Correlation Pattern Recognition by B. V. K. Vijaya Kumar PDF

By B. V. K. Vijaya Kumar

ISBN-10: 0521571030

ISBN-13: 9780521571036

Correlation is a strong and normal approach for trend attractiveness and is utilized in many purposes, equivalent to computerized aim reputation, biometric attractiveness and optical personality reputation. The layout, research and use of correlation development popularity algorithms calls for heritage details, together with linear platforms thought, random variables and strategies, matrix/vector tools, detection and estimation conception, electronic sign processing and optical processing. This 2005 publication presents a wanted assessment of this various heritage fabric and develops the sign processing thought, the development popularity metrics, and the sensible program information from simple premises. It exhibits either electronic and optical implementations. It additionally includes expertise provided by way of the staff that constructed it and contains case stories of important curiosity, equivalent to face and fingerprint popularity. appropriate for graduate scholars taking classes in trend reputation thought, when attaining technical degrees of curiosity to the pro practitioner.

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34) would be q=0. For a non-trivial solution of Eq. , jA À lIj ¼ 0 (2:35) 22 Mathematical background Expanding the determinant in Eq. 35) yields a polynomial (of degree less than or equal to N when A is an N Â N matrix) in l, and that polynomial is known as the characteristic polynomial of A. The roots of the characteristic polynomial are the eigenvalues li, which can be back-substituted into Eq. 34) to obtain the corresponding eigenvectors qi. Note from Eq. 33) that if q is an eigenvector of A, then q is also an eigenvector of A when is a scalar.

The (i, j)th entry of A is aij. Let us first consider the case of M ¼ N where the transformation matrix A is invertible. The Jacobian (defined as the determinant of the matrix containing qyi as its (i, j) element) of this transformation is jAj, the determinant of the qxj transformation matrix. Thus the PDF of y can be related to the PDF of x as follows: fY ðyÞ ¼ 1 À À1 Á fX A y jAj (2:104) Applying the above result and the N-variate Gaussian PDF in Eq. 101), we can see that the transformed random vector is also Gaussian, but with a new mean vector and new covariance matrix.

Their joint PDF is a function only of X 2 þ Y 2 ), then they are Gaussian with zero means n o andÈ equal É variances. It is easy to verify that E jZj2 ¼ E X 2 þ Y 2 ¼ 22 whereas E{Z2} ¼ E{X2 À Y2} ¼ 0. Finally, it is useful to realize that the central limit theorem applies to complex RVs also, in the sense that adding many identical and independent complex RVs results in Gaussian complex RVs. This can be seen by applying the central limit theorem to the real part and imaginary part separately.

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Correlation Pattern Recognition by B. V. K. Vijaya Kumar

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