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The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 535 (12 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...
Navigating through Triangle Meshes Implemented as Linear Quadtrees
 ACM Transactions on Graphics
, 1998
"... Techniques are presented for navigating between adjacent triangles of greater or equal size in a hierarchical triangle mesh where the triangles are obtained by a recursive quadtreelike subdivision of the underlying space into four equilateral triangles. These techniques are useful in a number of ap ..."
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Cited by 30 (1 self)
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Techniques are presented for navigating between adjacent triangles of greater or equal size in a hierarchical triangle mesh where the triangles are obtained by a recursive quadtreelike subdivision of the underlying space into four equilateral triangles. These techniques are useful in a number of applications including finite element analysis, ray tracing, and the modeling of spherical data. The operations are implemented in a manner analogous to that used in a quadtree representation of data on the twodimensional plane where the underlying space is tessellated into a square mesh. A new technique is described for labeling the triangles which is useful in implementing the quadtree triangle mesh as a linear quadtree (i.e., a pointerless quadtree); the navigation can then take place in this linear quadtree. When the neighbors are of equal size, the algorithms take constant time. The algorithms are very efficient, as they make use of just a few bit manipulation operations and can be impl...
A framework for optimization of a multiresolution remote image retrieval system
 In Proceedings of the 13th Annual Joint Conference of the IEEE Computer and Communications Societies on Networking for Global Communication
, 1994
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Octree Approximation and Compression Methods
 In Proc. of the 1st Intl. Symp. on 3D Data Processing Visualization and Transmission
, 2002
"... www.cs.umd.edu/˜hjs Techniques are presented to progressively approximate and compress in a lossless manner twocolored (i.e. binary) 3D objects (as well as objects of arbitrary dimensionality). The objects are represented by a region octree implemented using a pointerless representation based on lo ..."
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www.cs.umd.edu/˜hjs Techniques are presented to progressively approximate and compress in a lossless manner twocolored (i.e. binary) 3D objects (as well as objects of arbitrary dimensionality). The objects are represented by a region octree implemented using a pointerless representation based on locational codes. Approximation is achieved through the use of a forest. This method labels the internal nodes of the octree as GB or GW, depending on the number of children being of type GB or GW. In addition, all BLACK nodes are labeled GB, while all WHITE nodes are labeled GW. A number of different image approximation methods are discussed that make use of a forest. The advantage of these methods is that they are progressive which means that as more of the object is transmitted, the better is the approximation. This makes these methods attractive for use on the worldwide web. Progressive transmission has the drawback that there is an overhead in requiring extra storage. Aprogressive forestbased approximation and transmission method is presented where the total amount of data that is transmitted is not larger than MIN(B,W), where B and W are the number of BLACK and WHITE blocks, respectively, in the region octree of the set of objects. 1
A generalized comparison of quadtree and bintree storage requirements
 Image and Vision Computing
, 1993
"... The quadtree and the bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadand bintrees ..."
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Cited by 8 (0 self)
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The quadtree and the bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadand bintrees is determined by two factors: the relative node sizes for the two representations as determined by the data structure implementation, and the number of quadtree leaf node pairs that merge to form a single leaf node after conversion to the bintree representation. A probabilistic model for images is developed to analyze the merging probability of quadtree leaf node pairs. The analysis reveals that exactly one half of such pairs are expected to merge. Empirical results closely match these calculations. The resulting storage efficiency for a number of representative implementations is discussed. Each of the data structures has implementations (and associated applications) for which it is more space efficient.
An Evaluation of Transmitting Compressed Images in a Wide Area Network
, 1995
"... Retrieving large data objects (of the order of hundreds of thousands of kilobytes) in a wide area network such as the Internet takes several seconds and occasionally minutes. As a step towards reducing response time we have studied the possibility of reducing the size of the data object by "los ..."
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Cited by 6 (5 self)
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Retrieving large data objects (of the order of hundreds of thousands of kilobytes) in a wide area network such as the Internet takes several seconds and occasionally minutes. As a step towards reducing response time we have studied the possibility of reducing the size of the data object by "losing" some of the data and then retrieving it. We have focussed on transmission of images across a wide area network. Images are amenable to losing data without losing the semantics of the image. Lossy compression techniques result in a smaller size, lower quality image. We have studied how the quality of the image can be sacrificed to achieve higher speed in retrieval over a wide area network. We have identified parameters involved in the retrieval process and conducted experiments to see how they can be varied to speed up retrieval. We have developed a scheme to reduce response time at the expense of the quality of the object depending on the current values of the parameters. 1 Introduction Dig...
A Probabilistic Analysis of TrieBased Sorting of Large Collections of Line Segments in Spatial Databases
, 2000
"... The size of five triebased methods of sorting large collections of line segments in a spatial database is investigated analytically using a random lines image model and geometric probability techniques. The methods are based on sorting the line segments with respect to the space that they occupy. ..."
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Cited by 6 (6 self)
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The size of five triebased methods of sorting large collections of line segments in a spatial database is investigated analytically using a random lines image model and geometric probability techniques. The methods are based on sorting the line segments with respect to the space that they occupy. Since the space is twodimensional, the trie is formed by interleaving the bits corresponding to the binary representation of the x and y coordinates of the underlying space and then testing two bits at each iteration. The result of this formulation yields a class of representations that are referred to as quadtrie variants, although they have been traditionally referred to as quadtree variants. The analysis differs from prior work in that it uses a detailed explicit model of the image instead of relying on modeling the branching process represented by the tree and leaving the underlying image unspecified. The analysis provides analytic expressions and bounds on the expected size of these quadtree variants. This enables the prediction of storage required by the representations and of the associated performance of algorithms that rely on them. The results are useful in two ways: 1. They reveal the properties of the various representations and permit their comparison using analytic, nonexperimental, criteria. Some of the results confirm previous analyses (e.g., that the storage requirement of the MX quadtree is proportional to the total lengths of the line segments). An important new result is that for a PMR and Bucket PMR quadtree with sufficiently high values of the splitting threshold (i.e., # 4) the number of nodes is proportional to the numberof line segments and is independent of the maximum depth of the tree. This provides a theoretical justification for ...
Using Ordered BinaryDecision Diagrams for Compressing Images and Image Sequences
, 1995
"... The Ordered BinaryDecision Diagram (OBDD) has been used to reduce the amount of space and computation required for verifying digital circuits by removing redundant copies of subfunctions. Similarly, image compression algorithms attempt to reduce their space requirements by finding replicated patter ..."
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Cited by 5 (0 self)
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The Ordered BinaryDecision Diagram (OBDD) has been used to reduce the amount of space and computation required for verifying digital circuits by removing redundant copies of subfunctions. Similarly, image compression algorithms attempt to reduce their space requirements by finding replicated patterns or features in images. OBDDs would therefore appear to be a good candidate as a data structure for representing images. We show how images can be encoded using Ordered BinaryDecision Diagrams and compare our results to quadtrees. We also show how using this method extends naturally to compressing sequences of related images such those that comprise movies. This research is sponsored by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant F336159311330. The US Government is authorized to reproduce and distribute reprints for Government purposes, notwithstanding any copyright notation thereon. ...