Uniqueness of Blur Measures

After discussing usual approaches to measuring blur, we show theoretically that there is essentially a unique way to quantify blur by a single number. It is the variance of position and therefore is given by the second derivative at the origin of the Fourier transform. This somewhat surprisingly implies that blur should be especially sensitive to attenuation of the low frequencies. This is confirmed by a series of experiments. We verify that the blur measure behaves as expected with respect to the standard ”blur” and ”sharpen” tools of usual softwares. We apply our measure to assess quality of cameras, natural images and image processings.