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31
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 533 (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.
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 327 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Octrees for faster isosurface generation
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2000
"... The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within ..."
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Cited by 323 (3 self)
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The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within the volume. This paper discusses research into the use of the octree hierarchical data structure when the regions of current interest can vary during the application, and are not known a priori. Octrees are well suited to the sixsided cell structure of many volumes. A new spaceefficient design is introduced for octree representations of volumes whose resolutions are not conveniently a power of two; octrees following this design are called branchonneed octrees (BONOs). Also, a caching method is described that essentially passes information between octree neighbors whose visitation times may be quite different, then discards it when its useful life is over. Using the application of octrees to isosurface generation as a focus, space and time comparisons for octreebased versus more traditional "marching" methods are presented.
Pyramidal parametrics
 Computer Graphics (SIGGRAPH ’83 Proceedings
, 1983
"... The mapping of images onto surfaces may substantially increase the realism and information content of computergenerated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the pr ..."
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Cited by 305 (1 self)
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The mapping of images onto surfaces may substantially increase the realism and information content of computergenerated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the projected scale of the surface increases, interpolation between the original samples of the source image is necessary; as the scale is reduced, approximation of multiple samples in the source is required. Thus a constantly changing sampling window of viewdependent shape must traverse the source image. To reduce the computation implied by these requirements, a set of prefiltered source images may be created. This approach can be applied to particular advantage in animation, where a large number of frames using the same source image must be generated. This paper advances a "pyramidal parametric " prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images. Although the mapping of texture onto surfaces is an excellent example of the process and provided the original motivation for its development, pyramidal parametric data structures admit of wider application. The aliasing of not only surface texture, but also highlights and even the surface representations themselves, may be minimized by pyramidal parametric means.
Interference detection and collision avoidance among three dimensional objects
 Stanford University
, 1980
"... Two methods for detecting intersections among three dimensional objects are described. The first method involves detecting overlap among the projections of the objects on a given set of planes. The second method uses a three dimensional octree representation of the objects. Intersections are detec ..."
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Cited by 15 (1 self)
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Two methods for detecting intersections among three dimensional objects are described. The first method involves detecting overlap among the projections of the objects on a given set of planes. The second method uses a three dimensional octree representation of the objects. Intersections are detected by traversing the trees for the obstacles and the moving objects. Application of the methods to collision avoidance is discussed. I
Image Compression via Improved Quadtree Decomposition Algorithms
"... AbstractQuadtree decomposition is a simple technique used to obtain an image representation at different resolution levels. This representation can be useful for a variety of image processing and image compression algorithms. This paper presents a simple way to get better compression performances ( ..."
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Cited by 14 (0 self)
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AbstractQuadtree decomposition is a simple technique used to obtain an image representation at different resolution levels. This representation can be useful for a variety of image processing and image compression algorithms. This paper presents a simple way to get better compression performances (in MSE sense) via quadtree decomposition, by using: Near to optimal choice of the threshold for quadtree decomposition. Bit allocation procedure based on the equations derived from ratedistortion theory. The ratedistortion performance of the improved algorithm is calculated for some Gaussian field, and it is examined vie simulation over benchmark graylevel images. In both these cases, significant improvement in the compression performances is shown. I.
Algorithms for the conversion of quadtrees to rasters
 IEEE Trans. Pattern Anal. and Machine Intelligence PAMI3
, 1981
"... A number of algorithms are presented for obtaining~a~i&?ter representation for an image given its quadtree. The algorithms are given in an evolutionary manner starting with the straightforward topdown approach that visits each run in a row in succession starting at the root of the tree. The rem ..."
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Cited by 11 (5 self)
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A number of algorithms are presented for obtaining~a~i&?ter representation for an image given its quadtree. The algorithms are given in an evolutionary manner starting with the straightforward topdown approach that visits each run in a row in succession starting at the root of the tree. The remaining algorithms proceed in a manner akin to an inorder tree traversal. All of the algorithms are analyzed and an indication is given as to when each is preferable. The execution time of all of the algorithms is shown to be proportional to the sum of the heights of the blocks comprising the image. 1.
Approximate Pattern Matching in a Pattern Database System
 Info. Sys
, 1979
"... This paper is also concerned with the complexity of picture operations using pyramidlike data structures In particular, we are interested in discovering that two binary pictures (normalized for size, rotation, and position) "almost" match Our motivation for studying this problem is the ..."
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Cited by 7 (0 self)
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This paper is also concerned with the complexity of picture operations using pyramidlike data structures In particular, we are interested in discovering that two binary pictures (normalized for size, rotation, and position) "almost" match Our motivation for studying this problem is the design of errortolerant pattern database systems. Too often, in pattern analysis, matching algorithms are proposed without regard to the global organization of the representations of the models they are to match Consequently, the algorithms are only practical for small databases This paper will discuss the matching problem along with the design of a pattern database system. Section 2 contains definitions. Section 3 describes both depthfirst and breadthfirst approximate matching algorithms. Section 4 contains a probabilistic analysis of approximate matching both with and without pyramids. Section 5 describes the organization of the pattern database. Finally, Section 6 contains conclusions. 2. Definitions Definition: A binary image, I, is a 2nx2 n array of O's and 1's
ScaleSpace Trees and Applications as Filters, for Stereo Vision and Image Retrieval
 in British Machine Vision Conference (T. Pridmore and
, 1999
"... Images are remapped as scalespace trees. The minimal data structure is then augmented by "complement nodes" to increase the practical value of the representation. It is then shown how the resulting ctree can be used to remove noise from images, provide a hierarchical way to estimate a ..."
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Cited by 5 (2 self)
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Images are remapped as scalespace trees. The minimal data structure is then augmented by "complement nodes" to increase the practical value of the representation. It is then shown how the resulting ctree can be used to remove noise from images, provide a hierarchical way to estimate a dense disparity map from a stereo pair and to provide a basic segmentation of images for image retrieval purposes.
Quad Tree Structures For Image Compression Applications
, 1992
"... Traditionally, lossy compression schemes have focused on compressing data at fixed bit rates to either communicate information over limited bandwidth communi cation channels, or to store information in a fixedsize storage media. In this paper we describe a class of 1ossy algorithms that is capa ..."
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Cited by 4 (0 self)
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Traditionally, lossy compression schemes have focused on compressing data at fixed bit rates to either communicate information over limited bandwidth communi cation channels, or to store information in a fixedsize storage media. In this paper we describe a class of 1ossy algorithms that is capable of compressing image data over a wide range of rates so that quick browsing of large amounts of information as well as detailed examination of high resolution areas can be achieved by the same compression system.