Efficient Component Labeling of Images of Arbitrary Dimension Represented by Linear Bintrees

@article{Samet1988EfficientCL,
  title={Efficient Component Labeling of Images of Arbitrary Dimension Represented by Linear Bintrees},
  author={Hanan Samet and Markku Tamminen},
  journal={IEEE Trans. Pattern Anal. Mach. Intell.},
  year={1988},
  volume={10},
  pages={579-586}
}
An algorithm is presented to perform connected-component labeling of images of arbitrary dimension that are represented by a linear bintree. The bintree is a generalization of the quadtree data structure that enables dealing with images of arbitrary dimension. The linear bintree is a pointerless representation. The algorithm uses an active border which is represented by linked lists instead of arrays. This results in a significant reduction in the space requirements, thereby making it feasible… 

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References

SHOWING 1-10 OF 27 REFERENCES

Computing Geometric Properties of Images Represented by Linear Quadtrees

A general algorithm to compute geometric image properties such as the perimeter, the Euler number, and the connected components of an image is developed and analyzed and implementation experience has confirmed its superiority to existing approaches to computing geometric properties for images represented by quadtrees.

Connected Component Labeling Using Quadtrees

Analysis of the algorithm reveals that its worst case average execution time is bounded by a quantity proportional to the product of the log of the region's diameter and the number of blocks comprising the area connected by the components.

Geometric modeling using octree encoding

Comment on Quad- and Octtrees

It is claimed that studying the case of binary division provides for a more general understanding of the underlying structures and that less attention is needed on the separate results concerning quadand octtrees.

Quad-Trees, Oct-Trees, and K-Trees: A Generalized Approach to Recursive Decomposition of Euclidean Space

The algorithm provides a method for computing the perimeter of a quad-tree encoded image or the surface area of an oct- tree encoded object in worst case time proportional to the number of nodes in the tree, improves upon the expected-case linear-time method of Samet for the perimeter problem.

A hierarchical data structure for multidimensional digital images

A tree data structure for representing multidimensional digital binary images and an algorithm for constructing the tree of a d-dimensional binary image from the trees of its (d - 1 )-dimensional cross sections are given.

Efficient octree conversion by connectivity labeling

An algorithm for converting from the boundary representation of a solid to the corresponding octree model is presented, utilizing an efficient new connected components labeling technique and demonstrating that all processing can be performed directly on linear quad and octree encodings.

Oct-trees and their use in representing three-dimensional objects

An effective way to represent quadtrees

The sorted array of black nodes is referred to as the “linear quadtree” and it is shown that it introduces a saving of at least 66 percent of the computer storage required by regular quadtrees.