Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images

Masilamani, V.; Krithivasan, Kamala; Subramanian, K. G.; Ang, Miin Huey

doi:10.1007/978-3-540-89646-3_113

Cited by 5 publications

(4 citation statements)

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“…Properties of such matrices are obtained in the case of binary and ternary arrays, some of Also, in the area of discrete tomography, reconstruction of binary images has been extensively studied (See for example [4,11]). It is worth examining whether the theoretical properties obtained here can be used in the problem of reconstruction of picture arrays or images.…”

Section: Resultsmentioning

confidence: 99%

“…Among a number of problems of interest related to digitized picture arrays (see for example [4,9,11]), investigation of combinatorial properties of arrays has been done (see for example [5,6,17]). A two-dimensional connected digitized rectangular picture array with m rows and n columns or simply, a m × n picture array is made of a finite number of pixels with each pixel in a cell having a label taken from a finite alphabet Σ.…”

Section: Introductionmentioning

confidence: 99%

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Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Subramanian

Mahalingam

Abdullah

et al. 2013

Int. J. Found. Comput. Sci.

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Abstract:Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays $A$ and $B$ are defined to be $M-$equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of $M-$ambiguity to a picture array. In the binary and ternary cases, conditions that ensure $M-$ambiguity are then obtained. Response to Reviewers:The authors are again grateful to the referee for a very meticulous reading of the revised version1 and thank the referee for further suggestions on improving the work. The authors have now revised the paper and revision2 has been submitted.Details of the changes done in revision2 are listed in "Author Response to comments on revision 1" as responses to the comments. Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M −equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M −ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M −ambiguity are then obtained. Powered by Editorial Manager® and Preprint Manager® from Aries Systems Corporation

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Subramanian

Mahalingam

Abdullah

et al. 2013

Int. J. Found. Comput. Sci.

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“…But the manner in which our Algorithm A constructs the rows of the binary image, is different yet simpler than that considered in [?]. In fact only matrices with the same number of rows and columns are reconstructed in [15].…”

Section: Algorithm Amentioning

confidence: 99%

Binary image reconstruction based on prescribed numerical information

Subramanian

Isawasan

Budiarto

et al. 2015

Acta Math. Appl. Sin. Engl. Ser.

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The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.Keywords discrete tomography and binary image and reconstruction and subwords and Parikh matrix 2000 MR Subject Classification 94A08

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“…e notion of the Parikh matrix of a word has been extended to row and column Parikh matrices of picture arrays in [21], and their properties have been studied. e problem of reconstruction of 2D binary images has been studied [22] based on Parikh matrices.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Properties of Parikh Matrices of Binary Picture Arrays

Bera

Sriram

Nagar

et al. 2020

Journal of Mathematics

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A word is a finite sequence of symbols. Parikh matrix of a word is an upper triangular matrix with ones in the main diagonal and nonnegative integers above the main diagonal which are counts of certain scattered subwords in the word. On the other hand, a picture array, which is a rectangular arrangement of symbols, is an extension of the notion of a word to two dimensions. Parikh matrices associated with a picture array have been introduced, and their properties have been studied. Here, we obtain certain algebraic properties of Parikh matrices of binary picture arrays based on the notions of power, fairness, and a restricted shuffle operator extending the corresponding notions studied in the case of words. We also obtain properties of Parikh matrices of arrays formed by certain geometric operations.

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Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images

Cited by 5 publications

References 5 publications

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Binary image reconstruction based on prescribed numerical information

Algebraic Properties of Parikh Matrices of Binary Picture Arrays

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