Subsampling is the process by which a discrete image is obtained from a continuous image. This is different from the analogue-digital conversion which relates to the image values,ie, to the discretization process.
Subsampling Theorem (Shannon)
Given a signal S it is possible to reconstruct it exactly from the
sequence of sample S(n T) if the signal is B
band-limited (ie, the Fourier
transform of the signal has compact support contained in [-B,+B]),
and the sampling frequency 1/T = B/pi.
The space of the B band-limited functions is called Paley-Wiener space PB, and is a subspace of L2(R).
Proff
Since F^ is B band-limited, the inverse Fourier transform
is
Practically a signal is never band-limited from a strictly mathematical point of view. However it is usually the case that the high frequency components are negligable so that the signal is "physically" band-limited.
The choice of the sampling step T (called also spatial resolution) is a key feature of any vision system. The optical resolution is determined by the physics of the imaging system. The scanner nominal resolution is usually not a true resolution because they often interpolate the sensed values.
Marco Corvi - Page hosted by geocities.com.