How to convolve an image with a 2D function and plot the result

David Okeson (view profile)

on 14 Oct 2018
Latest activity Commented on by Image Analyst

on 14 Oct 2018

Image Analyst (view profile)

Hi, I have a bar phantom image attached that I want to convolve with the 2d function h1(x,y)=e^(-5x^2-5y^2). I'm not very familiar with Matlab or similar programs so bear with me.
I have created and plotted the function h1 using the following code:
x = [-1: .01: 1];
y = [-1: .01: 1];
[x_,y_] = meshgrid(x,y);
h1_ = exp((-5.*x_.^2)-(5.*y_.^2));
surf(x_,y_,h1_)
I then inserted the bar phantom image into Matlab using:
From here I'm stuck and I've tried a number of things unsuccessfully. I've tried:
H1_ = abs(fft2(h1_));
I1 = abs(fft2(I));
g = ifft2(H1_.*I1);
And get the error: Array dimensions must match for binary array op.
I tried changing the dimensions of my x and y variables to match the dimensions of my image but the result g is a blank white image.
I also played tried to avoid using fft2 using imfilter, double, and conv2 but only got all white or black resulting images. Any help would be greatly appreciated.

Image Analyst (view profile)

on 14 Oct 2018

Try this:
kernel = h1_ / sum(h1_(:));
filteredImage = conv2(double(I), kernel, 'same');
imshow(filteredImage, []);

David Okeson

David Okeson (view profile)

on 14 Oct 2018
When entering
filteredImage = conv2(double(I), kernel, 'same');
I got the error
Error using conv2
N-D arrays are not supported.
I figured out how to fix this though, the bar phantom I was a 484x307x3 matrix, I used rgb2gray to create a new image of size 484x307 and it worked perfectly.
Thank you.
Image Analyst

Image Analyst (view profile)

on 14 Oct 2018
For a color image, you can use imfilter() or split the color image into individual color channels and process each one at a time:
% Extract the individual red, green, and blue color channels.
redChannel = rgbImage(:, :, 1);
greenChannel = rgbImage(:, :, 2);
blueChannel = rgbImage(:, :, 3);
filteredImageR = conv2(double(redChannel), kernel, 'same');
filteredImageG = conv2(double(greenChannel), kernel, 'same');
filteredImageB = conv2(double(blueChannel), kernel, 'same');