log_gabor

menpo.math.log_gabor(image, **kwargs)

Creates a log-gabor filter bank, including smoothing the images via a low-pass filter at the edges.

To create a 2D filter bank, simply specify the number of phi orientations (orientations in the xy-plane).

To create a 3D filter bank, you must specify both the number of phi (azimuth) and theta (elevation) orientations.

This algorithm is directly derived from work by Peter Kovesi.

Parameters

• image ((M, N, ...) ndarray) – Image to be convolved

• num_scales (int, optional) –

  Number of wavelet scales.

  Default 2D	4
  Default 3D	4

• num_phi_orientations (int, optional) –

  Number of filter orientations in the xy-plane

  Default 2D	6
  Default 3D	6

• num_theta_orientations (int, optional) –

  Only required for 3D. Number of filter orientations in the z-plane

  Default 2D	N/A
  Default 3D	4

• min_wavelength (int, optional) –

  Wavelength of smallest scale filter.

  Default 2D	3
  Default 3D	3

• scaling_constant (int, optional) –

  Scaling factor between successive filters.

  Default 2D	2
  Default 3D	2

• center_sigma (float, optional) –

  Ratio of the standard deviation of the Gaussian describing the Log Gabor filter’s transfer function in the frequency domain to the filter centre frequency.

  Default 2D	0.65
  Default 3D	0.65

• d_phi_sigma (float, optional) –

  Angular bandwidth in xy-plane

  Default 2D	1.3
  Default 3D	1.5

• d_theta_sigma (float, optional) –

  Only required for 3D. Angular bandwidth in z-plane

  Default 2D	N/A
  Default 3D	1.5

Returns

• complex_conv ((num_scales, num_orientations, image.shape) ndarray) – Complex valued convolution results. The real part is the result of convolving with the even symmetric filter, the imaginary part is the result from convolution with the odd symmetric filter.

• bandpass ((num_scales, image.shape) ndarray) – Bandpass images corresponding to each scale s

• S ((image.shape,) ndarray) – Convolved image

Examples

Return the magnitude of the convolution over the image at scale s and orientation o

np.abs(complex_conv[s, o, :, :])

Return the phase angles

np.angle(complex_conv[s, o, :, :])

References

1

D. J. Field, “Relations Between the Statistics of Natural Images and the Response Properties of Cortical Cells”, Journal of The Optical Society of America A, Vol 4, No. 12, December 1987. pp 2379-2394