invar_fourier

invar_fourier_coeff ( : : RealCoef, ImaginaryCoef, NormPar, InvarType : RealInvar, ImaginaryInvar )

Normalize the Fourier coefficients.

Elimination of affine information from the Fourier coefficients, determination of affine invariants. The Fourier coefficients will be normalized suitably so that all affine correlated contours will be projected to one and the same contour. The following levels of affine mappings are available:

   Translations  (InvarType = 'transl_invar')
   + Rotations   (InvarType = 'congr_invar')
   + Scalings    (InvarType = 'simil_invar')
   + Slanting    (InvarType = 'affine_invar')

The control parameter InvarType indicates up to which level the affine representation shall be normalized. Please note that indicating a certain level implies that the normalizing is executed with regard to all levels below. For most applications a subsequent normalizing of the starting point is recommended!

Parameters

`RealCoef` (input_control)	real-array `->` real
Real parts of the Fourier coefficients.

`ImaginaryCoef` (input_control)	real-array `->` real
Imaginary parts of the Fourier coefficients.

`NormPar` (input_control)	integer `->` integer
Input of the normalizing coefficients.
Default value: 1
Suggested values: 1, 2
Restriction: `NormPar >= 1`

`InvarType` (input_control)	string `->` string
Indicates the level of the affine mappings.
Default value: 'affine_invar'
List of values: 'affine_invar', 'simil_invar', 'congr_invar', 'transl_invar'

`RealInvar` (output_control)	real-array `->` real
Real parts of the normalized Fourier coefficients.

`ImaginaryInvar` (output_control)	real-array `->` real
Imaginary parts of the normalized Fourier coefficients.

Example

prep_contour_fourier(trow,tcol,"unsigned_area",&param_scale);
fourier_1dim(trow,tcol,param_scale,&frow,&fcol);
invar_fourier_coeff(frow,fcol,1,"affine_invar",&invrow,&invcol);
abs_invar_fourier_coeff(invrow,invcol,1,2,"az_invar1",&absrow,&abscol);

Parallelization Information

invar_fourier_coeff is reentrant and processed without parallelization.

Possible Predecessors

fourier_1dim

Possible Successors

invar_fourier_coeff

Module

Fourier descriptors