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

The operator abs_invar_fourier_coeff normalizes the Fourier coefficients with regard to the displacements of the starting point. These occur when an object is rotated. The contour tracer get_region_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 starting 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.

get_region_contour(single,&row,&col);
length_of_contour = length_tuple(row);
move_contour_orig(row,col,&trow,&tcol); 
prep_contour_fourier(trow,tcol,"unsigned_area",&param_scale);
fourier_1dim(trow,tcol,param_scale,50,&frow,&fcol);
invar_fourier_coeff(frow,fcol,1,"affine_invar",&invrow,&invcol);
abs_invar_fourier_coeff(invrow,invcol,1,2,"az_invar1",&absrow,&abscol);
fourier_1dim_inv(absrow,abscol,length_of_contour,&fsynrow,&fsyncol);

abs_invar_fourier_coeff is reentrant and processed without parallelization.

invar_fourier_coeff

fourier_1dim_inv, match_fourier_coeff

Fourier descriptors