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Images are often corrupted by noise, random fluctuations that
can be characterized by their probability distribution. Two
distributions are commonly used to model noise processes: the Gaussian
(normal) distribution and the uniform distribution. While several
noise processes affecting digital images can be described well by
these distributions, quantum nature of light results in a different
kind of noise, photon noise, following a Poisson distribution (see
Section TM:2.1.4).
Codelet 2 Digital camera photon noise (../TeMa/R/tm.photonNoise.R)
-2
- Quantum nature of light manifests itself as a Poisson noise
affecting digital imaging. In order to simulate this noise process
correctly we need to now a few parameters: the maximum number of electrons
that fit within a pixel well and the corresponding ISO sensitivity,
the ISO sensitivity at which the picture is taken, the maximum intensity
value, and the gamma correction factor if any. These data allow us to
map an intensity value in the digital image into and absolute number of electrons
which is proportional to the number of photons. The latter provides
the (single) parameter 31#31 controlling the Poisson process.
The default fullWell value is typical of a high-end digital
reflex camera
32#32
The first step is mapping the intensity value
into a number proportional to the number of
photons:
33#33
A new, noisy value is generated according to
the corresponding Poisson distribution:
34#34
and it is mapped back the digital image context
35#35
36#36
Photon noise is (proportionally) more significant in the darker areas of
images: we choose a new sample image with a dark background and we
apply to it a plausible amount of photon noise for a high ISO
value of 3200 (the scale parameter of function
tm.addNoise).
37#37
We can visually appreciate the effect of noise with a simple compositing
operation:
38#38
and having a detailed look at a sample row of the image
39#39
Figure 2.4:
Photon noise is due to the quantum nature of light: as its
variance is proportional to the square root of the average number
of photons, its relative impact can be reduced by increasing the
average number of photons, e.g. using large pixels.
[width=7cm]figures/photonNoiseComposite.jpg
[width=7cm]figures/photonNoiseProfile.jpg |
Next: Digital imaging artifacts
Up: The Imaging Process
Previous: Diffraction Effects
Roberto Brunelli
2008-11-25