# Fast and Robust Object Tracking Using Tracking Failure Detection in Kernelized Correlation Filter
## 3 The Proposed Method
### Tracking Failure Prediction by Analyzing Correlation Values  
KCF-based trackers calculate correlation values between target and reference using cyclic shift within the pre-specified search window. A correlation value from each cyclic shift corresponds to a cell in the response map. Position of each cell in the response map means the vertical and horizontal shifts. Trackers estimate position of the target by finding the position of a cell with the highest correlation value in the response map and determining the corresponding coordinate in the search window. Most trackers can successfully track an object if sequences does not include challenging scenes, where there exists a single peak value. As shown in Figure 2a, trackers trace the coordinates of the peak every frame under an ideal tracking condition. On the other hand, under a challenging circumstance, the peak value relatively decreases and its neighboring values increase as shown in Figure 2b. If a scene contains, for example, a severely blurred target, there is not a single distinct peak correlation value. Since a peak value does not occur at the position of real target in challenging sequences, tracking failure can be predicted by analyzing peak value and neighbor values of the peak. Let \(c_{t(i,j)}\), for \(i=0,1,2...n-1,\ j=0,1,2...m-1\), be the correlation value of the response map of size \(m\times n\) in \(t\)th frame. Then, average correlation value of \(5\times 5\) neighboring region around \((p,q)\) is expressed as  
\[N_{t(p,q)}=\frac{1}{24}((\sum_{i=p-2}^{p+2}\sum_{j=q-2}^{q+2}c_{t(i,j)})-c_{t( p,q)}) \tag{1}\]  
Since the peak coordinate is \((\bar{p},\bar{q})\) in the response map, the peak and average correlation values can be expressed as \(c_{t(p,q)}\) and \(N_{t(p,q)}\), respectively. In Equation (1), average value of \(c_{t(p,q)}\) and \(N_{t(p,q)}\) over recent \(\sigma\) frames can be derived as Equations (2) and (3). \[P_{\text{aver}}=\frac{1}{\sigma}\sum_{k=t-\sigma+1}^{t}c_{k(\bar{p},\bar{q})} \tag{2}\]  
Figure 1: Block diagram of the proposed method. Figure 2: (a) Common form of correlation distribution from successful tracking sequences. (b) An example of correlation distribution from tracking sequences with challenging scenes. \[N_{\text{aver}}=\frac{1}{\sigma}\sum_{k=t-\sigma+1}^{t}N_{k(p,q)} \tag{3}\]  
Tracking failure can be predicted by analyzing \(P_{\text{aver}}\) and \(N_{\text{aver}}\) over frames. In Figure 3, Peak and Neighbor respectively denote \(c_{t(p,q)}\) and \(N_{\text{aver}}\). Figure 3a shows \(c_{t(p,q)}\) and \(N_{\text{aver}}\) over frames for successful tracking cases, where \(c_{t(p,q)}\) is relatively high and sufficiently distinct from \(N_{\text{aver}}\). On the other hand, Figure 3b shows the failure cases, where the \(c_{t(p,q)}\) significantly dropped, and the difference from \(N_{\text{aver}}\) becomes indistinct with some oscillations because of the severe blur. Furthermore, if the peak occurs at a wrong position, the tracking process totally fails. Figure 3: Comparison of peak values and average values of neighbor area around the peak. (**a**) Correlation developments with successfully tracked targets. (**b**) Correlation developments in sequences including tracking failures. To determine when tracking failure occurs, we use a conditional expression such as \(\frac{c_{t(p,d)}}{P_{\text{aver}}}\) and \(\frac{c_{t(p,d)}}{N_{\text{aver}}}\), then a conditional expression to decide tracking failure can be defined as  
\[\left(\frac{c_{t(p,d)}}{P_{\text{aver}}}<T_{1}\right)\text{ or }\left(\frac{c_{t(p,d)}}{N_{\text{aver}}}<T_{2}\right) \tag{4}\]  
where \(T_{1}\) and \(T_{2}\) denote thresholds. In (4), we determine the optimal \(T_{1}\) as  
\[T_{1}=\alpha+\beta\cdot\sigma \tag{5}\]  
where, \(\sigma\) represents the standard deviation of the peak, and \(\alpha\) and \(\beta\) be a pair of appropriately chosen constants to increase the accuracy of tracking failure detection.