Keywords and Synonyms
Multidimensional array matching; Image matching ; Template registration
Problem Definition
Given two two-dimensional arrays, the text \( T[1\,\ldots\, n,\,1\,\ldots\, n] \) and the pattern \( P[1\,\ldots\, m,\,1\,\ldots\, m] \), \( m\leq n \), both with element values from alphabet Σ of size σ, the basic two-dimensional string matching (2DSM) problem is to find all occurrences of P in T, i. e., all \( m\times m \) subarrays of T that are identical to P. In addition to the basic problem, several types of generalizations are considered: approximate matching (allow local errors), invariant matching (allow global transformations), indexed matching (preprocess the text), and multidimensional matching.
In approximate matching, an occurrence is a subarray S of the text, whose distance d(S, P) from the pattern does not exceed a threshold k. Different distance measures lead to different variants of the problem. When no distance is explicitly mentioned, the Hamming distance...
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Kärkkäinen, J., Ukkonen, E. (2008). Multidimensional String Matching. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_247
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DOI: https://doi.org/10.1007/978-0-387-30162-4_247
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