\section{Ball detection}

The very first task that needed to be accomplished was to detect the ball,
which is uniformly red-colored and measures about 6 cm in diameter. We decided
to use a popular algorithm based on color segmentation \cite{ball-detect}. The
idea behind this algorithm is to find the biggest red area in the image and
assume that this is the ball. First, the desired color needs to be defined as
an interval of HSV (Hue-Saturation-Value) values. After that, the image itself
needs to be transformed into HSV colorspace, so that the regions of interest
can be extracted into a \textit{binary mask}. The contours of the regions can
then be identified in a mask \cite{contours}, and the areas of the regions can
be calculated using the routines from the OpenCV library. The center and the
radius of the region with the largest area are then determined and are assumed
to be the center and the radius of the ball.

It is sometimes recommended \cite{ball-detect} to eliminate the noise in the
binary mask by applying a sequence of \textit{erosions} and \textit{dilations},
but we found, that for the task of finding the \textit{biggest} area the noise
doesn't present a problem, whereas performing erosions may completely delete
the image of the ball, if it is relatively far from the robot and the camera
resolution is low. For this reason it was decided not to process the binary
mask with erosions and dilations, which allowed us to detect the ball even over
long distances.

The advantages of the presented algorithm are its speed and simplicity. The
major downside is that the careful color calibration is required for the
algorithm to function properly. If the HSV interval of the targeted color is
too narrow, then the algorithm might miss the ball; if the interval is too
wide, then other big red-shaded objects in the camera image will be detected as
the ball. A possible approach to alleviate these issues to a certain degree
will be presented further in this chapter. To conclude, we found this algorithm
to be robust enough for our purposes, if the sensible color calibration was
provided.

\section{Goal detection}

The goal detection presented itself as a more difficult task. The color of the
goal is white, and there are generally many white areas in the image from the
robot camera, which have area larger than that of the image of the goal, for
example the white field lines and the big white wall in the room with the
field. To deal with the multitude of the possible goal candidates, we
propose the following heuristic algorithm.

First, all contours around white areas are extracted by using a procedure
similar to that described in the section on ball detection. Next, the
\textit{candidate preselection} takes place. During this stage only $N$
contours with the largest areas are considered further (in our experiments it
was empirically determined that $N=5$ provides good results). Furthermore, all
convex contours are rejected, since the goal is a highly non-convex shape.
After that, a check is performed, how many points are necessary to approximate
the remaining contours. The motivation behind this is the following: it is
clearly visible that the goal shape can be perfectly approximated by a line
with 8 straight segments. On an image from the camera, the approximation is
almost perfect when using only 6 line segments, and in some degenerate cases
when the input image is noisy, it might be necessary to use 9 line segments to
approximate the shape of the goal. Any contour that requires a different number
of line segments to be approximated is probably not the goal. The preselection
stage ends here, and the remaining candidates are passed to the scoring
function.

The scoring function calculates, how different are the properties of the
candidates are from the properties, an idealized goal contour is expected to
have. The evaluation is happening based on two properties. The first property
is based on the observation, that the area of the goal contour is much smaller
than the area of its \textit{enclosing convex hull} \cite{convex-hull}. The
second observation is that all points of the goal contour must lie close to the
enclosing convex hull. The mathematical formulation of the scoring function
looks like the following \todo{mathematical formulation}:

The contour, that minimizes the scoring function, while keeping its value under
a certain threshold is considered the goal. If no contour scores below the
threshold, then the algorithm assumes that no goal was found.

Our tests have shown, that when the white color is calibrated correctly, the
algorithm can detect the goal almost without mistakes, when the goal is present
in the image. The downside of this algorithm, is that in some cases the field
lines might appear the same properties, that the goal contour is expected to
have, therefore the field lines can be mistaken for the goal. We will describe,
how we dealt with this problem, in the following section.

\section{Field detection}

The algorithm for the field detection is very similar to the ball detection
algorithm, but some concepts introduced in the previous section are also used
here. This algorithm extracts the biggest green area in the image, finds its
enclosing convex hull, and assumes everything inside the hull to be the field.

Such rather simple field detection has two important applications. The first
one is that the robot should be aware, where the field is, so that it doesn't
try to walk away from the field. Due to time constraints, we didn't implement
this part of the behavior. The second application of field detection is the
improvement of the quality of goal and ball recognition. As was mentioned in
the section on ball detection, the current algorithm might get confused, if
there are any red objects in the robot's field of view. However, there
shouldn't be any red objects on the field, except the ball itself. So, if
everything that's not on the field is ignored, when trying to detect the ball,
the probability of identifying a wrong object decreases. On the other hand, the
problem with the goal detection algorithm was that it could be distracted by
the field lines. So, if everything on the field is ignored for goal
recognition, then the accuracy can be improved.