Graphics Reference
In-Depth Information
Chapter 4
Point Spread Function-Based Approaches
to Three-Dimensional Scene Reconstruction
Basically, there are two distinct approaches to utilising focus information for depth
estimation. Section
4.1
gives an outline of the concept of the point spread function
(PSF) of an optical system. The depth from defocus approach described in Sect.
4.2
consists of acquiring a small number of images at different focus settings, where the
differences of the PSF across the set of images are exploited to estimate the depth
of scene points. The depth from focus method described in Sect.
4.3
aims for deter-
mining depth by acquiring several images at different known focus settings, where
the configuration for which the best focused image is observed is used to compute
the distance to the scene point based on the known intrinsic camera parameters.
4.1 The Point Spread Function
In contrast to the pinhole camera model assumed in the previous chapters, a real
optical system must be described as a two-dimensional linear filter characterised by
a (generally spatially non-uniform) point spread function (PSF).
According to the description by Kuhl et al. (
2006
), for monochromatic light an
exact description of the PSF due to diffraction of light at a circular aperture is given
by the radially symmetric Airy pattern
J
1
(r)
r
2
A(r)
∝
,
(4.1)
where
J
1
(r)
is a Bessel function of the first kind of first order (Pedrotti,
1993
).
A cross section of the Airy pattern with its central maximum and concentric rings
of decreasing brightness is shown in Fig.
4.1
. The central maximum is also called
the 'Airy disk'. For practical purposes, however, particularly when a variety of ad-
ditional lens-specific influencing quantities (e.g. chromatic aberration) is involved,
the Gaussian function is a reasonable approximation to the PSF according to
( u
−
u
c
)
2
+
( v
−
v
c
)
2
2
σ
2
1
2
πσ
2
e
−
G
σ
(
u,
ˆ
v)
ˆ
=
(4.2)
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