Example: A Small Database

     
Figure 4.4: The initial images and landmark candidates.

As a concrete example, we will step through the tracking method over a series of three images, applying Algorithm 2.1 to each. The images used are shown in Figure 4.4 with their initial candidate landmarks superimposed as squares. At each step the landmarks under consideration will be depicted along with their matching prototypes in the database. As new prototypes are detected, they are added to the set of depicted prototypes.

1. The image closest to the centroid of the configuration space is selected as the bootstrap image. Hence we choose the image in Fig. 4.4(b), and initialise the set of tracked landmarks to the candidate landmarks in the image as shown in Figure 4.5(a).

       
   Figure 4.5: Tracked landmarks and eigenlandmarks built from the bootstrap image.
   

2. The principal components subspace of the prototypes is constructed (Figure 4.5(b)).
3. The remaining images are sorted on increasing distance from the centroid of the explored configuration space. In this particular example, the choice of which image comes first is arbitrary, since both images are equidistant from the centroid.
4. Algorithm 2.1 is applied to the candidate landmarks in Figure 4.4(a). The positions of some of the candidate landmarks are adjusted to obtain better matches (compare the resulting set of candidate landmarks in Figure 4.6(a) with the originals in Figure 4.4(a)), while others have no suitable match and hence become prototypes for new tracked landmarks. The updated set of prototypes is depicted in Figure 4.6(b).

       
   Figure: Results of adding Figure 4.4(a) to the database.
   

5. Since the set of prototypes changed with the last addition, the principal components subspace is recomputed (Figure 4.6(c)).
6. Algorithm 2.1 is applied once again to the candidate landmarks in Figure 4.4(c). Again, some of the candidates change positions, and others become new prototypes. A new subspace is also constructed (Figure 4.7).

        
   Figure: Results of adding Figure 4.4(c) to the database.
   

Figure 4.8(a) depicts the set of prototypes for all the tracked landmarks found for a wider sampling of the environment depicted in Figure 4.4. The images are collected at 20cm intervals over a 3.0m by 1.2m grid. The principal components of the subspace are depicted in Figure 4.8(b).

    
Figure: The final set of a) prototypes and b) principal components for a traversal of the environment depicted in part in Figure 4.4.

Once tracking has been performed, a minor filtering operation is conducted on the tracked landmarks in order to remove outlier candidates and tracked landmarks. A tracked landmark is considered to be an outlier if very few candidate landmarks were matched to its prototype. Typically, we reject a tracked landmark if it has fewer than five matched candidates. Determining whether a particular candidate landmark is an outlier (in the context of the tracked landmark to which it matched) is less straightforward. We will tend to favour tracked landmarks which are ``well-behaved''. Ideally, this implies that the subspace encodings and image positions of the candidates in a tracked landmark behave smoothly as a function of camera pose. Assuming smoothness, however, implies that the best method for filtering the candidates is to fit them to a surface, which can be extremely problematic in the presence of outliers. Instead, we choose to model the distribution of candidates as a normal distribution and remove candidates which lie outside a two standard deviation envelope in the space defined by the subspace encodings and further augmented by the image position. Furthermore, we will later present a method for measuring a priori, the goodness of a particular tracked landmark, and which will help reduce any ill effects of missing outliers, or mistakenly removing good candidates.

In this Chapter, we developed a method for recognising and tracking landmarks over the configuration space. The results in Figure 4.3 suggest that the method works quite well. Chapter 5 will present the central contribution of this thesis - a method for estimating camera pose given a set of tracked landmarks and the image currently in view.