## Neighbour finding in images represented by octrees (1989)

Venue: | Computer Vision, Graphics and Image Processing |

Citations: | 16 - 6 self |

### BibTeX

@INPROCEEDINGS{Samet89neighbourfinding,

author = {Hanan Samet},

title = {Neighbour finding in images represented by octrees},

booktitle = {Computer Vision, Graphics and Image Processing},

year = {1989},

pages = {367--386}

}

### Years of Citing Articles

### OpenURL

### Abstract

Algorithms are presented for moving between adjacent blocks in an octree representation of an image. Motion is possible in the direction of a face, edge, and a vertex, and between blocks of arbitrary size. The algorithms are based on a generalization and simplification of techniques developed earlier for two dimensions (i.e., in quadtrees). They are also applicable to quadtrees. The difference lies in the graph-theoretical classification of adjacencies-i.e., in terms of vertices, edges, and faces. Algorithms are given for octrees that are implemented with pointers and with pointerless representations such as the linear octree. 0 1989 Academic PRSS. ITIC. 1.

### Citations

1248 | The Design and Analysis of Spatial Data Structures - Samet - 1989 |

185 | Space Subdivision for Fast Ray Tracing - Glassner - 1984 |

184 |
Mathematical elements of computer graphics
- Rogers, Adams
- 1989
(Show Context)
Citation Context ...ent a ray tracing algorithm that made use of an octree representation of a scene. Ray tracing is an approximate simulation of how the light that is propagated through a scene lands on the image plane =-=[15]-=-. This task is useful in computer graphics. However, it is also the basis of performing line of sight (in an arbitrary direction) and field of view computations in determining visibility in applicatio... |

120 | Geometric Modeling using Octree Encoding - Meagher - 1982 |

65 | Operations on images using quad trees - Hunter, Steiglitz - 1979 |

60 | Oct-trees and their use in representing three-dimensional objects - Jackins, Tanimoto - 1980 |

54 | Hierarchical data structures and algorithms for computer graphics - Samet, Webber - 1988 |

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

19 |
On a methodof binary picture representation and its application to data compression
- Endo
- 1980
(Show Context)
Citation Context ... is known as a linear octree [4]. We show how a neighbor of greater than or equal size is computed in the direction of a face, edge, or vertex. The second category is exemplified by the DF-expression =-=[11]-=- (denoting depthfirst). Neighbor finding is very complicated when this representation is used sincesNEIGHBOR FINDING IN IMAGES 381 there is no notion of random access. For example, a node is only iden... |

16 |
A geographic information system using quadtrees
- Samet, Rosenfeld, et al.
- 1984
(Show Context)
Citation Context ...ifference is of no consequence when the tree is represented in internal memory. However, when storage requirements are such that the tree is represented in external memory (e.g., using a B-tree as in =-=[22]-=-), then this difference is very important for it means that there is no need to traverse links between nodes that may be on different pages, a situation that could cause a page fault. In such a situat... |

16 | Calculations of geometric properties using quadtrees - Shneier - 1981 |

15 |
Efficient octree representation of moving objects
- Osse, Ahuja
(Show Context)
Citation Context .... For example, computing perimeters [17], labeling connected components [16], finding the genus of an image [2], and computing set properties [7, 271. Operations in three dimensions are also possible =-=[9, 1,28,29]-=-. The operations are frequently implemented as tree traversals. The difference between them is in the nature of the computation that is performed at the node. Often, these computations involve the exa... |

15 |
Computing the Euler number of an image from its quadtree. Computer Graphics Image Process
- Dyer
- 1980
(Show Context)
Citation Context ... of the traditional image processing operations can be performed using quadtrees and octrees. For example, computing perimeters [17], labeling connected components [16], finding the genus of an image =-=[2]-=-, and computing set properties [7, 271. Operations in three dimensions are also possible [9, 1,28,29]. The operations are frequently implemented as tree traversals. The difference between them is in t... |

14 | A Functional Model for Constructive Solid Geometry - Wyvill, Kunii - 1985 |

13 |
Patterns and Search Statistics, in Optimizing Methods in Statistics
- Klinger
- 1971
(Show Context)
Citation Context ... and then searching through the tree for it. As we will see. the method we describe is simpler. 2. DEFINITIONS AND NOTATION The region octree [6, 8, 141 is an extension of the quadtree data structure =-=[12]-=- to represent 3-dimensional data. We start with a 2” x 2” x 2” object array of unit cubes (termed voxels or obels). The octree is based on the successive subdivision of an object array into octants. I... |

11 | A model for the analysis of neighbor finding in pointer-based quadtrees - Shaffer - 1985 |

10 |
Computing perimeters of images represented by quadtrees
- Samet
- 1981
(Show Context)
Citation Context ...ise from this aggregation are often of equal or greater importance. Many of the traditional image processing operations can be performed using quadtrees and octrees. For example, computing perimeters =-=[17]-=-, labeling connected components [16], finding the genus of an image [2], and computing set properties [7, 271. Operations in three dimensions are also possible [9, 1,28,29]. The operations are frequen... |

9 | Parallel processing of an object space for image synthesis using ray tracing - KOBAYASHI, NAKAMURA, et al. - 1987 |

7 | The use of spatial coherence in ray tracing. Techniques for Computer Graphics - Kaplan - 1987 |

7 | Octrees of objects in arbitrary motion: Representation and efficiency
- Weng, Ahuja
- 1987
(Show Context)
Citation Context .... For example, computing perimeters [17], labeling connected components [16], finding the genus of an image [2], and computing set properties [7, 271. Operations in three dimensions are also possible =-=[9, 1,28,29]-=-. The operations are frequently implemented as tree traversals. The difference between them is in the nature of the computation that is performed at the node. Often, these computations involve the exa... |

2 |
Detection of Connectivity for Regions Represented by Linear Quadtrees
- Gargantini
- 1982
(Show Context)
Citation Context ...is that performing neighbor finding is more complex than when using a pointer-based representation. In this section we concentrate on a variant of the first category which is known as a linear octree =-=[4]-=-. We show how a neighbor of greater than or equal size is computed in the direction of a face, edge, or vertex. The second category is exemplified by the DF-expression [11] (denoting depthfirst). Neig... |

2 |
Quad-trees, act-trees, and k-trees-A generalized approach to recursive decomposition of Euclidean space
- Jackins, Tanimoto
- 1983
(Show Context)
Citation Context .... For example, computing perimeters [17], labeling connected components [16], finding the genus of an image [2], and computing set properties [7, 271. Operations in three dimensions are also possible =-=[9, 1,28,29]-=-. The operations are frequently implemented as tree traversals. The difference between them is in the nature of the computation that is performed at the node. Often, these computations involve the exa... |

2 |
Octree Generation from Silhouette Views of an Object
- Veenstra, Ahuja
- 1985
(Show Context)
Citation Context |

1 |
Linear octrees for fast processing of three dimensional objects
- Gargantim
- 1982
(Show Context)
Citation Context ...e easily extended to deal with images of higher dimension. We show how it can be used for octrees that are implemented using both a pointer and a pointer-less representation such as the linear octree =-=[3]-=-. The rest of this paper is organized as follows. Section 2 contains some definitions and a description of our notation. Section 3 presents the algorithms for computing the neighbors. The algorithms a... |

1 |
Connected component labeling using quadtrees
- Same&
- 1981
(Show Context)
Citation Context ...of equal or greater importance. Many of the traditional image processing operations can be performed using quadtrees and octrees. For example, computing perimeters [17], labeling connected components =-=[16]-=-, finding the genus of an image [2], and computing set properties [7, 271. Operations in three dimensions are also possible [9, 1,28,29]. The operations are frequently implemented as tree traversals. ... |

1 | Neighbor hnding techniques for images represented by quadtrees - Samet - 1982 |

1 | The quadtree and related hierarchical data structures - Same& - 1984 |

1 | A Comparison of the Space - Samet, Webber - 1986 |