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

Question

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:

I = imread('bar phantom1.png');

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.

Answer 1

Try this:

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