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There are many motivations for using features rather than pixels
directly. For mobile robots, a critical motivation is that
feature based systems operate much faster than pixel based
systems [22]. The features are called Haar-like,
since they follow the same structure as the Haar basis, i.e.,
step functions introduced by Alfred Haar to define wavelets.
They are also used
in [13,3,20,22].
Fig. 3 (right) shows the eleven basis features, i.e.,
edge, line, diagonal and center surround features. The base
resolution of the object detector is
pixels, thus,
the set of possible features in this area is very large (642592
features, see [13] for calculation details).
A single feature is effectively computed on input images
using integral images [22], also known as summed area
tables [13]. An integral image is
an intermediate representation for the image and contains the sum of
gray scale pixel values of image with height and width ,
i.e.,
The integral image is computed recursively, by the formulas:
with
, therefore requiring only one scan over the input
data. This intermediate representation allows the computation
of a rectangle feature value at with height and width
using four references (see Fig. 4 (left)):
For the computation of the rotated features, Lienhart
et. al. introduced rotated summed area tables that contain the
sum of the pixels of the rectangle rotated by 45 with the
bottom-most corner at and extending till the boundaries of the
image (see Fig. 4 (middle and right)) [13]:
The rotated integral image is computed recursively, i.e.,
using the start values
. Four table lookups are required to
compute the pixel sum of any rotated rectangle with the formula:
Since the features are compositions of rectangles, they are
computed with several lookups and subtractions weighted with the area
of the black and white rectangles.
To detect a feature, a threshold is required. This threshold is
automatically determined during a fitting process, such that a minimum
number of examples are misclassified. Furthermore, the return
values
of the feature are determined, such that the
error on the examples is minimized. The examples are given in a set of
images that are classified as positive or negative samples. The set is
also used in the learning phase that is briefly described next.
Next: Learning Classification Functions
Up: Color-Independent Ball Classification
Previous: Color Invariance using Linear
root
2005-01-27