Personal Property Estimation

Personal properties are known to have a great influence on personal behavior and are viewed as random variables in our proposed structure. To avoid estimating large random variables at the same time, we fix some of variables in our structure. Namely, the fixed variables are deterministic variables. As for those remaining random variables, we estimate them by using data-driven method. Below, we will talk about which variables are fixed while which are not. We will also talk about how to determine or estimate these variables.

S

K

The behavior of pedestrian, in general, obeys some rules which are established by society. For example, normally we do not climb trees or street lights and we also do not enter the region where prohibitory enter sign is set up. Having scene prior knowledge is useful to detect those behaviors which do not occur often.

The scene knowledge we adopt in our proposed system is locations of obstacles and restricted region. We assume that the scene knowledge is known in advance and is labeled manually.

24

D

Pedestrian always moves toward his destination if there is no accidental event happened. Knowing the pedestrian destination is useful for us to predict his next move.

The importance of pedestrian’s destination is shown in [11]. [11] also shows that even roughly guess the destination helps to make more accurate prediction.

The possible destinations, in fact, can be trained at the beginning of surveillance system by simply recording the exit and entry points of scene. However, we do not take destination information into our proposed structure. We treat it as the optional information. Because our scene is relatively simple and most abnormal events we used are designed, the destination information in our proposed system is not as useful as in daily life scene.

C

D

Comfortable distance is used to describe the avoidance phenomenon as pedestrian confront other unfamiliar objects. Everyone feels different comfortable distance.

Knowing the comfortable distance of pedestrian improves the prediction of pedestrian behavior since next possible actions which pedestrian might take are under our controlled.

However, estimating comfortable distance for everyone seems to be complex and difficult not only because the comfortable distance for everyone is different but also because the comfortable distance might vary as the surrounding changes. As a result, we make a simplified assumption here that everyone has the same comfortable distance and we take it as a deterministic variable. The exact value of this comfortable distance is obtained in training step.

25

P

V

The property of preferred velocity is very similar to the property of comfortable distance. That is, everyone has his own preferred walking velocity and it varies as surrounding changes. Estimating preferred walking velocity for each one sounds impracticable which is just like the comfortable distance.

Therefore, we take previous observed velocity as the preferred velocity of this object since we believe that the object always tries to maintain a constant velocity. To be more specific, if the object is individual pedestrian, we take his previous velocity as his preferred velocity; if the object is a group consists of several pedestrians, we take group’s previous mean velocity as the group’s preferred velocity.

S

G

Knowing the social group is important to model pedestrian behavior, since the behavior of pedestrian in groups tends to be very different from the behavior of pedestrian in single. In general, pedestrian behavior in group is hard to predict, however, the whole group behavior, in most case, is relatively simple and easy to model. By tracking object in group unit, tracking performance can be improved drastically.

However, estimating the social group is not an easy job because of often changing of group size. Therefore, we use pair-wise feature with bottom-up grouping to solve the problem of various group sizes. That is, we take features from every two pedestrians. Then, we adopt Support Vector Machine (SVM) to help us classify whether these two pedestrians belong to the same group. We extract eight features which are illustrated in Figure 3-5 and summary at Table 3-1. These features are the time difference of showing up, relative distance, velocity magnitude differences of

26

past two steps, velocity orientation differences of past two steps and number of neighboring pedestrians.

Figure 3-5 Illustration of extracting group features

Table 3-1 Features for group estimation

No. Notation Feature Description

1 ∆𝒕_{𝑑𝑠𝑑𝑔𝑦}^𝑖𝑗 Normalized time difference of showing up 2 ∆𝑷^𝑖𝑗 Relative distance

3,4 ∆𝒗₋₁^𝑖𝑗 , ∆𝒗₋₂^𝑖𝑗 Normalized past two magnitudes of speed 5,6 ∆𝜙₋₁^𝑖𝑗 , ∆𝜙₋₂^𝑖𝑗 Past two directions of speed

7,8 𝑵^𝑖 , 𝑵^𝑗 The number of nearby objects

The output of SVM is a binary number. In other words, it shows that whether these two pedestrians are in the same group. Based on SVM result, we group pedestrians from bottom to top. Since we believe that connected pedestrians are always exist to connect individual pedestrian to a large group as shown in Figure 3-6. At the end of grouping, we will obtain the best group size which is mainly determined by SVM.

Figure 3-6 Illustration of bottom-up grouping (a) Pair-wise grouping (b) Final group size

27