*4.3. Feature-Tracking Efficiency Comparison*

The efficiency of WF-MHT-BP is compared with PDAT, HTRT, and EKLT since they have different numbers of initialized features, which is meaningful for real applications, as lower time complexity will lead to more abundant time for frame processing. Since different methods have a different number of tracked features, the efficiency is quantified by the consumed time per tracked feature T*PerFea*, which is calculated as:

$$T\_{PerFca} = \frac{T\_{PerFarm}}{N\_{NumFca}} \tag{10}$$

where *TPerFrm* is the consumed time on each frame, and *NNumFea* is the number of tracked features on each frame. Note that all the visualization parts of all algorithms are closed to ensure accurate consumed-time statistics.

As shown in Table 3, HTRT has the highest computational complexity, which reaches 1062 ms for tracking one feature in "dynamic\_rotation" scenario, which is not practical for real-time high-level tasks. EKLT still needs tens of milliseconds to track one feature between two intensity images. PDAT consumes less time to track one feature point than EKLT, but in the scenario of "dynamic\_translation" and "outdoors\_walking", it reaches 56 ms and 52 ms, respectively. WF-MHT-BP achieves the best efficiency among the four featuretracking methods, which generally improves the efficiency by approximately three orders of magnitude compared with PDAT and EKLT and four orders compared with HTRT.

**Table 3.** The consumed time per tracked features of PDAT/HTRT/EKLT/WF-MHT-BP methods (unit: ms).


The main reason for high computational complexities of PDAT and HTRT is that the registration between two patches is done one by one. Besides, EM (Expectation Maximization) and ICP algorithms used in these methods are not suitable for real-time processing. Another reason for the high time consumption of HTRT is that the related event information to be processed needs to be searched from external memory for every event frame. The time consumption is at approximately the same level with EKLT at the beginning. As feature tracking continues processing, the time consumption becomes larger, resulting in the larger overall time consumption.

For EKLT algorithm, it involves the complex optimization of object function for tracking error and also does not have a batch-processing mechanism. Therefore, their consumed time is much larger than WF-MHT-BP. The efficiency problem is optimized in WF-MHT-BP by the batch-processing mechanism and simple loose integration with KLT tracking solution, which enables the lowest computational complexity of WF-MHT-BP.
