Execution and Profiling: computational performance

A profiling implementation showed that both approaches could achieve real-time performance, with results obtained shown on TABLE 4.6. This table presents the average

computation times required per frame for several processes: the raw DI-D Monocular SLAM, the same DI-D approach using a batch validation technique (without the cost of the technique itself), and the penalization of the JCBB and the HOHCT. The results were obtained in an average powered laptop, running on a Linux system (Ubuntu Lucid Lynx), using OpenCV 2.1 as support library.

TABLE 4.6:AVERAGE TIMING OBTAINED BY THE DI-D ALONE, WITH BATCH VALIDATION, AND BY THE JCBB AND HOHCT PROCESSES

Process measured average time (ms) σ

DI-D MonoSLAMa

37.98 7.12

DI-D MonoSLAM with validationb

38.43 6.93

JCBBc

24.58 16.35

HOHCTd

2.36 4.37

a_{For an average sequence over the aggregated 20 indoor sequences.} b_{HOHCT/JCBB searches due optimistic hypothesis failing the SMD test.} c,d _{JCBB/HOHCT penalization added to DI-D MonoSLAM with validation (a).}

It is noticeable that the Delayed I-D SLAM itself is a computationally expensive procedure, requiring by itself 37.98ms per frame on average. This statistic grows with the introduction of a batch validation technique, as they introduce a slight penalization in the form of computational effort spent in map management and state augmentation (removing the non- compliant landmarks and searching for new ones). The JCBB and HOHCT produce each one a noticeable penalization by themselves, with the penalization for the JCBB being an order of magnitude greater. This difference is lower than what TABLE 4.3 would predict, but

the number of search does not account for the reduction to quadratic cost of the iterative matrix inversion required, which cannot be implemented into the HOHCT method. This optimization hugely reduces the cost of the SMD tests in the JCBB, partly compensating for the wider hypotheses space. Also, this means that the cost for each test is cubic (n3 _w.r.t.

the number of landmarks) for the HOHCT, and the advantage comes from the lower number of SMD tests. Given the cumulative nature of the cost for HOHCT (in SMD tests as in 4.6.2.1) seen in FIGURE 4.17, it is clear that the advantage of the HOHCT is clearly

local and depends intrinsically on the quality of the features initialization process and the robustness of the data association process.

4.7 Conclusions

The data association problem has been studied in this chapter, starting with a theoretical overview of the main procedures, until dealing with the actual problems found in the monocular DI-D SLAM. The main aspects dealt with were on one side, the correlation based search, and the suitability of the available operators, and on the other side, the need of introducing a data association validation procedure. This would lead to the development of the HOHCT algorithm, which would constitute one of the main contributions of this dissertation.

The testing of the different matching operators was performed in order to evaluate with some objective metrics not subjected to sampling bias or unknown effects produced by

probing them inside the monocular SLAM technique. The robustness of the delayed I-D monocular SLAM is known, and would have impacted any study, so the tests were performed independently. As many of the literature (commented in section 4.3.2) already discussed the operators performance and efficiency against lighting variations, our tests focused on the disturbances that were expected to have greater impact: the different kinds of noises expected to be introduced by the utilization of inexpensive sensors; and the motion blur, typically aggravated by the CMOS technology. The tests modelled said disturbances over a set of images, from insignificant levels to those at the limit of what could be realistically expected, and tested each operator. As it was expected, the cross- correlation based operators outperformed those based on aggregation/squared aggregation. To conclude, the chosen operator was ZNCC, which presented the robustness to motion blur of the cross-correlation technique, with the invariance to contrast variation from the normalization and to illumination due the zero-mean modification.

As it is discussed and probed in section 4.5.1.2, even a robust SLAM technique like the DI- D monocular SLAM can benefit from the introduction of a validation method. The main characteristic of the DI-D monocular SLAM (discussed in Chapter 3) is that landmarks are only introduced into the EKF once the depth estimation is accurate enough, finding this estimation through the parallax effect. This introduces a slight computational burden on the algorithm, compensated by the fact that as the information about landmarks present at the map and filter is more accurate, the filter can proceed with fewer landmarks mapped than in the undelayed approach. Although the landmarks mapped are highly precise, it is still needed a data association gating technique to treat with multiple disruptions that may arise from incorrect or inconsistent matching obtained through active search.

The computational issues produced by the JCBB introduction (the golden rule in data association for a decade) in the early tests motivated the development of the proposed HOHCT, the Highest Order Hypothesis Compatibility Test. This techniques is largely based in the Squared Mahalanobis Distance test, just like the JCBB, but optimized the search to prioritize hypotheses based on the order of the solution.

Both the effectiveness and the efficiency of the HOHCT have been validated theoretically and experimentally, including indoor and outdoor experiments. These experiments results show how the introduction of the batch validation based on joint compatibility improves the technique resilience to erroneous data association and false features or landmarks, produced by difficult illumination and feature detection errors. At the same time, the HOHCT costs have been studied and compared to that of JCBB. While having worst case scenario of exponential cost, just like the JCBB, the HOHCT has been probed to tend most of the time to the linear, quadratic and cubic cases. This tendency to linearity of cost has been probed experimentally, compiling statistics over tens of sequences. It is worth noting that, as it is discussed in sections 4.6.2.1 and 4.6.2.3, the structure of the JCBB enables using matrix inversion optimization, while HOHCT algorithm makes this optimization much more

complex to apply, with greater memory requirements. In any case, the HOHCT clearly outperforms JCBB in the context of the DI-D monocular SLAM by over an order of magnitude in the average case.

Equation Chapter 5 Section 1

Part III

Collaborative sensing for