gaussz2d

Compute the 2D z order derivative of Gaussian

Syntax

[out] = gaussz2d(kx,ky,order,sigma[,sigmax][,sigmay])

Description

This function computes the 2D x order derivative of Gaussian. That is, the wavelet given by

PSIHAT (kx,ky) = i*(kx + i*ky).^order .* exp( - (A*K).^2 / 2 )

where PSIHAT is the Fourier transform of PSI;
      K = (kx,ky);
      A = diag(sigmax,sigmay).

Notice that for real images, inside a CWT computed with the gaussz2d wavelet: - order = 1: gives the gradient of the smoothed analyzed image in complex representation - order = 2: gives the maximum curvature of this smoothed image vector in complex coordinates.

This wavelet depends of three parameters: order, sigmax, sigmay. This function is used by the cwt2d routine which compute continuous wavelet transform in 2D.

Input Data

kx,ky

[REAL MATRICES]: The frequency plane. Use meshgrid to create it.

order, sigma, sigmax, sigmay

[REAL SCALARS]: The wavelet parameters. By default, sigmax = sigmay = sigma (isotropic case).

Output Data

out

[REAL MATRIX]: The wavelet in frequency plane.

Example(s)

>> step = 2*pi/128;
>> [kx,ky] = meshgrid( -pi : step : (pi-step) );
>> wav = gaussz2d(kx,ky,6,1);
>> imagesc(wav);

References

See Also

cwt2d cwt2d_yashow meshgrid samcwt2d samcwt2d_yashow sarcwt2d

Location

continuous/2d/wave_defs/gaussz2d.m