Results 1  10
of
10
Analysis of the clustering properties of the Hilbert spacefilling curve
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... AbstractÐSeveral schemes for the linear mapping of a multidimensional space have been proposed for various applications, such as access methods for spatiotemporal databases and image compression. In these applications, one of the most desired properties from such linear mappings is clustering, whic ..."
Abstract

Cited by 141 (10 self)
 Add to MetaCart
AbstractÐSeveral schemes for the linear mapping of a multidimensional space have been proposed for various applications, such as access methods for spatiotemporal databases and image compression. In these applications, one of the most desired properties from such linear mappings is clustering, which means the locality between objects in the multidimensional space being preserved in the linear space. It is widely believed that the Hilbert spacefilling curve achieves the best clustering [1], [14]. In this paper, we analyze the clustering property of the Hilbert spacefilling curve by deriving closedform formulas for the number of clusters in a given query region of an arbitrary shape (e.g., polygons and polyhedra). Both the asymptotic solution for the general case and the exact solution for a special case generalize previous work [14]. They agree with the empirical results that the number of clusters depends on the hypersurface area of the query region and not on its hypervolume. We also show that the Hilbert curve achieves better clustering than the z curve. From a practical point of view, the formulas given in this paper provide a simple measure that can be used to predict the required disk access behaviors and, hence, the total access time.
Improving FineGrained Irregular SharedMemory Benchmarks by Data Reordering
 IN PROC. OF THE IEEE/ACM SUPERCOMPUTING’2000: HIGH PERFORMANCE NETWORKING AND COMPUTING CONFERENCE (SC’2000
, 2000
"... We demonstrate that data reordering can substantially improve the performance of finegrained irregular sharedmemory benchmarks, on both hardware and software sharedmemory systems. In particular, we evaluate two distinct data reordering techniques that seek to colocate in memory objects that are i ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
We demonstrate that data reordering can substantially improve the performance of finegrained irregular sharedmemory benchmarks, on both hardware and software sharedmemory systems. In particular, we evaluate two distinct data reordering techniques that seek to colocate in memory objects that are in close proximity in the physical system modeled by the computation. The effects of these techniques are increased spatial locality and reduced false sharing. We evaluate the effectiveness of the data reordering techniques on a set of five irregular applications from SPLASH2 and Chaos. We implement both techniques in a small library, allowing us to enable them in an application by adding less than 10 lines of code. Our results on one hardware and two software sharedmemory systems show that, with data reordering during initialization, the performance of these applications is improved by 12%99% on the Origin 2000, 30%366% on TreadMarks, and 14%269% on HLRC.
On MultiDimensional Hilbert Indexings
 Theory of Computing Systems
, 1998
"... Indexing schemes for grids based on spacefilling curves (e.g., Hilbert indexings) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them hav ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
Indexing schemes for grids based on spacefilling curves (e.g., Hilbert indexings) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular spacefilling indexing scheme. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability. We define and analyze in a precise mathematical way rdimensional Hilbert indexings for arbitrary r 2. Moreover, we generalize and simplify previous work and clarify the concept of Hilbert curves for multidimensional grids. As we show, Hilbert indexings can be completely described and analyzed by "generating elements of order 1", thus, in comparison with previous work, reducing their structural comp...
MultiLinearization Data Structure for Image Browsing
 In SPIE { The International Society for Optical Engineering
, 1999
"... Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find images of interests. In this paper, we present a new data structure built on the multilinearization of image attributes for efficient organization of the data set and fast visual browsing of the images. We describe new techniques for multilinearization based on multiple spacefilling curves and hierarchical clustering techniques. In addition to providing fast navigation, our proposed data structure allows computationally efficient insertion and deletion of images from the data set. We then present a novel image navigator and browser built on duallinearization data structure and intuitive presentation of image relevance and relationships, demonstrate the image navigation process, and repo...
On Multidimensional Curves with Hilbert Property
, 2000
"... Indexing schemes for grids based on spacefilling curves (e.g., Hilbert curves) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won c ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Indexing schemes for grids based on spacefilling curves (e.g., Hilbert curves) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular spacefilling indexing schemes. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability.
Tensor product formulation for Hilbert spacefilling curves
 In Proceedings of the 2003 International Conference on Parallel Processing
, 2003
"... We present a tensor product formulation for Hilbert spacefilling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert spacefilling curve as a permutation which maps twodimensional ¥§¦©¨�¥� ¦ data elements stored in the row major or column major order to the ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
We present a tensor product formulation for Hilbert spacefilling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert spacefilling curve as a permutation which maps twodimensional ¥§¦©¨�¥� ¦ data elements stored in the row major or column major order to the order of traversing a Hilbert spacefilling curve. The tensor product formula of Hilbert spacefilling curves uses several permutation operations: stride permutation, radix2 Gray permutation, transposition, and antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including Rtree indexing, image processing, and process llocation, etc. Key words: tensor product, block recursive algorithm, Hilbert spacefilling curve, stride
Data Parallel Performance Optimizations Using Array Aliasing
, 1997
"... . The array aliasing mechanism provided in the Connection Machine Fortran (CMF) language and runtime system provides a unique way of identifying the memory address spaces local to processors within the global address space of distributed memory architectures, while staying in the data parallel pro ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
. The array aliasing mechanism provided in the Connection Machine Fortran (CMF) language and runtime system provides a unique way of identifying the memory address spaces local to processors within the global address space of distributed memory architectures, while staying in the data parallel programming paradigm. We show how the array aliasing feature can be used effectively in optimizing communication and computation performance. The constructs we present occur frequently in many scientific and engineering applications, and include various forms of aggregation and array reshaping through array aliasing. The effectiveness of the optimization techniques is demonstrated on an implementation of Anderson's hierarchical O(N) N body method. Key words. Data parallel programming, array aliasing, hierarchical N body methods. AMS(MOS) subject classifications. 68N15, 68N20, 7008, 70F10 1. Introduction. Data parallel programming provides an effective way to write maintainable, portabl...
Entropy Thresholding and Its Parallel Algorithm on the Reconfigurable Array of Processors with Wider Bus Networks
, 1999
"... Thresholding is the most commonly used technique in image segmentation. In this paper, we first propose an efficient sequential algorithm to improve the relative entropybased thresholding technique. This algorithm combines the concepts of the relative entropy with that of the local entropy and also ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Thresholding is the most commonly used technique in image segmentation. In this paper, we first propose an efficient sequential algorithm to improve the relative entropybased thresholding technique. This algorithm combines the concepts of the relative entropy with that of the local entropy and also includes the quadtree hierarchical structure in it. Second, we derive a constant time parallel algorithm to solve this problem on the reconfigurable array of processors with wider bus networks (RAPWBN).
Algebraic formulation and program generation of threedimensional hilbert spacefilling curves
 In The 2004 International Conference on Imaging Science, Systems, and Technology
, 2004
"... Abstract: We use a tensor product based multilinear algebra theory to formulate threedimensional Hilbert spacefilling curves. A 3D Hilbert spacefilling curve is specified as a permutation which rearranges threedimensional 2 n 2 n 2 n data elements stored in the row major order as in C language ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract: We use a tensor product based multilinear algebra theory to formulate threedimensional Hilbert spacefilling curves. A 3D Hilbert spacefilling curve is specified as a permutation which rearranges threedimensional 2 n 2 n 2 n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing a 3D Hilbert spacefilling curve. The tensor product formulation of 3D Hilbert spacefilling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of 3D Hilbert spacefilling curves. In addition, we derive a tensor product formula of inverse 3D Hilbert spacefilling curve permutation. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.
Lossless Compression of Medical Images Using Hilbert SpaceFilling Curves
"... A Hilbert spacefilling curve is a curve of 2^n x 2^n twodimensional space that it visits neighboring points consecutively without crossing itself. The application of Hilbert spacefilling curves in image processing is to rearrange image pixels in order to enhance pixel locality. An iterative progr ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
A Hilbert spacefilling curve is a curve of 2^n x 2^n twodimensional space that it visits neighboring points consecutively without crossing itself. The application of Hilbert spacefilling curves in image processing is to rearrange image pixels in order to enhance pixel locality. An iterative program of the Hilbert spacefilling curve ordering generated from a tensor product formulation is used to rearrange pixels of medical images. We implement four lossless encoding schemes, runlength encoding, LZ77 coding, LZW coding, and Huffman coding, along with the Hilbert spacefilling curve ordering. Combination of these encoding schemes are also implemented to study the effectiveness of various compression methods. In addition, differential encoding is employed to medical images to study different format of image representation to the above encoding schemes. In the paper, we report the testing results of compression ratio and performance evaluation. The experiments show that the preprocessing operation of differential encoding followed by the Hilbert spacefilling curve ordering and the compression method of LZW coding followed by Huffman coding will give the best compression result.