Small Work Space Algorithms for Some Basic Problems on Binary Images

  • Tetsuo Asano
  • Sergey Bereg
  • Lilian Buzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7655)


This paper presents space-efficient algorithms for some basic tasks (or problems) on a binary image of n pixels, assuming that an input binary image is stored in a read-only array with random-access. Although efficient algorithms are available for those tasks if O(n) work space (of O(n logn) bits) is available, we aim to propose efficient algorithms using only limited work space, i.e., O(1) or \(O(\sqrt{n})\) space. Tasks to be considered are (1) CCC to count the number of connected components, (2) MERR to report the minimum enclosing rectangle of every connected component, and (3) LCCR to report a largest connected component. We show that we can solve each of CCC, MERR, and LCCR in O(n logn) time using only O(1) space. If we can use \(O(\sqrt{n})\) work space, we can solve them in O(n), O(n), and O(n + m logm) time, respectively, where m is the number of pixels in the largest connected component.


Connected component Minimum enclosing rectangle Largest connected component Space-efficient algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tetsuo Asano
    • 1
  • Sergey Bereg
    • 2
  • Lilian Buzer
    • 3
    • 4
  1. 1.School of Information ScienceJAISTJapan
  2. 2.Department of Computer ScienceUniversity of Texas at DallasUSA
  3. 3.LABINFO-IGM, UMR CNRS 8049Université Paris-EstFrance
  4. 4.Department of Computer ScienceESIEEFrance

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