Part 3. DISCRETE LINEAR TWO-DIMENSIONAL TREATMENT

Part 3. DISCRETE LINEAR TWO-DIMENSIONAL TREATMENT

In the third part of the book, discrete linear operations performed during two-dimensional processing are analyzed from a unified position. Definitions of generalized linear operators and pseudo-inversion operators are given. Several types of discrete two-dimensional superposition and convolution operators are introduced, and relations between them are established. Two-dimensional transformations are presented, such as Fourier, Hadamard, Karuyen-Loeve transforms, and fast computation algorithms are described. The question of the use of two-dimensional transformations as an effective means of performing convolution is considered. Finally, recurrent methods for linear image processing are described.

Chapter 8. LINEAR OPERATORS

Many of the operations performed in image processing are linear in nature. Such operations include superposition, convolution, unitary transformations and discrete linear filtering.

LITERATURE

1. Pratt W. K., Vector Formulation of Two Dimensional Signal Processing Operations, J. Computer Graphics and Image Processing, 4, 1, 1-24 (March 1975), Academic Press, New York.

2. Eklundh JO, A Fast Computer Method for Matrix Transposing, IEEE Trans. Computers, C-21, 7, 801-803 (July 1972).

3. Twogood RE, Ekstrom MP, IEEE Trans. Computers, C-25, 9, 950-952 (September 1976).

4. Gray bill FA, Wads-Worth, Belmont, Cal., 1969.

5. Rao CR, Mitra S. K, Generalized Inverse of Matrices and Its Applications, Wiley, New York, 1971.

6. Albert A., Regression and the Moore - Penroce Pseudoinverse, Academic Press, New York, 1972. [There is a translation: Albert A., Regression, pseudo-inversion and recurrent estimation. - M .: Science, 1977.]