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.
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Subramanian, K.G., Mahalingam, K., Abdullah, R., Nagar, A.K. (2011). Binary Images, M −Vectors, and Ambiguity. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds) Combinatorial Image Analysis. IWCIA 2011. Lecture Notes in Computer Science, vol 6636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21073-0_23
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DOI: https://doi.org/10.1007/978-3-642-21073-0_23
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