By Anil K. Jain

Offers a radical evaluation of the key issues of electronic photograph processing, starting with the fundamental mathematical instruments wanted for the topic. contains a finished bankruptcy on stochastic types for electronic snapshot processing. Covers facets of photograph illustration together with luminance, colour, spatial and temporal homes of imaginative and prescient, and digitization. Explores a number of photo processing strategies. Discusses set of rules improvement (software/firmware) for photograph transforms, enhancement, reconstruction, and snapshot coding.

Table of Contents

Introduction.

1. Dimensional structures and Mathematical Preliminaries.

2. photograph Perception.

three. picture Sampling and Quantization.

four. photograph Transforms.

five. photo illustration through Stochastic Models.

6. snapshot Enhancement.

7. picture Filtering and Restoration.

eight. photo research and desktop Vision.

nine. snapshot Reconstruction From Projections.

10. picture facts Compression.

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108), where Ry and rxy represent the covariance and cross-covariance arrays. If x, y (n) are non-Gaussian, then (2. 104) and (2. 109) still give the best linear mean square estimate. However, this is not necessarily the conditional mean. 13 SOME RESULTS FROM INFORMATION THEORY Information theory gives some important concepts that are useful in digital repre sentation of images. Some of these concepts will be used in image quantization (Chapter 4), image transforms (Chapter 5), and image data compression (Chap ter 11).

48 ) This is an M1 x M2 block matrix of basic dimension N1 x N2 • Note that A @ B =F B @ A. Kronecker products are useful in generating high-order matrices from low-order matrices, for example, the fast Hadamard transforms that will be studied in Chapter 5 . 7. 49) It expresses the matrix multiplication of two Kronecker products as a Kronecker product of two matrices. 7 Properties of Kronecker Products 1 . (A + B) @ C = A @ C + B @ C 2 . (A @ B) @ C = A @ (B @ C) 3. a (A ® B) = (aA) ® B = A ® (aB), where a is scalar.

6 Matrix Theory Definitions Definition Item Matrix A = {a (m, n)} Comments m = row index, n = column index Rows and columns are interchanged. Transpose Complex conjugate Conjugate transpose A* = {a* (m, n)} A *T = {a* (n, m)} Identity matrix 1 = {8 (m - n)} Null matrix O = {O} A square matrix with unity along its diagonal. All elements are zero. Matrix addition A + B = {a (m, n) + b (m, n)} A, B have same Scalar multiplication aA = {aa (m, n )} Matrix multiplication c(m, n) � L a (m, k=l Commuting matrices K k)b(k, n) AB = BA Vector inner product (x, y) � x * Ty = L: x* (n) y (n) Vector outer product xy T = {x (m) y (n)} Symmetric Hermitian C � AB, A is M x K, B is K x N, C is M x N.