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5.2 Efficient Extraction of Oriented Edge Features 137

of the contrasts in the scene. These are some of the general environmental parame-
ters to be collected in parallel (right-hand part of Figure 5.1).

5.2.2 Search Paths and Subpixel Accuracy

The masks defined in the previous section are applied to rectangular search ranges
to find all possible candidates for an edge in these ranges. The smaller these search
ranges can be kept, the more efficient the overall algorithm is going to be. If the
high-level interpretation via recursive estimation is stable and good information on
the variances is available, the search region for specific features may be confined
to the 3 ı region around the predicted value, which is not very large, usually (ı =
standard variation). It does not make sense first to perform the image processing
part in a large search region fixed in advance and afterwards sort out the features
according to the variance criterion. In order not to destabilize the tracking process,
prediction errors > 3 ı are considered outliers and are usually removed when they
appear for the first time in a sequence.]
Figure 5.6 shows an example of edge localization with a ternary mask of size n w
= 17, n d = 2, and n 0 = 1 (i.e., mask depth m d = 5). The mask response is close to
zero when the region to which it is applied is close to homogeneously gray (irre-
spective of the gray value); this is an important design factor for abating sensitivity
to light levels. It means that the plus– and minus regions have to be the same size.
The lower part of the figure shows the resulting correlation values (mask re-
sponses) which form the basis for determining edge location. If the image areas
within each field of the mask are homogeneous, the response is maximal at the lo-
cation of the edge. With different light levels, only the magnitude of the extreme
value changes but not its location. Highly discernible extreme values are obtained
also for neighboring mask orientations. The larger the parameter n 0, the less pro-
nounced is the extreme value in the search direction, and the more tolerant it is to
deviations in angle. These robustness aspects make the method well suited for
natural outdoor scenes.
Search directions (horizontal or vertical) are automatically chosen depending on
the feature orientation specified. The horizontal search direction is used for mask
orientations between 45 to 135° as well as between 225 and 315°; vertical search is
applied for mask directions between 135 to 225° and 315 to 45°. To avoid too fre-
quent switching between search directions, a hysteresis (dead zone of about one di-
rection–increment for the larger mask widths) is often used that means switching is
actually performed (automatically) 6 to 11° beyond the diagonal lines, depending
on the direction from which these are approached.

5.2.2.1 Subpixel Accuracy by Second-Order Interpolation

Experience with several interpolation schemes, taking up to two correlation values
on each side of the extreme value into account, has shown that the simple second-
order parabola interpolation is the most cost-effective and robust solution (Figure
5.12). Just the neighboring correlation values around a peak serve as a basis.