those candidates which could be just small parts of the original text. We present algorithms for both k-mismatch and k-approximate pattern matching in BWT compressed text. A typical compression system based on BWT has Move-to-Front and Huffman coding stages after the transformation. We propose a novel approach to replace the Move-to-Front stage in order to extend compressed domain search capability all the way to the entropy coding stage. A modification to the Move-to-Front makes it possible to randomly access any part of the compressed text without referring to the part before the access point. (3) Modified LZW algorithm that allows random access and partial decoding for the compressed text retrieval: Although many compression algorithms provide good compression ratio and/or time complexity, LZW is the first one studied for the compressed pattern matching because of its simplicity and efficiency. Modifications on LZW algorithm provide the extra advantage for fast random access and partial decoding ability that is especially useful for text retrieval systems. Based on this algorithm, we can provide a dynamic hierarchical semantic structure for the text, so that the text search can be performed on the expected level of granularity. For example, user can choose to retrieve a single line, a paragraph, or a file, etc. that contains the keywords. More importantly, we will show that parallel encoding and decoding algorithm is trivial with the modified LZW. Both encoding and decoding can be performed with multiple processors easily and encoding and decoding process are independent with respect to the number of processors.
Show less
Date Issued
2005
Identifier
CFE0000438, ucf:46396
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000438
COMPRESSED PATTERN MATCHING FOR TEXT AND IMAGES
Title
COMPRESSED PATTERN MATCHING FOR TEXT AND IMAGES.
Creator
Tao, Tao, Mukherjee, Amar, University of Central Florida
Abstract / Description
The amount of information that we are dealing with today is being generated at an ever-increasing rate. On one hand, data compression is needed to efficiently store, organize the data and transport the data over the limited-bandwidth network. On the other hand, efficient information retrieval is needed to speedily find the relevant information from this huge mass of data using available resources. The compressed pattern matching problem can be stated as: given the compressed format of a text...
Show moreThe amount of information that we are dealing with today is being generated at an ever-increasing rate. On one hand, data compression is needed to efficiently store, organize the data and transport the data over the limited-bandwidth network. On the other hand, efficient information retrieval is needed to speedily find the relevant information from this huge mass of data using available resources. The compressed pattern matching problem can be stated as: given the compressed format of a text or an image and a pattern string or a pattern image, report the occurrence(s) of the pattern in the text or image with minimal (or no) decompression. The main advantages of compressed pattern matching versus the naïve decompress-then-search approach are: First, reduced storage cost. Since there is no need to decompress the data or there is only minimal decompression required, the disk space and the memory cost is reduced. Second, less search time. Since the size of the compressed data is smaller than that of the original data, a searching performed on the compressed data will result in a shorter search time. The challenge of efficient compressed pattern matching can be met from two inseparable aspects: First, to utilize effectively the full potential of compression for the information retrieval systems, there is a need to develop search-aware compression algorithms. Second, for data that is compressed using a particular compression technique, regardless whether the compression is search-aware or not, we need to develop efficient searching techniques. This means that techniques must be developed to search the compressed data with no or minimal decompression and with not too much extra cost. Compressed pattern matching algorithms can be categorized as either for text compression or for image compression. Although compressed pattern matching for text compression has been studied for a few years and many publications are available in the literature, there is still room to improve the efficiency in terms of both compression and searching. None of the search engines available today make explicit use of compressed pattern matching. Compressed pattern matching for image compression, on the other hand, has been relatively unexplored. However, it is getting more attention because lossless compression has become more important for the ever-increasing large amount of medical images, satellite images and aerospace photos, which requires the data to be losslessly stored. Developing efficient information retrieval techniques from the losslessly compressed data is therefore a fundamental research challenge. In this dissertation, we have studied compressed pattern matching problem for both text and images. We present a series of novel compressed pattern matching algorithms, which are divided into two major parts. The first major work is done for the popular LZW compression algorithm. The second major work is done for the current lossless image compression standard JPEG-LS. Specifically, our contributions from the first major work are: 1. We have developed an "almost-optimal" compressed pattern matching algorithm that reports all pattern occurrences. An earlier "almost-optimal" algorithm reported in the literature is only capable of detecting the first occurrence of the pattern and the practical performance of the algorithm is not clear. We have implemented our algorithm and provide extensive experimental results measuring the speed of our algorithm. We also developed a faster implementation for so-called "simple patterns". The simple patterns are patterns that no unique symbol appears more than once. The algorithm takes advantage of this property and runs in optimal time. 2. We have developed a novel compressed pattern matching algorithm for multiple patterns using the Aho-Corasick algorithm. The algorithm takes O(mt+n+r) time with O(mt) extra space, where n is the size of the compressed file, m is the total size of all patterns, t is the size of the LZW trie and r is the number of occurrences of the patterns. The algorithm is particularly efficient when being applied on archival search if the archives are compressed with a common LZW trie. All the above algorithms have been implemented and extensive experiments have been conducted to test the performance of our algorithms and to compare with the best existing algorithms. The experimental results show that our compressed pattern matching algorithm for multiple patterns is competitive among the best algorithms and is practically the fastest among all approaches when the number of patterns is not very large. Therefore, our algorithm is preferable for general string matching applications. LZW is one of the most efficient and popular compression algorithms used extensively and both of our algorithms require no modification on the compression algorithm. Our work, therefore, has great economical and market potential Our contributions from the second major work are: 1 We have developed a new global context variation of the JPEG-LS compression algorithm and the corresponding compressed pattern matching algorithm. Comparing to the original JPEG-LS, the global context variation is search-aware and has faster encoding and decoding speeds. The searching algorithm based on the global-context variation requires partial decompression of the compressed image. The experimental results show that it improves the search speed by about 30% comparing to the decompress-then-search approach. Based on our best knowledge, this is the first two-dimensional compressed pattern matching work for the JPEG-LS standard. 2 We have developed a two-pass variation of the JPEG-LS algorithm and the corresponding compressed pattern matching algorithm. The two-pass variation achieves search-awareness through a common compression technique called semi-static dictionary. Comparing to the original algorithm, the compression of the new algorithm is equally well but the encoding takes slightly longer. The searching algorithm based on the two-pass variation requires no decompression at all and therefore works in the fully compressed domain. It runs in time O(nc+mc+nm+m^2) with extra space O(n+m+mc), where n is the number of columns of the image, m is the number of rows and columns of the pattern, nc is the compressed image size and mc is the compressed pattern size. The algorithm is the first known two-dimensional algorithm that works in the fully compressed domain.
Show less
Date Issued
2005
Identifier
CFE0000471, ucf:46366
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000471
TRANSFORM BASED AND SEARCH AWARE TEXT COMPRESSION SCHEMES AND COMPRESSED DOMAIN TEXT RETRIEVAL
Title
TRANSFORM BASED AND SEARCH AWARE TEXT COMPRESSION SCHEMES AND COMPRESSED DOMAIN TEXT RETRIEVAL.
Creator
Zhang, Nan, Mukherjee, Amar, University of Central Florida
Abstract / Description
In recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need...
Show moreIn recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need from this huge mass of data. Sometimes, a single site may also contain large collections of data such as a library database, thereby requiring an efficient search mechanism even to search within the local data. To facilitate the information retrieval, an emerging ad hoc standard for uncompressed text is XML which preprocesses the text by putting additional user defined metadata such as DTD or hyperlinks to enable searching with better efficiency and effectiveness. This increases the file size considerably, underscoring the importance of applying text compression. On account of efficiency (in terms of both space and time), there is a need to keep the data in compressed form for as much as possible. Text compression is concerned with techniques for representing the digital text data in alternate representations that takes less space. Not only does it help conserve the storage space for archival and online data, it also helps system performance by requiring less number of secondary storage (disk or CD Rom) accesses and improves the network transmission bandwidth utilization by reducing the transmission time. Unlike static images or video, there is no international standard for text compression, although compressed formats like .zip, .gz, .Z files are increasingly being used. In general, data compression methods are classified as lossless or lossy. Lossless compression allows the original data to be recovered exactly. Although used primarily for text data, lossless compression algorithms are useful in special classes of images such as medical imaging, finger print data, astronomical images and data bases containing mostly vital numerical data, tables and text information. Many lossy algorithms use lossless methods at the final stage of the encoding stage underscoring the importance of lossless methods for both lossy and lossless compression applications. In order to be able to effectively utilize the full potential of compression techniques for the future retrieval systems, we need efficient information retrieval in the compressed domain. This means that techniques must be developed to search the compressed text without decompression or only with partial decompression independent of whether the search is done on the text or on some inversion table corresponding to a set of key words for the text. In this dissertation, we make the following contributions: (1) Star family compression algorithms: We have proposed an approach to develop a reversible transformation that can be applied to a source text that improves existing algorithm's ability to compress. We use a static dictionary to convert the English words into predefined symbol sequences. These transformed sequences create additional context information that is superior to the original text. Thus we achieve some compression at the preprocessing stage. We have a series of transforms which improve the performance. Star transform requires a static dictionary for a certain size. To avoid the considerable complexity of conversion, we employ the ternary tree data structure that efficiently converts the words in the text to the words in the star dictionary in linear time. (2) Exact and approximate pattern matching in Burrows-Wheeler transformed (BWT) files: We proposed a method to extract the useful context information in linear time from the BWT transformed text. The auxiliary arrays obtained from BWT inverse transform brings logarithm search time. Meanwhile, approximate pattern matching can be performed based on the results of exact pattern matching to extract the possible candidate for the approximate pattern matching. Then fast verifying algorithm can be applied to those candidates which could be just small parts of the original text. We present algorithms for both k-mismatch and k-approximate pattern matching in BWT compressed text. A typical compression system based on BWT has Move-to-Front and Huffman coding stages after the transformation. We propose a novel approach to replace the Move-to-Front stage in order to extend compressed domain search capability all the way to the entropy coding stage. A modification to the Move-to-Front makes it possible to randomly access any part of the compressed text without referring to the part before the access point. (3) Modified LZW algorithm that allows random access and partial decoding for the compressed text retrieval: Although many compression algorithms provide good compression ratio and/or time complexity, LZW is the first one studied for the compressed pattern matching because of its simplicity and efficiency. Modifications on LZW algorithm provide the extra advantage for fast random access and partial decoding ability that is especially useful for text retrieval systems. Based on this algorithm, we can provide a dynamic hierarchical semantic structure for the text, so that the text search can be performed on the expected level of granularity. For example, user can choose to retrieve a single line, a paragraph, or a file, etc. that contains the keywords. More importantly, we will show that parallel encoding and decoding algorithm is trivial with the modified LZW. Both encoding and decoding can be performed with multiple processors easily and encoding and decoding process are independent with respect to the number of processors.
Show less
Date Issued
2005
Identifier
CFE0000488, ucf:46358
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000488
ALGORITHMS FOR HAPLOTYPE INFERENCE AND BLOCK PARTITIONING
Title
ALGORITHMS FOR HAPLOTYPE INFERENCE AND BLOCK PARTITIONING.
Creator
Vijaya Satya, Ravi, Mukherjee, Amar, University of Central Florida
Abstract / Description
The completion of the human genome project in 2003 paved the way for studies to better understand and catalog variation in the human genome. The International HapMap Project was started in 2002 with the aim of identifying genetic variation in the human genome and studying the distribution of genetic variation across populations of individuals. The information collected by the HapMap project will enable researchers in associating genetic variations with phenotypic variations. Single Nucleotide...
Show moreThe completion of the human genome project in 2003 paved the way for studies to better understand and catalog variation in the human genome. The International HapMap Project was started in 2002 with the aim of identifying genetic variation in the human genome and studying the distribution of genetic variation across populations of individuals. The information collected by the HapMap project will enable researchers in associating genetic variations with phenotypic variations. Single Nucleotide Polymorphisms (SNPs) are loci in the genome where two individuals differ in a single base. It is estimated that there are approximately ten million SNPs in the human genome. These ten million SNPS are not completely independent of each other - blocks (contiguous regions) of neighboring SNPs on the same chromosome are inherited together. The pattern of SNPs on a block of the chromosome is called a haplotype. Each block might contain a large number of SNPs, but a small subset of these SNPs are sufficient to uniquely dentify each haplotype in the block. The haplotype map or HapMap is a map of these haplotype blocks. Haplotypes, rather than individual SNP alleles are expected to effect a disease phenotype. The human genome is diploid, meaning that in each cell there are two copies of each chromosome - i.e., each individual has two haplotypes in any region of the chromosome. With the current technology, the cost associated with empirically collecting haplotype data is prohibitively expensive. Therefore, the un-ordered bi-allelic genotype data is collected experimentally. The genotype data gives the two alleles in each SNP locus in an individual, but does not give information about which allele is on which copy of the chromosome. This necessitates computational techniques for inferring haplotypes from genotype data. This computational problem is called the haplotype inference problem. Many statistical approaches have been developed for the haplotype inference problem. Some of these statistical methods have been shown to be reasonably accurate on real genotype data. However, these techniques are very computation-intensive. With the international HapMap project collecting information from nearly 10 million SNPs, and with association studies involving thousands of individuals being undertaken, there is a need for more efficient methods for haplotype inference. This dissertation is an effort to develop efficient perfect phylogeny based combinatorial algorithms for haplotype inference. The perfect phylogeny haplotyping (PPH) problem is to derive a set of haplotypes for a given set of genotypes with the condition that the haplotypes describe a perfect phylogeny. The perfect phylogeny approach to haplotype inference is applicable to the human genome due to the block structure of the human genome. An important contribution of this dissertation is an optimal O(nm) time algorithm for the PPH problem, where n is the number of genotypes and m is the number of SNPs involved. The complexity of the earlier algorithms for this problem was O(nm^2). The O(nm) complexity was achieved by applying some transformations on the input data and by making use of the FlexTree data structure that has been developed as part of this dissertation work, which represents all the possible PPH solution for a given set of genotypes. Real genotype data does not always admit a perfect phylogeny, even within a block of the human genome. Therefore, it is necessary to extend the perfect phylogeny approach to accommodate deviations from perfect phylogeny. Deviations from perfect phylogeny might occur because of recombination events and repeated or back mutations (also referred to as homoplasy events). Another contribution of this dissertation is a set of fixed-parameter tractable algorithms for constructing near-perfect phylogenies with homoplasy events. For the problem of constructing a near perfect phylogeny with q homoplasy events, the algorithm presented here takes O(nm^2+m^(n+m)) time. Empirical analysis on simulated data shows that this algorithm produces more accurate results than PHASE (a popular haplotype inference program), while being approximately 1000 times faster than phase. Another important problem while dealing real genotype or haplotype data is the presence of missing entries. The Incomplete Perfect Phylogeny (IPP) problem is to construct a perfect phylogeny on a set of haplotypes with missing entries. The Incomplete Perfect Phylogeny Haplotyping (IPPH) problem is to construct a perfect phylogeny on a set of genotypes with missing entries. Both the IPP and IPPH problems have been shown to be NP-hard. The earlier approaches for both of these problems dealt with restricted versions of the problem, where the root is either available or can be trivially re-constructed from the data, or certain assumptions were made about the data. We make some novel observations about these problems, and present efficient algorithms for unrestricted versions of these problems. The algorithms have worst-case exponential time complexity, but have been shown to be very fast on practical instances of the problem.
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Date Issued
2006
Identifier
CFE0001244, ucf:46894
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001244