This isn't going to be a technical explanation, but consider the following:
- I don't know where the source image came from, but be aware that you're comparing two different images.
- Blurring does not mean that high frequency content does not generally exist. It means it's been attenuated.
- Bear in mind that a motion blur is not symmetric. It acts as a low-pass filter primarily in a specific direction.
Let's take one source image and compare a motion blur against a radially symmetric blur with the (approximately) same directional profile and width.
A = imread('cameraman.tif');
A = im2double(A);
% generate filters
radius = 30;
fkm = fspecial('motion',2*radius,-45);
fkg = fspecial('disk',radius);
imshow(fkm,[])
imshow(fkg,[])
% filter the image
B = imfilter(A,fkm,'replicate'); % motion filter
C = imfilter(A,fkg,'replicate'); % disk filter
% do FFT
Fa = getfft(A);
Fb = getfft(B);
Fc = getfft(C);
imshow([A B C; Fa Fb Fc]); % Display the results
function F = getfft(A)
F = fftshift(fft2(A));
F = abs(F); % magnitude
F = mat2gray(log(F+1));
end
As you can see, the motion filter only reduces HF content in one direction. The symmetric filter reduces HF content in all directions. As the filter widths are the same, it should be clear that this behavior is attributable to the filter shape.
