Convert cycles per degree to sigma in imgaussfilt

Hello,

I am trying to filter my images to a certain cycles per degree (cpd). I have obtained the visual angle of the image, and I would like to low-pass filter my images to under 1 cpd using a Gaussian filter. However, I couldn't figure out what sigma I should use in the imgaussfilt function. Is there a direct formula for the conversion?

I was looking at a similar question here, where we first calculate the visual angle, but it does not mention how it relates to the second formula to obtain sigma. Additionally, there is a constant k in the formula, but I am not sure how to determine what is an appropriate k to use. I would appreciate any help. Thank you!

Answer 1

[Nipun]

Hi Ling,

I understand that you want to apply a low-pass Gaussian filter to your image at under 1 cycle per degree (cpd). Here's how to determine the appropriate sigma for the imgaussfilt function in MATLAB:

1. Calculate the desired cutoff frequency in pixels:

• Convert the cutoff frequency from cpd to pixels using the visual angle.
• For a visual angle of "theta" degrees and image resolution of "R" pixels, the frequency in pixels per degree is "R / theta".

2. Convert to standard deviation:

• Use the relationship between the standard deviation (sigma) and the cutoff frequency. The standard deviation in pixels is approximately given by: "sigma = R / (theta * 2 * pi * 1.5)"

Here's an example MATLAB code for your reference:

% Given parameters
visual_angle = 30; % example value in degrees
image_resolution = 1080; % example value in pixels

% Convert 1 cpd to pixels
cpd = 1;
frequency_pixels = (image_resolution / visual_angle) * cpd;

% Calculate sigma
sigma = image_resolution / (visual_angle * 2 * pi * 1.5);

% Apply Gaussian filter
filtered_image = imgaussfilt(input_image, sigma);

% Display filtered image
imshow(filtered_image);
title('Low-pass Filtered Image');

For more details on Gaussian filtering, refer to the following MathWorks documentation:

https://www.mathworks.com/help/images/ref/imgaussfilt.html

Hope this helps.

Regards,

Nipun

[Ling C]

Hi Nipun,

Thank you for your reply. May I ask how was this formula sigma = R / (theta * 2 * pi * 1.5) obtained? Also, I believe the sigma calculation should include cpd.

Ling