Master Thesis - Fachbereich Informatik

2.4. TEMPLATE MATCHING 29
accuracy of 0.01 pixels, while the error increases to about 0.1 pixels for low-contrast edges.
Lyvers et al. [41] proposed a subpixel edge detector based on spatial moments of a gray
level edge with an accuracy of better than 0.05 pixels for real image data. Aström [6] analyzes
subpixel edge detection by stochastic models. A survey on subpixel measurements
techniques can be found in [71].
2.4. Template Matching
A common task in vision applications is to search whether a particular pattern is part
of an image, and if so, where it is located [28]. Template matching is one method to
tackle this problem. The search pattern or template can be represented as an image and is
usually considerably smaller than the inspected input image. Then, the template is shifted
over the input image and compared with the underlying values. A measure of similarity is
computed at each position. Positions reaching a high score are likely to match the pattern,
or the other way around, if the template matches at a certain location, the score has a
maximum at this location.
A technique denoted as cross-correlation is widely used as measure of similarity between
image patches [64]. It can be derived from the sum of squared differences (SSD):
cSSD(x, y) =
W� −1
i=0
H−1 �
j=0
(T (i, j) − I(x + i, y + j)) 2
(2.27)
where I is the discrete image function and T the discrete template function. W and
H indicate the template width and height respectively. Expanding the squared quantity
yields:
cSSD(x, y) =
W� −1
i=0
H−1 �
j=0
T 2 (i, j) − 2T (i, j)I(x + i, y + j)+I 2 (x + i, y + j) (2.28)
Since the template is constant, the sum over the template patch T 2 (i, j) is constant as
well and does not contain any information on similarity. The same holds approximately
for the sum over the image patch I 2 (x + i, y + j) if there are no strong variances in image
intensity. Hence, the term T (i, j)I(x+i, y +j) remains the only real indicator of similarity
that depends on both the image and the template. This leads to the cross-correlation
equation:
c(x, y) =
W� −1
i=0
H−1 �
j=0
T (i, j)I(x + i, y + j) (2.29)
It turns out that the correlation looks very similar to the discrete convolution. Indeed,
the only difference between correlation and convolution is the sign of the summation in the
second term [28]. Thus, theoretically a correlation can be replaced by a convolution with a
flipped version of the template [64]. Like convolution, correlation is an expensive operation
if applied to large images and templates. In some cases it is faster to convert the spatial
images into the frequency domain using the (discrete) Fast Fourier Transformation (FFT),