Binary images, M-vectors, and ambiguity

  • Authors:

  • K. G. Subramanian;Kalpana Mahalingam;Rosni Abdullah;Atulya K. Nagar

  • Affiliations:

  • School of Computer Sciences, Universiti Sains Malaysia, Penang, Malaysia;Department of Mathematics, Indian Institute of Technology Madras, Chennai, India;School of Computer Sciences, Universiti Sains Malaysia, Penang, Malaysia;Department of Computer Science, Liverpool Hope University, Liverpool, UK

  • Venue:
  • IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
  • Year:
  • 2011

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Abstract

Mateescu et al (2001) introduced the notion of Parikh matrix of a word as an extension of the well-known concept of Parikh vector of a word. The Parikh matrix provides more numerical information about a word than given by the Parikh vector. Here we introduce the notion of M-vector of a binary word which allows us to have a linear notation in the form of a unique vector representation of the Parikh matrix of the binary word. We then extend this notion of M-vector to a binary image treating it as a binary array over a two-symbol alphabet. This is done by considering the M-vectors of the words in the rows and columns of the array. Among the properties associated with a Parikh matrix, M-ambiguity or simply ambiguity of a word is one which has been investigated extensively in the literature. Here M-ambiguity of a binary array is defined in terms of its M-vector and we obtain conditions for M-ambiguity of a binary array.