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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
are taken. Via epipolar geometry the distance from ev- 
ery point to the according epipolar line is taken as a qual- 
ity measure for image matching. Image matching is done 
by extracting points of interest using Harris operator (Har- 
ris and Stephens, 1988) and trying to reallocate them by 
area based matching using normalized cross correlation as 
similarity measure. We normalize the cross correlation to 
get correlation coefficients using the definition of (Haral- 
ick and Shapiro, 1992) generalized to two-dimensions. For 
refining the results to subpixel accuracy a least squares ap- 
proach is used which fits a paraboloid into the correlation 
coefficient matrix (Gleason et al., 1990). Then the epipolar 
geometry is estimated based on MAPSAC algorithm (Torr, 
2002a) which is implemented within a free Matlab toolbox 
( Torr, 2002b). The MAPSAC algorithm is an extension of 
standard eight point algorithms (Zhang, 1997). 
2.2 Edge response 
The quality of an imaging system may be evaluated using 
the amount of blurring at edges. The edge spread func- 
tion of a 1D signal is the response of the system to an 
ideal edge. The first derivative of the edge spread func- 
tion, called the point spread function (PSF), is usually used 
to describe the quality of an imaging system (Luxen and 
Fôrstner, 2002). 
We choose two different measures to characterize the edge 
response function. 
Blonski edge response 
The modern measurement of geometric resolution is the 
edge response. The transition from bright to dark defines 
the edge sharpness and is considered to be a measure of ge- 
ometric resolution. Every ideal step edge is blurred when 
captured with an imaging device (see figure 1). This blur- 
ring describes a measure for the optical system. (Blonski et 
al., 2002) suggest to fit a sigmoid function f(x) — itd 
into the edge profile and characterize spatial resolution by 
full width at half maximum of the first derivative of this 
sigmoid edge signal (see figure 2). This first derivative is 
called a line spread function and its full width (measured 
in pixels) at 50% of maximum amplitude characterizes the 
whole imaging process. 
* / \ = 
Sich Mi 
(a) (b) (c) 
Figure 1: Edge response: Ideal step edge (a) is corrupted 
by blurring, noise or other distortions (b) which leads to a 
loss of edge sharpness (c). 
EUR T 
Luxen edge response 
The basic idea of (Luxen and Fórstner, 2002) is to measure 
the PSF by calculating the edge direction and edge magni- 
tude of a sensed image. Then the magnitudes get plotted 
1137 
d 
ES 
E 
(a) (b) 
Figure 2: Edge response: (a) Fitted sigmoid function into 
the edge profile and (b) first derivative of (a) with marked 
full width at half maximum. 
according to the edge directions and the surrounding el- 
lipse describes the parameters of the PSF. This process is 
very sensitive to noise, so we are not using the surrounding 
but a fitted ellipse in the least squares sense. The width of 
the ellipse is normalized within the interval [0. 1] where a 
width of 1 stands for an ideal edge. The width of the el- 
lipse is increasing in size reciprocally quadratic with image 
sharpness. This relation is important for comparison of dif- 
ferent image resolutions. For calculating the first derivative 
optimally rotation-equivariant directional derivative kernels 
by (Farid and Simoncelli, 1997) are used. Figure 3 shows 
the calculated magnitude image of an Siemens star and the 
plotted edges according to their directions. 
  
(a) (b) 
Figure 3: Luxen edge response test: (a) Edge magnitude of 
a Siemens star image (b) magnitude plotted according to 
edge direction with ellipse fitted in the least squares sense. 
2.3 Siemens star test 
A Siemens star is a special bar-pattern containing a very 
wide range of spatial frequencies. The Siemens star con- 
sists of an even number of tapered wedges pointing to a 
common center. Along each concentric circle centered on 
the star a rectangular signal may be achieved. For smaller 
radii the signal frequency is increasing until it reaches the 
limiting spatial frequency. The limited spatial frequency 
where all edges of the Siemens star could be detected is a 
measurement of image quality and is described by the min- 
imal radius in pixels. Figure 4 shows a Siemens star and 
the according bar patterns for different radii. 
2.4 Noise estimation via entropy 
Noise is an important criterion for measuring image qual- 
ity. In our test data, noise in the scanned film images is 
mainly caused by the granularity of the film. To measure 
noise the entropy H, is calculated in homogenous patches