Gift Siromoney

Picture languages with array rewriting rules

Generative models of picture languages with array rewriting rules are presented. The rewriting rules are regular, context-free or context-sensitive with arrays of terminals in the place of strings of terminals. Derivations are restricted by the condition for row and column catenation. The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. A distinct hierarchy is shown to exist between the different classes introduced. The models are closed under reflection (about base and rightmost vertical), halfturn, quarter-turn, transpose, and conjugation. Further closure properties such as union, product, star and homomorphism are examined. The models can be applied to generate several interesting patterns of kolam and to describe the repetitive patterns of two-dimensional crystallography. Each letter of the alphabet of different sizes can be generated by a context-free array grammar.

Computer recognition of printed Tamil characters

Abstract Computer recognition of machine-printed letters of the Tamil alphabet is described. Each character is represented as a binary matrix and encoded into a string using two different methods. The encoded strings form a dictionary. A given text is presented symbol by symbol and information from each symbol is extracted in the form of a string and compared with the strings in the dictionary. When there is agreement the letters are recognized and printed out in Roman letters following a special method of transliteration. The lengthening of vowels and hardening of consonants are indicated by numerals printed above each letter.

Array Grammars and Kolam

Kolam designs of South Indian folk art are treated as examples of two-dimensional picture languages, Many of the complicated kolain patterns are seen to be generable by context-free array grammars. Two methods of kolam generation are discussed. One method is to generate the kolam patterns by array grammars with a finite number of primitives as terminals. The other is to generate labeled dots by array grammars and then to give a finite number of simple instructions to draw the kolam pattern on the framework of labeled dots.

Extended controlled table L-arrays

A generative two-dimensional rectangular array model which allows for growth along the edges is proposed. The growth takes place in parallel, restricted by tables, and growth along the four different edges is controlled by a control set. Special classes of these models where the distinction between terminals and nonterminals is removed, provide for rectangular developmental arrays; the hierarchy within these classes is studied. The generative power of the new model is compared with that of earlier array models.

Hexagonal arrays and rectangular blocks

Hexagonal arrays on a triangular grid are treated as two-dimensional representations of three-dimensional rectangular parallelepipeds. Grammatical models for generating hexagonal arrays are introduced. Properties of special classes of hexagons are studied. A new kind of catenation called arrowhead catenation is defined so that the hexagonal shape is maintained, in every generation. Perceptual twins of a given set of blocks are obtained formally from the grammar generating the original set of blocks.

Computer Recognition of Tamil, Malayalam and Devanagari Characters

Computer recognition of multifont Tamil characters and special sets of printed Malayalam and Devanagari characters is described. Each character is converted manually into a rectangular binary array in which a zero represents a blank, and a one, a nonblank. Using the pattern encoding techniques developed by us, features in the form of strings are extracted by row-wise and column-wise scanning of the array. These features depend upon the number and nature of runs of ones in the rows and columns. Feature strings of printed prototype characters of an alphabet form a dictionary. Printed test input characters are fed into the computer, one by one, for recognition. Feature strings of each of the test input characters are obtained and compared with those of the prototype characters. A perfect match between the feature strings of the test input with a prototype would indicate that the two are identical and the test character is recognized as the corresponding prototype. Recognized characters are printed out in Rom...

Entropy of Tamil prose

The proportions of the different letters of the alphabet in Tamil prose are estimated from a large sample and an optimum code is constructed. The prose is compared with the Tamil poetry of different periods and the one-gram entropy of prose is significantly different from the entropies of the poetical works considered. An estimate is made, experimentally, of the entropy of Tamil prose.

Radial Grammars and Radial L-Systems

Abstract Models to generate two-dimensional circular patterns are proposed. The first one generates circular patterns with a finite number of radii and growth takes place in parallel along the radii. Examples are given which reflect growth patterns on biological objects. The second system is an extension which takes care of growth along the radii, the number of radii being unlimited. Comparison is made with cycle languages. Catenation and star operation are extended to radial and transversal operations and closure is examined. The third system includes developmental models which reflect radial and transversal growth. Radial and transversal generations take place in parallel, controlled by a control set, and describe circular developmental patterns.

n-dimensional array languages and description of crystal symmetry—I

Following the general linguistic approach proposed by Narasimhan to pattern recognition we proposed two generative models,viz., the matrix models and the more powerful two-dimensional array models. In this paper we generalize the matrix models ton-dimensions and establish that then-dimensional matrix models are closed under union, concatenation, Kleene closure, ∈-free homomorphism, inverse homomorphism and intersection with regular matrices. Symmetry operations such as translation, reflection and half-turn are examined.

A note on an extension of matrix grammars generating two-dimensional languages☆

Abstract An extended version of the parallel/sequential table matrix models called extended table matrix grammars (Ex-TMG), generating arrays of symbols, is proposed. The effect of imposing different types of control on the sequence of application of the tables is studied. The notion of assigning “terminal weights” to matrix grammars for describing parquet deformations is extended to Ex-TMGs.