Formal description, compression and transformation of digital pictures

Krishnamurthy, EV and Subramanian, K and Rao, TM (1974) Formal description, compression and transformation of digital pictures. In: Proceedings Mathematical Sciences, 79 (3). pp. 139-158.

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Abstract

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.

Item Type:	Journal Article
Publication:	Proceedings Mathematical Sciences
Publisher:	Sprigner Link
Additional Information:	Copyright of this article belongs to Sprigner Link.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	28 Jan 2010 10:42
Last Modified:	19 Sep 2010 05:46
URI:	http://eprints.iisc.ac.in/id/eprint/23528

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