absolute_invariant ( : : RealInvar, ImaginaryInvar, CoefP, CoefQ, AZInvar : RealAbsInvar, ImaginaryAbsInvar )

Normalizing of the Fourier coefficients with regard to the displacment of the starting point.

The operator absolute_invariant normalizes the Fourier coefficients with regard to the displacements of the starting point. These occur when an object is rotated. The contour tracer fetch_contour starts with recording the contour in the upper lefthand corner of the region and follows the contour clockwise. If the object is rotated, the start value for the contour point chain is different which leads to a phase shift in the frequency space. The following two kinds of normalizing are available:

  abs_amount:  The phase information will be eliminated; the 
               normalizing does not retain the structure, i.e.\ if 
               the AZ-invariants are backtransformed, no
               similarity with the pattern can be recognized 
               anymore.
  az_invar1:   AZ-invariants of the 1st order execute the normalizing
               with respect to displacing the starting point so that
               the structure is retained; they are however
               more prone to local and global disturbances,
               in particular to projective distortions.


Parameters

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

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

CoefP (input_control)
integer -> integer
Normalizing coefficients p.
Default value: 1
Suggested values: 1, 2
Restriction: CoefP >= 1

CoefQ (input_control)
integer -> integer
Normalizing coefficients q.
Default value: 1
Suggested values: 1, 2
Restriction: (CoefQ >= 1) && (CoefQ != CoefP)

AZInvar (input_control)
string -> string
Order of the AZ-invariants.
Default value: 'abs_amount'
List of values: 'abs_amount', 'az_invar1'

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

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


Example
fetch_contur(single,&row,&col);
length_of_contour = length_tuple(row);
move_contour_orig(row,col,&trow,&tcol); 
create_param_cont(trow,tcol,"unsigned_area",¶m_scale);
fourier_1dim(trow,tcol,param_scale,50,&frow,&fcol);
invariances(frow,fcol,1,"affine_invar",&invrow,&invcol);
absolute_invariant(invrow,invcol,1,2,"az_invar1",&absrow,&abscol);
fourier_1dim_inv(absrow,abscol,length_of_contour,&fsynrow,&fsyncol);

Possible Predecessors

invariances


Possible Successors

fourier_1dim_inv, compare_coef



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