Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Connected Component Labeling Using Quadtrees
Journal of the ACM (JACM)
A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
Region representation: quadtrees from boundary codes
Communications of the ACM
Region representation: boundary codes from quadtrees
Communications of the ACM
Computer representation of planar regions by their skeletons
Communications of the ACM
Report on the algorithmic language ALGOL 60
Communications of the ACM
Digital Picture Processing
Efficient computation and data structures for graphics.
Efficient computation and data structures for graphics.
Data structures for quadtree approximation and compression
Communications of the ACM
TID—a translation invariant data structure for storing images
Communications of the ACM
A compendium of key search references
ACM SIGIR Forum
SCG '85 Proceedings of the first annual symposium on Computational geometry
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
A virtual memory system for picture processing
Communications of the ACM
Efficient query processing on spatial networks
Proceedings of the 13th annual ACM international workshop on Geographic information systems
Fast distance transformation on irregular two-dimensional grids
Pattern Recognition
Multidimensional data structures for spatial applications
Algorithms and theory of computation handbook
A new data structure for efficient storing of images
Pattern Recognition Letters
SAC: semantic adaptive caching for spatial mobile applications
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Seeder finder: identifying additional needles in the Twitter haystack
Proceedings of the 6th ACM SIGSPATIAL International Workshop on Location-Based Social Networks
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As printedQuadtree skeletons are exact representations of the image andare used because they are observed to yield space efficiently and adecreased sensitivity to shifts in contrast with the quadtree. TheQMAT can be used as the underlying representation when solving mostproblems that can be solved by using a quadtree. An algorithm ispresented for the computation of the QMAT of a given quadtree byonly examining each BLACK node's adjacent and abuttingneighbors. Corrected Abstract (published as corrigendum in CACM 27, 2(February 1984) p. 151)The skeletal and medial axis transform concepts used intraditional image processing representations are adapted to thequadtree representation. The result is the definition of of a newdata structure termed the Quadtree Medial Axis Transform (QMAT). AQMAT results in a partition of the image into a set of nondisjointsquares having sides whose lengths are sums of powers of 2 ratherthan, as is the case with quadtrees, a set of disjoint squareshaving sides of lengths which are powers of 2. The motivation isnot to study skeletons for the usual purpose of obtainingsapproximations of the image. Instead, quadtree skeletons are exactrepresentations of the image and are used because they are observedto yield space efficiency and a decreased sensitvity to shifts incontrast with the quadtree. The QMAT can be used as the underlyingrepresentation when solving most problems that can be solved byusing a quadtree. An algorithm is presented for the computation ofthe QMAT of a given quadtree by only examining each BLACK node'sadjacent and abutting neighbors. Analysis of the algorithm revealsan average execution time proportional to the complexity of theimage, i.e., the number of BLACK blocks.