Why is my Gabor patch not resizing as a function of the bounding box?

Question

I'm trying to create a Gabor patch of variable size for an upcoming experiment.

Below is the python function used to generate the code. The code was ported from this tutorial for Matlab (assume import numpy as np):

def gabor_patch(size, lambda_, theta, sigma, phase, trim=.005):
    """Create a Gabor Patch

    size : int
        Image size (n x n)

    lambda_ : int
        Spatial frequency (px per cycle)

    theta : int or float
        Grating orientation in degrees

    sigma : int or float
        gaussian standard deviation (in pixels)

    phase : float
        0 to 1 inclusive
    """
    # make linear ramp
    X0 = (np.linspace(1, size, size) / size) - .5

    # Set wavelength and phase
    freq = size / float(lambda_)
    phaseRad = phase * 2 * np.pi

    # Make 2D grating
    Xm, Ym = np.meshgrid(X0, X0)

    # Change orientation by adding Xm and Ym together in different proportions
    thetaRad = (theta / 360.) * 2 * np.pi
    Xt = Xm * np.cos(thetaRad)
    Yt = Ym * np.sin(thetaRad)
    grating = np.sin(((Xt + Yt) * freq * 2 * np.pi) + phaseRad)

    # 2D Gaussian distribution
    gauss = np.exp(-((Xm ** 2) + (Ym ** 2)) / (2 * (sigma / float(size)) ** 2))

    # Trim
    gauss[gauss < trim] = 0

    return grating * gauss

I would like the size of the Gabor patch to increase proportionally to the size parameter. In other words, I would like the dimensions of the bounding box to dictate the diameter of the patch. The problem is that this function does not behave in this way. Instead, the bounding box increases in size while the patch retains the same dimensions.

Example 1: size = 100

Example 2: size = 500

It's not at all obvious to me what I'm doing incorrectly. Could somebody please point me in the right direction?

Please let me know if I can provide further information. Thank you!

Answer 1

The size parameter in your code simply means the size of the patch, i. e. the interval in x and y over which you sample your Gabor function. What you are thinking of is the support of the function, i. e. the interval where it is noticeably different from 0. This is determined by the sigma parameter, which is the bandwidth of the Gaussian.

So if you just increase size, you will get a bigger image back, but the area where you can see the ripples will stay the same. If you increase sigma, the area with the ripples will get larger, and then you may have to increase size as well to see all of it.

By the way, IMHO, the right place to ask this question is on dsp.stackexchange.com.