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ZER_MOM

Section: C Library Functions (3)
Updated: 16 Mar 1998
Index

NAME

zer_mom, zer_pol, zer_rec, zer_con - Zernike moments

SYNTAX

#include <xite/zernike.h>

int zer_mom( IBAND inband, int n, int m,
DCOMPLEX *res );

int zer_pol( int n, int m, double x, double y,
DCOMPLEX *res );

int zer_con( int n, IBAND inband, IBAND outband );

int zer_rec( int order, IBAND inband, IBAND outband );

DESCRIPTION

The Zernike moment of order nand repetition mofan image f(x,y) is defined as follows:
n+1 *
A(n,m) = ---- Sum Sum f(x,y)[V(n,m, x,y)]
pi x y

where x^2+y^2 <= 1

The image V(n,m, x,y) is the Zernike basis images oforder nand repetition m.These basis images arecomplex and orthogonal. The Zernike moments areessentially the projections of the input image ontothese basis images.

The original image can be reconstructed from theZernike moments. The N-th order approximation is givenby
  ^         N
  f(x,y) = Sum Sum A(n,m) V(n,m, x,y)
           n=0  m

The contribution or information content of the n-thorder moments is

I(x,y, n) = Sum A(n,m) V(n,m, x,y)
m

zer_momcomputes A(n,m).

zer_polcomputes the zernike basis functionV(n,m,x,y).

zer_concomputes the absolute value of the contributionof the n-th order moments, i.e. the absolute value ofI(x,y, n).

zer_recdemonstrates how the input image can bereconstructed from the Zernike basis functions and theZernike moments.

RETURN VALUE

0 : OK.

AUTHOR

Řivind Due Trier, Dept. Informatics, Univ. Oslo

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