# Connected Component Labeling Using Quadtrees

@article{Samet1981ConnectedCL, title={Connected Component Labeling Using Quadtrees}, author={Hanan Samet}, journal={J. ACM}, year={1981}, volume={28}, pages={487-501} }

Abstract : An algorithm is presented for labeling the connected components of an image represented by a quadtree. The algorithm proceeds by exploring all possible adjacencies for each node once and only once. Once this is done, any equivalences generated by the adjacency labeling phase are propagated. 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…

#### 204 Citations

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- Computer Science
- 2009

An algorithm of linear time complexity to label connected components of a binary image by a quadtree that has shown the best performance in large images.

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Using the modified linear quadtree proposed in [1,9], this paper presents an O(n·N) algorithm for labeling connected components of a region consisting of N BLACK nodes in a 2n by 2n binary image. As…

Computing Perimeters of Regions in Images Represented by Quadtrees

- Computer Science, MedicineIEEE Transactions on Pattern Analysis and Machine Intelligence
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An algorithm is presented for computing the total perimeter of a region in a binary image represented by a quadtree. The algorithm explores each segment of the boundary of the region once and only…

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- Mathematics
- 1984

Abstract In a recent paper by Gargantini, an algorithm for evaluating the connected regions of an image represented as a linear quadtree is presented. This note observes a case where the algorithm…

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- Mathematics
- 1980

Abstract An algorithm is presented which computes the Euler number, i.e., the number of components minus the number of holes, of a binary image represented by a quadtree. The local property-counting…

Path-Length distances for quadtrees

- Mathematics, Computer ScienceInf. Sci.
- 1981

An algorithm is presented that calculates the distance from the center of each black node to the border of the nearest white node, and the worst-case average execution time is shown to be proportional to the product of the logarithm of the image diameter and the number of blocks in the image.

Neighbor finding techniques for images represented by quadtrees

- Computer ScienceComput. Graph. Image Process.
- 1982

Algorithms are given for determining adjacencies in the horizontal, vertical, and diagonal directions and the execution times of the algorithms are analyzed using a suitably defined model.

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

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1988

An algorithm is presented to perform connected-component labeling of images of arbitrary dimension that are represented by a linear bintree that uses an active border which is represented by linked lists instead of arrays, resulting in a significant reduction in the space requirements, thereby making it feasible to process three- and higher-dimensional images.

Efficient octree conversion by connectivity labeling

- Computer ScienceSIGGRAPH
- 1984

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.

MAINTAINING CONNECTED COMPONENTS IN QUADTREE-BASED REPRESENTATION OF IMAGES

- Computer Science
- 2003

This paper considers the problem of maintaining connected components in quadtree representation of binary images when a small portion of the image undergoes change and proposes algorithms to update the quadtree and the connected components labeling when a homogeneous region in the Quadtree is changed.

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