Results 1  10
of
10
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 ..."
Abstract

Cited by 453 (11 self)
 Add to MetaCart
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.
Reconstruction of quadtrees from quadtree medial axis transforms
 Computer Science Dept., University of Maryland
"... An algorithm is presented for reconstructing a quadtree from its quadtree medial axis transform (QMAT). It is useful when performing operations for which the QMAT is well suited (e.g., thinning of an image). The algorithm is a postorder tree traversal which propagates the subsumption of each BLACK Q ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
An algorithm is presented for reconstructing a quadtree from its quadtree medial axis transform (QMAT). It is useful when performing operations for which the QMAT is well suited (e.g., thinning of an image). The algorithm is a postorder tree traversal which propagates the subsumption of each BLACK QMAT node in the eight possible directions. Analysis of the algorithm shows that its average execution time is proportional to the number of leaf nodes in the quadtree. The algorithm also serves to reinforce the appropriateness of the definition of the quadtree skeleton which does not permit a BLACK quadtree node to require more than one element of the quadtree skeleton for its subsumption. 0 1%?5 Academic PKSS. IX 1.
A Sorting Approach to Indexing Spatial Data
, 2008
"... Spatial data is distinguished from conventional data by having extent. Therefore, spatial queries involve both the objects and the space that they occupy. The handling of queries that involve spatial data is facilitated by building an index on the data. The traditional role of the index is to sort t ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Spatial data is distinguished from conventional data by having extent. Therefore, spatial queries involve both the objects and the space that they occupy. The handling of queries that involve spatial data is facilitated by building an index on the data. The traditional role of the index is to sort the data, which means that it orders the data. However, since generally no ordering exists in dimensions greater than 1 without a transformation of the data to one dimension, the role of the sort process is one of differentiating between the data and what is usually done is to sort the spatial objects with respect to the space that they occupy. The resulting ordering is usually implicit rather than explicit so that the data need not be resorted (i.e., the index need not be rebuilt) when the queries change (e.g., the query reference objects). The index is said to order the space and the characteristics of such indexes are explored further.
SORTING SPATIAL DATA BY SPATIAL OCCUPANCY
 GEOSPATIAL VISUAL ANALYTICS: GEOGRAPHICAL ORMATION PROCESSING AND VISUAL ANALYTICS FOR ENVIRONMENTAL SECURITY
, 2009
"... The increasing popularity of webbased mapping services such as Microsoft Virtual Earth and Google Maps/Earth has led to a dramatic increase in awareness of the importance of location as a component of data for the purposes of further processing as a means of enhancing the value of the nonspatial da ..."
Abstract
 Add to MetaCart
The increasing popularity of webbased mapping services such as Microsoft Virtual Earth and Google Maps/Earth has led to a dramatic increase in awareness of the importance of location as a component of data for the purposes of further processing as a means of enhancing the value of the nonspatial data and of visualization. Both of these purposes inevitably involve searching. The efficiency of searching is dependent on the extent to which the underlying data is sorted. The sorting is encapsulated by the data structure known as an index that is used to represent the spatial data thereby making it more accessible. The traditional role of the indexes is to sort the data, which means that they order the data. However, since generally no ordering exists in dimensions greater than 1 without a transformation of the data to one dimension, the role of the sort process is one of differentiating between the data and what is usually done is to sort the spatial objects with respect to the space that they occupy. The resulting ordering should be implicit rather than explicit so that the data need not be resorted (i.e., the index need not be rebuilt) when the queries change. The indexes are said to order the space and the characteristics of such indexes are explored further.
UndulantBlock Elimination and IntegerPreserving Matrix Inversion 1
, 1995
"... 1 c 1994,1995 by the author. This work has been accepted for publication by Science ..."
Abstract
 Add to MetaCart
1 c 1994,1995 by the author. This work has been accepted for publication by Science
The Quadtree and Related Hierarchical Data Structures
"... 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 ..."
Abstract
 Add to MetaCart
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
Data Structures I Hierarchical Data Structures
"... This is the first part of a twopart overview of the use of hierarchical data structures and algorithms in computer graphics. In Part I, the focus is on fundamentals. Part II focuses on more advanced applications. Methods based on hierarchical data structures and algorithms have found many uses in ..."
Abstract
 Add to MetaCart
This is the first part of a twopart overview of the use of hierarchical data structures and algorithms in computer graphics. In Part I, the focus is on fundamentals. Part II focuses on more advanced applications. Methods based on hierarchical data structures and algorithms have found many uses in image rendering and solid modeling. While such data structures are not necessary for the processing of simple scenes, they are central to the efficient processing of largescale realistic scenes. Objectspace hierarchies are discussed briefly, but the main emphasis is on hierarchies constructed in the image space, such as quadtrees and oc t rees. C omputer graphics applications require the manipulation of two distinct data formats: vector and raster (see Figure 1). The raster format enables the modeling of a graphics image as a collection of square cells of uniform size (called pixels]. A color is associated with each pixel. To attain maximum flexibility, an attempt is made to model directly the addressability of the phosphors on the display screen so that each pixel corresponds to a phosphor. This format has also proven useful in computer vision, since it corresponds to the digitized output of a television camera. In contrast, instead of modeling the display screen directly, the vector format models the
Neighbor Finding Techniques for Images Represented by Quadtrees*
, 1980
"... Image representation plays an important role in image processing applications. Recently there has been a considerable interest in the use of quadtrees. This has led to the development of algorithms for performing image processing tasks as well as for performing converting between the quadtree and ot ..."
Abstract
 Add to MetaCart
(Show Context)
Image representation plays an important role in image processing applications. Recently there has been a considerable interest in the use of quadtrees. This has led to the development of algorithms for performing image processing tasks as well as for performing converting between the quadtree and other representations. Common to these algorithms is a traversal of the tree and the performance of a given computation at each node. These computations typically require the ability to examine adjacencies between neighboring nodes. Algorithms are given for determining such adjacencies in the horizontal, vertical, and diagonal directions. The execution times of the algorithms are analyzed using a suitably defined model. I. JNTRODUCTJON Region representation is an important aspect of image processing with numerous representations finding use. Recently, there has emerged a considerable amount of interest in the quadtree [38, 111. This stems primarily from its hierarchical nature, which lends itself to a compact representation. It is also quite efficient for a number of traditional image processing operations such as computing perimeters [14], labeling connected components [ 131, finding the genus of an image [I], and comput
~ ~i ~i ~ ~i ~ ~i ~....
"... interests are data structures, image processing, programming languages, artificial intelligence, and database management systems. Arpa Network Address: his @ cvl The support of the Defense Advanced Research Projects Agency and the U.S. Army ..."
Abstract
 Add to MetaCart
interests are data structures, image processing, programming languages, artificial intelligence, and database management systems. Arpa Network Address: his @ cvl The support of the Defense Advanced Research Projects Agency and the U.S. Army
UndulantBlock Elimination and IntegerPreserving Matrix Inversion
, 1995
"... A new formulation for $LU$ decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during ``undulantblock'' elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are con ..."
Abstract
 Add to MetaCart
A new formulation for $LU$ decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during ``undulantblock'' elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such encapsulizations are deferred. Its algorithms, expressed naturally as functional programs, are well suited to parallel and distributed processing. A given matrix, $A$ is decomposed into two matrices (in the space of just one), plus two permutations. The permutations, $P$ and $Q$, are the row/column rearrangements usual to complete pivoting. %(one of which is $I$ under partial pivoting). The principal results are $L$ and $U'$, where $L$ is properlylower quasitriangular; $U'$ is upper quasitriangular with its quasidiagonal being the inverse of that of $U$ from the usual factorization ($PAQ = (IL)U$), and its proper upper portion identical to $U$. The matrix result is $L+U'$. Algorithms for solving linear systems and matrix inversion follow directly. An example of a motivating data structure, the quadtree representation for matrices, is reviewed. Candidate pivots for Gaussian elimination under that structure are the subtrees, both constraining and assisting the pivot search, as well as decomposing to independent block/tree operations. %block operations decompose nicely there. The elementary algorithms are provided, coded in {\sc Haskell}. Finally, an integerpreserving version is presented replacing Bareiss's algorithm with a parallel equivalent. The decomposition of an integer matrix $A$ to integer matrices $\bar L$, $\bar U'$, and $d$ $=\det A$ follows $L+U'$ decomposition, but the followon algorithm to compute $dA^{1}$ is complicated by the requirement to maintain minimal denominators at every step and to avoid divisions, restricting them to necessarily exact ones.