## Algorithms for the conversion of quadtrees to rasters (1981)

Venue: | IEEE Trans. Pattern Anal. and Machine Intelligence PAMI--3 |

Citations: | 10 - 5 self |

### BibTeX

@ARTICLE{Samet81algorithmsfor,

author = {Hanan Samet},

title = {Algorithms for the conversion of quadtrees to rasters},

journal = {IEEE Trans. Pattern Anal. and Machine Intelligence PAMI--3},

year = {1981},

volume = {1},

pages = {1--16}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 top-down 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.

### Citations

284 |
Quad trees: A data structure for retrieval on composite keys
- Finkel, Bentley
- 1974
(Show Context)
Citation Context ...des, also termed GRAY nodes, denote nonterminal nodes. Note that the quadtree representation discussed here should not be confused with the quadtree representation of two-dimensional point space data =-=[3]-=-. 2. DEFINITIONS AND NOTATION Let each node in a quadtree be stored as a record containing six fields. The first five fields contain pointers to the node’s father and its four sons, i.e., quadrants, l... |

59 |
Oct-trees and their use in representing three-dimensional objects
- Jackins
- 1980
(Show Context)
Citation Context ... which is to be output. For example, in locating the block containing the segment starting at row 0 and column 0 in Fig. 1, FINDBLOCK is successively invoked with blocks having lower right corners at =-=(7,7)-=-, (3,3), and (l,l). The result is block A. All of our algorithms make use of procedures OUTPUTRUN and OCJTPUTENDOFROW to do the actual output of the runs. For each BLACK or WHITE node of width W that ... |

45 | Ejkient Computation and Data Structures for Graphics - Hunter - 1979 |

29 | Experiments in picture representation using regular decomposition, Comput. Graphics Image Process - Klinger, Dyer - 1976 |

26 |
Region representation: Boundary codes from quadtrees
- Dyer, Rosenfeld, et al.
(Show Context)
Citation Context ...he sum of the heights of the blocks comprising the image. 1. INTRODUCTION Region representation is an important issue in applications such as image processing, computer graphics, and cartography (see =-=[2]-=- for a brief review of representations currently in use). Recently there has been much interest in the quadtree [2,4-lo], a compact hierarchical representation which, depending on the nature of the im... |

17 | Region representation: quadtrees from binary arrays - Samet - 1980 |

14 | Linear transformation of pictures represented by quadtrees, Comput. Graphics Image Process - Hunter, Steiglitz |

13 | Patterns and Search Statistics, in Optimizing Methods in Statistics - Klinger - 1971 |

10 | Organization and access of image data by areas - KLINGER, RHODES - 1979 |

10 |
Revised report on the algorithmic language
- Naur
- 1963
(Show Context)
Citation Context ... define the representations used. Sections 3 and 4 contain the algorithms and an analysis of their execution times. We also include a formal presentation of the algorithms using a variant of ALGOL 60 =-=[12]-=- as well as motivations for their various steps. We assume that the given image is a 2” by 2” array of unit square “pixels.” The quadtree is an approach to image representation based on successive sub... |

1 | Preserving average proximity in arrays, (bmm - DeMillo, Eisenstat, et al. - 1978 |

1 | Operations on images using quadtrees, lEEE Truns - Hunter, Steigiitz - 1979 |

1 | Region representation: Quadtrees from boundary codes - &met - 1980 |

1 | An algorithm for converting rasters to quadtrees - Same& - 1981 |