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A new run-based algorithm for Euler number computing

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Abstract

The Euler number of a binary image is an important topological feature for many image processing, image analysis, pattern recognition, and computer vision applications. This paper proposes a new run-based Euler number computation algorithm. The conventional run-based algorithm processes rows of the given image one-by-one from top to bottom in a single phase. For each row, it finds the runs in the row and records the start and end locations of each run to compute neighbor runs. In contrast, our algorithm calculates the Euler number of an image in two phases. In the first phase, we process odd rows alternately to find runs and only record its end location. In the second phase, we process each of the remaining even rows to find runs and calculate neighboring runs between the current row and the rows immediately above and below using the recorded run data. Using this method, the number of accesses required to compute the Euler number decreases in almost all cases. Analysis of the time complexity and experimental results demonstrate that our algorithm outperforms conventional Euler number computation algorithms.

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Notes

  1. A basic square is a \(\left[ {\begin{array}{*{20}c} a & b \\ c & d \\ \end{array} } \right]\) pattern in a binary image.

  2. A basic right-angled triangle is one of \(\left[ {\begin{array}{*{20}c} 1 & 0 \\ 1 & 1 \\ \end{array} } \right]\), \(\left[ {\begin{array}{*{20}c} 1 & 1 \\ 1 & 0 \\ \end{array} } \right]\), \(\left[ {\begin{array}{*{20}c} 1 & 1 \\ 0 & 1 \\ \end{array} } \right]\), or \(\left[ {\begin{array}{*{20}c} 0 & 1 \\ 1 & 1 \\ \end{array} } \right]\) \(\left[ {\begin{array}{*{20}c} 0 & 1 \\ 1 & 1 \\ \end{array} } \right]\) patterns in a binary image.

  3. The authors of the LB algorithm could not calculate the time complexity of this algorithm either.

  4. http://sampl.ece.ohiostate.edu/data/stills/sidba/index.html.

  5. http://sipi.usc.edu/database/.

  6. http://www1.cs.columbia.edu/CAVE/software/curet/.

  7. The density of a binary image is the percentage of object pixels in an image.

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Acknowledgments

We thank the anonymous referees for their valuable comments that greatly improved this paper.

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Authors and Affiliations

  1. Artificial Intelligence Institute, College of Electrical and Information Engineering, Shaanxi University of Science and Technology, Xian, China

    Bin Yao, Lifeng He & Xiao Zhao

  2. Graduate School of Information Science and Technology, Aichi Prefectural University, Nagakute, Aichi, Japan

    Lifeng He

  3. School of Information Engineering, Xianyang Normal University, Shaanxi, China

    Shiying kang

  4. Graduate School of Environment Management, Nagoya Sangyo University, Owariasahi, Japan

    Yuyan Chao

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  1. Bin Yao
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  2. Lifeng He
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  3. Shiying kang
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  4. Xiao Zhao
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Correspondence to Lifeng He.

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Yao, B., He, L., kang, S. et al. A new run-based algorithm for Euler number computing. Pattern Anal Applic 20, 49–58 (2017). https://doi.org/10.1007/s10044-015-0464-4

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