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Optimizing two-pass connected-component labeling algorithms

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Abstract

We present two optimization strategies to improve connected-component labeling algorithms. Taking together, they form an efficient two-pass labeling algorithm that is fast and theoretically optimal. The first optimization strategy reduces the number of neighboring pixels accessed through the use of a decision tree, and the second one streamlines the union-find algorithms used to track equivalent labels. We show that the first strategy reduces the average number of neighbors accessed by a factor of about 2. We prove our streamlined union-find algorithms have the same theoretical optimality as the more sophisticated ones in literature. This result generalizes an earlier one on using union-find in labeling algorithms by Fiorio and Gustedt (Theor Comput Sci 154(2):165–181, 1996). In tests, the new union-find algorithms improve a labeling algorithm by a factor of 4 or more. Through analyses and experiments, we demonstrate that our new two-pass labeling algorithm scales linearly with the number of pixels in the image, which is optimal in computational complexity theory. Furthermore, the new labeling algorithm outperforms the published labeling algorithms irrespective of test platforms. In comparing with the fastest known labeling algorithm for two-dimensional (2D) binary images called contour tracing algorithm, our new labeling algorithm is up to ten times faster than the contour tracing program distributed by the original authors.

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Notes

  1. An implementation of the Contour Tracing algorithm distributed by the original authors of the algorithm is available from http://www.iis.sinica.edu.tw/∼fchang/03src.html.

  2. Note that we have made an arbitrary choice of denoting a background pixel by 0 and an object pixel by 1; however, there are other equally valid choices [38]. It is also possible to use other types of labels than the integers used in this paper.

  3. In C++ convention, all indices to arrays start from 0. The word array or vector in all pseudo-code segments is a short-hand of C++ STL type std::vector<unsigned> .

  4. The computation uses the function lsqlin from the optimization toolbox of MATLAB.

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Acknowledgment

This work was supported in part by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.

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Authors and Affiliations

  1. Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, USA

    Kesheng Wu & Ekow Otoo

  2. Department of Radiology, The University of Chicago, Chicago, IL, USA

    Kenji Suzuki

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  1. Kesheng Wu
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  2. Ekow Otoo
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  3. Kenji Suzuki
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Correspondence to Kesheng Wu.

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Wu, K., Otoo, E. & Suzuki, K. Optimizing two-pass connected-component labeling algorithms. Pattern Anal Applic 12, 117–135 (2009). https://doi.org/10.1007/s10044-008-0109-y

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