Gaussian filter

Nearest neighboring pixels have the most influence
F(x, y)
H(u, v)
1 2 1
2 4 2
1 2 1
this kernel is an approximation of a Gaussian function
h(u, v) = 1/2πσ^2 e ^(- u^2+v^2/σ^2)

Gaussian filters
Variance(σ^2), standard deviation(σ): determines extent of smoothing

hsize = 31;
sigma = 5;
h = fspecial('gaussian', hsize, sigma);

surf(h);
imagesc(h);

outim = imfilter(im, h);
imshow(outim);

for sigma = 1:3:10
	h = fspecial('gaussian', fsize, sigma);
	out = imfilter(im, h);
	imshow(out);
	pause;
end

img = imread('saturn.png');
imshow(img);

noise = randn(size(img)) .* 25;
noisy_img = img + noise;
imshow(noisy_img);

filter_size = 11;
filter_sigma = 2;
pkg load image;
filter = fspecial('gaussian', filter_size, filter_sigma);

smoothed = imfilter(noisy_img, filter);

When filtering with a Gaussian, the sigma is most important- it defines the blur kernel’s scale with respect to the image.
Altering the normalization coefficient does not effect the blur, only the brightness.