Calculate the Fourier coefficients of a parameterized contour.

The operator ::fourier_1dim calculates the Fourier coefficients of a parameterized contour by using a valid parameter scale. This parameter scale may, for instance, be created with the help of the procedure ::prep_contour_fourier. This function serves to calculate the Fourier coefficients of closed contours which are treated like complex-valued curves. Therefore, in order to determine the Fourier coefficients, the Fourier transform for periodical functions is used. Hereby the parameter MaxCoef determines the absolute value + 1 of the maximal number of Fourier coefficients, i.e. if n coefficients are indicated, the procedure will calculate coefficients ranging from -n to n. The contour will be approximated without loss, if n = number of the contour points, whereby n = 100 approximates the contour so well that an error can hardly be distinguished; n [40,50] however is sufficient for most applications. If the parameter MaxCoef is set to 0, all coefficients will be determined.

get_region_contour(single,&row,&col);
move_contour_orig(row,col,&trow,&tcol);
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);

::prep_contour_fourier

::invar_fourier_coeff, ::disp_polygon

Fourier descriptors