## 4 Experimental Results
### Computational Complexity  
After evaluating the proposed AMF-MSPF on several challenging video datasets, we obtained improved results in term of robustness and accuracy. However, the MSPF hybrid methodology implicitly has an additional cost of incorporating the MS optimization into the already complex PF algorithm. One innovation of the proposed research is the simplification of the MS optimization. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Constraint/Methods** & [24] & [27] & **Proposed Method** \\ \hline Full Occlusion & ✓ & ✓ & ✓ \\ Clutter Background & ✗ & ✓ & ✓ \\ Intensity Change & ✗ & ✗ & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of various trackers under challenging constraint. Figure 5: PETS 2007 sequence: Crowd. The simplification comes through an observation, that only a fraction of samples was required by the MS optimization procedure. The computational efficiency of the proposed MS was evaluated on a sequence extracted from the Browse4 dataset. As can be seen in Figure 6, the error introduced, due to dropping more than 75% of the samples, is negligible. And our simplified MS is able to track the object successfully in real-time, even under a Matlab implementation. This has led to a huge computational reduction in the MS method without significantly compromising its accuracy. This as a consequence saves resources for feature ranking module. Thereby, the proposed AMF-MSPF framework implements the feature ranking on top of the MSPF methodology without aggravating its computational complexity. The complexity of proposed framework is considerably reduced as compared to TSHT and PFKBOT because in those implementations, MS takes into account all the samples of object window. The AMF-MSPF framework can process 10-15 frames per second, which is perceived by humans, while none of the reference methods are able to run in real-time. Let us derive the overall computational cost of the proposed AMF-MSPF framework. Let \(I_{ter}\) be the total number of iteration for each MS procedure (in our case \(I_{ter}=5\)), \(T_{p\_gen\_wet}\) be the execution time required for sample generation and their associated weights, \(T_{re-sampling}\), \(T_{ms}\), and \(T_{mk}\) be the execution times for the resampling, MS procedure and ranking module respectively. Then the execution time of the AMF-MSPF framework is given in Equation (29):  
\[T_{Amf-mspf}=\left[T_{p\_gen\_wet}+T_{ms}+T_{re-sampling}+T_{mk}\right] \tag{30}\]  
Figure 6: A sequence from the Browse4 dataset: (top to bottom, left to right) (**a**) Centre of the tracked object using full range vs. fraction of pixels; (**b**) Visual tracked sequence; (**c**) Score obtained taking into account full range vs. a fraction of pixels; (**d**) Error for selecting only a fraction of pixels. Although MS is initialized in multiple features over all particles, however down sampling the number of pixels reduces its execution time by an order of magnitude. Thus with the reduced pixels, \(N_{h}\), the complexity of our proposed MS is \(O(m*N_{\mathsf{r}}*N_{h})\) which has no significant impact on Equation (29). This saves enormous computational power that is utilized by the ranking module. Since the MS optimization is applied multiple times to every particle until convergence, it moves the particles to new locations where it no longer conforms to the posterior distribution. This is what is known as the degeneracy problem in which a small number of particles dominate the weight race and therefore the estimates are heavily influenced by them. Consequently, the re-sampling stage is introduced to mitigate from the degeneracy problem by replicating particles with larger weights and removing the particles with negligible ones. This, however, constraints the system that re-sampling step be carried out after the particle weighting and normalization steps and that makes it a bottleneck in parallelizing the PF computations. The complexity of the re-sampling module is also equal to the particle generation and weighting step i.e., \(O(N_{\mathsf{s}})\).