Name
Abstract | ||
|---|---|---|
Quadtrees and linear quadtrees are well-known hierarchical data structures to represent square images of size 2r times 2r. Finding the neighbors of a specific leaf node is a fundamental operation for many algorithms that manipulate quadtree data structures. In quadtrees, finding neighbors takes O(r) computational time for the worst case, where r is the resolution (or height) of a given quadtree. Schrack [1] proposed a constant-time algorithm for finding equal-sized neighbors in linear quadtrees. His algorithm calculates the location codes of equal-sized neighbors; it says nothing, however, about their existence. To ensure their existence, additional checking of the location codes is needed, which usually takes O(r) computational time. In this paper, a new algorithm to find the neighbors of a given leaf node in a quadtree is proposed which requires just O(1) (i.e., constant) computational time for the worst case. Moreover, the algorithm takes no notice of the existence or nonexistence of neighbors. Thus, no additional checking is needed. The new algorithm will greatly reduce the computational complexities of almost all algorithms based on quadtrees. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/TPAMI.2008.145 | Pattern Analysis and Machine Intelligence, IEEE Transactions |
Keywords | Field | DocType |
computational complexity,image representation,quadtrees,computational time,linear quadtrees,quadtree data structures,square image representation,Graph and tree search strategies,Image Processing and Computer Vision,Image processing,linear quadtrees,neighbor finding.,quadtrees | Hierarchical control system,Data structure,Computer science,Tree (data structure),Image representation,Image processing,Algorithm,Theoretical computer science,Hierarchical database model,Computational complexity theory,Quadtree | Journal |
Volume | Issue | ISSN |
31 | 7 | 0162-8828 |
Citations | PageRank | References |
3 | 0.51 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kunio Aizawa | 1 | 3 | 0.51 |
| Shojiro Tanaka | 2 | 7 | 1.82 |