side
unc-
tion
be
ad
For
leter-
gives
p-
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an- .
led
necessary for data compression in image sequences. This suggests that only parts of the spectral
information are necessary for precise template matching.
Further research will show which spectral bands are decisive for high precision object loca-
tion and which impact multiimage correlation has on the precision and reliability of point
transfer.
3. Quality of Digital Image Correlation
This section presents several quality measures which can be used for the assessment of digital
image correlation. They are based on the matching algorithms presented in the previous section
especially on the least squares approach and on proper image models. The aim is to provide some
insight into the relations between the algorithm, the geometric model and the texture of the tem-
plate in order to visualize the limitations of the quality measures but also their value for in-
creasing the flexibility and the reliability of the procedures.
3.1 Image models
The prediction of correlation quality has to be based on an adequate image model. In this con-
text the image gray level function gj) usually is assumed to form a stochastic process consisting
of the true image g(x) and additive noise n(z): g,(æ) = g(x) + n(x), where g and z are mutually
uncorrelated stationary processes. If one further assumes them to be Gaussian the covariance func-
tions BE, and R, or the power spectra P, and P, being their Fourier transforms fully describe their
statistical properties.
There are three main types of processes in use to describe g and x (cf. table 4):
a. The white noise model is only used to describe n.
The exponentialmodel is proposed by Helava (1976) to describe g and is based on extensive
empirical investigations. Its parameters ? and a are measures for the brightness and the
contrast of the image. A value of a = 0.2 mm belongs to good imagery.
c. The autoregressive model (AR-model) is used very frequently in digital image processing (cf.
Rocca 1972, Pratt 1974, Emmert and McGillem 1973, Rosenfeld 1976). Also here P and » des-
cribe the brightness and the contrast. This model sometimes also is used to describe corre-
lated noise (cf. sect. 3). Fig. 2 Mu). Power spectra of
image models b. and c.
Table 4 Image and noise models P
t e AR-mode!
N° name (x) Plu) exponential
5 ^ ~ model
P €
(ac)
white noise ó c
/ (19 (21z/a)?)| P.
P
R
g +
b | exponential model R —aju|
R
m Uie
s e
4 79 12
0 E / (1+ (2mru)*) — 9 uu
1/a 2/a 3/a 4/a
c | autoregressive model
The difference between models b. and c. (cf. fig. 2) seems to be negligible. We can relate the
models e. g. by assuming both power spectra to have the same values at 0 and I/a. This leads to
the relation r = Ve=T/ 27a = a/5. The variance of the estimated shift however depends on the
effective bandwidth b of the signal which for white noise does not exist for the AR-image model.
b can be determined from
fu? P,/P, du pl) 2/a?, 1-dimensional signal =
= 8
fPJP d 3/a?, 2-dimensional signal
For the AR-image model and white noise the integral in the numerator is infinite. For the expo-
