New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

20 CHAPTER 2. PRELIMINARIES
Figure 2.2.8: Bricks of the two kinds of operas. Some of them are labeled with the
number of the group they belong to. Notice the difference in the two bricks of group 1
and recall that the only condition for a group membership is the position while other
properties such as color may be different.
Step 3: Analyze the groups
For each group from the previous step check if all its bricks roughly look the
same or if we can identify differences between bricks from an opera-A pile
versus an opera-B pile. For example, within the same group bricks from an
opera-A pile might be darker than bricks from an opera-B pile which would
then be two sub-groups with different average color. This is illustrated in
Figure 2.2.9: we are looking at seven random members of group 1 (see Figure
2.2.8) and there are obviously two sub-groups: the bricks from opera-B type
piles have a white spot so the average color of a brick in this opera-B subgroup
is around 230. Bricks from an opera-A type pile do not have this white
spot which decreases the average brightness value to about 200.
(a) B,
color:
231
(b) A,
color:
205
(c) B,
color:
134
(d) B,
color:
232
(e) A,
color:
204
(f) A,
color:
206
(g) A,
color:
201
Figure 2.2.9: Seven lego bricks of group 1 in Figure 2.2.8. Obviously, there exist
two sub-groups.
From now on we will call a group that has two different sub-groups a
feature. So here a feature has three properties: the group number and the
average color values of its two sub-groups (for group 1: 200 for the opera-A
type and 230 for the opera-B type).
Now, the usage of a feature to determine an unknown pile’s type is quite
simple: From our feature we know the average position (since it is still a
group) and the color a brick would have if it belongs to an opera-A or opera-B
type pile. Consequently, we just have to take the picture of the unknown pile,
identify the brick at this features position and determine its color and compare
it to the colors for an opera-A or an opera-B type. The closer it is to one of
them, the more likely it is that kind of opera.
Step 4: Check the feature quality
Use each feature found in the previous step to guess the label of a pile we
already know. If the answer is correct, we count this as a success. We now
test each feature with every (already labeled) picture we have and count the