log_gabor

menpo.math.convolution.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 : double, optional

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

Default 2D	0.65
Default 3D	0.65

d_phi_sigma : double, optional

Angular bandwidth in xy-plane

Default 2D	1.3
Default 3D	1.5

d_theta_sigma : double, optional

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

Default 2D	N/A
Default 3D	1.5

Returns:

complex_conv : (num_scales x num_orientations x 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 x image.shape) ndarray

Bandpass images corresponding to each scale s

S: (image.shape) ndarray :

Convolved image

References

[R10]

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

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, :, :])