Focusing on Spatio-Temporal Regions

Not all objects and respectively their trajectories within one database are of in- terest for a given analysis task. Therefore, only predefined trajectories within a region of interest (ROI) are considered for subsequent analysis. To focus on

(A) 1 2 3 4 5 6 7 8 9 Noise Levels 0 0.2 0.4 0.6 0.8 1 Ratio Lengths (B) 1 2 3 4 5 6 7 8 9 Noise Levels 0 5 10 15 20

Mean Curvilinear Speed

Figure 3.18:Impact of noise artifacts to group distinguishability for each trajectory using benchmark TDB S3. For different noise levels the mean time series for the two groups within benchmark TDB S3 (colored in magenta and blue) for the features ’ratio lengths’ (A) and the features ’mean curvilinear speed’ (B) are illustrated.

the region of interest, the database can be globally truncated to a fixed spa- tial region and by specifying the time interval of interest. The knowledge of the spatio-temporal occurrence of the groups of interest in advance reduces the data size dramatically [346]. Focusing on a region of interest is often used be- cause specific phenomena or behaviors of objects do not occur in the whole database but rather in specific regions. Therefore, the focusing enables to ana- lyze object movement pattern in a given region. For the analysis of the tracking data often features (Section 3.3.3) are used to describe characteristics of the tra- jectories. However, these features are only meaningful if they are calculated within a region of interest where the specific behavior occurs. If the features are calculated for the whole dataset, given characteristics are averaged out due to the global context for the calculation. It is also possible to use a feature- based region of interest selection approach (see Chapter 4 for more details) to improve the objectivity and reproducibility. Several influencing factors such as the size of the ROI, the choice of given features as well as the noise level of the underlying problem class have a great impact on the result of region of interest selection with subsequent analysis. In the following, these influencing factors are evaluated systematically using derivatives of database TDB S6 (Sec- tion 2.4). The database TDB S6 D1 contains one undirected movement period of length 10 at time point 10 (Figure C.10A) whereas the database TDB S6 D2 contains two undirected movement periods of length 10 at time point 50 and

time point 100 (Figure C.10B). The effect of the choice of the correct features is depicted in Figure 3.19. The corresponding statistical significance of the two

(A)Feature: Ratio lengths

25 50 75 100 125 150 175

ROI Start Time

0.4 0.5 0.6 0.7 0.8 0.9

Feature Ratio Lengths

Group1 Group2

(B)Feature: Mean curvilinear speed

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ROI Start Time

5.5 6 6.5 7 7.5

Mean Curvilinear Speed

Group1 Group2

Figure 3.19:Choice of region of interest with predefined appropriate size using bench- mark TDB S6. The window size of the ROI is set to be 20 time points. There is no noise added to the benchmark (QA,N oise= 0). (A) Mean time series of the two groups within

the benchmark (colored in magenta and blue) for the feature ’ratio lengths’. (B) Mean time series of the two groups within the benchmark (colored in magenta and blue) for the features ’mean curvilinear speed’.

groups is listed in Table C.6. The feature describing the ratio of the effective and absolute displacement of the trajectories (Figure 3.19A) is generally well-suited to address such a characteristic and find significant differences within the ex- isting groups (Table C.6). However, the mean curvilinear speed, representing a poorly suitable feature to describe the existing undirected movement patterns, is not able to well separate the two existing groups (Figure 3.19B). In the case of correctly chosen features, the choice of the size of the ROI has an enormous effect. Therefore, Figure C.11 shows the same characteristics as in Figure 3.19 with the only difference of choosing the size of the ROI too big. This leads

to a vanishing of the time-specific differences between the two groups (Table C.7). To systematically evaluate the effect of the size of the ROI, the database TDB S6 D1with a single undirected movement period at time point 10 is used (Figure 3.20). Here, the size of the region of interest is successively incremented starting with a size of 5 time points and ending with 180 time points. For each size of the ROI, the well suited feature describing the ratio of effective and ab- solute length of the tracks is calculated (Figure 3.20). It can be observed, that the greater the size of the ROI, the smaller the differences of the two groups leading to a vanishing of the distinguishability (Table C.8). In general, the opti- mal size of the ROI is application-dependent and has to be adapted manually. When choosing the ROI too big or too small (Figure 3.20) the separability of different groups is vanishing.

25 50 75 100 125 150 175 0.4 0.6 0.8 Size of ROI Featur e Ratio Lengths Group1 Group2

Figure 3.20:Impact of the correct size of the region of interest using benchmark TDB S6. The size of the region of interest varies starting from 5 time points up to 190 time points. For the feature ’ratio length’ the mean time series for the two groups (magenta and blue) are displayed for the varying size of the ROI. There is no noise added to the benchmark (QA,N oise= 0).

The complexity of the problem class of the tracking database (Section 2.1) has also a great impact for the region of interest extraction result. Here, the increas- ing noise added to the databases is exemplarily used to show the effect of an increasing difficulty of the problem classes to the ROI analysis. Different noise levels (Figure C.7) are applied to the dataset TDB S6 D2. A subsequent extrac- tion of the feature describing the ratio of effective and absolute lengths of the tracks is applied to the sliding ROI with different start points. The character- istic curves for the two groups is displayed in Figure C.7. It can be observed that an increase of the noise leads to a decreasing distinguishability of the two

groups pointing out that the complexity of the problem class has an enormous effect on the analysis result in the way that the higher the higher the fragmenta- tion and the noise level, the worse the distinguishability of extracted groups.