E V Krishnamurthy
Articles written in Proceedings – Section A
Volume 48 Issue 3 September 1958 pp 152-164
Volume 48 Issue 5 November 1958 pp 269-283
Volume 77 Issue 2 February 1973 pp 51-61
An algorithmic line-notation is suggested for the unambiguous description of the planar projection of a knot made with a single string. This may have applications in automatic knot-craft.
Volume 78 Issue 5 November 1973 pp 208-217
Some properties of the periods of prime-reciprocals in a general negative base representation are described.
Volume 79 Issue 3 March 1974 pp 139-158
This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression.
In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation.
This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.
Volume 79 Issue 4 April 1974 pp 195-211
In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture.
Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered.
It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.
Volume 81 Issue 2 February 1975 pp 58-79
A fractional weighted number system, based on Hensel’s
This new number system combines the best features and advantages of both the
Volume 82 Issue 5 November 1975 pp 165-175
Computer procedures are described for error-free matrix computations, using the