Estimation of Homography Dynamics on the Special Linear Group - Visual Servoing via Advanced Numerical Methods - page 141

h 11 h 12 h 13

h 21 h 22 h 23

h 31 h 32 h 33

Fig. 8.6 Corkes sequence. Each plot represents an element of the (3 × 3) homography matrix.
Plain line: the measured homography matrix H . Dashed line: the observed homography H

extracted from the sequence Corkes. The first image in the figure shows a rectangle
containing the area of interest that must be tracked in all the images of the video
sequence. For each image of the sequence, the output of the ESM visual tracking
algorithm is the homography that encodes the transformation of each pixels of the
rectangular area from the current to the first image.
The measured homographies are the input of the proposed nonlinear observer. In
this experiment the gains were k H = 5and k A = 1. The filtering effect of the observer
on the estimated homography are visible in Figure 8.6.
In this experiment with real data, the velocity A is unknown and not constant.
Nevertheless, the observer provides a smoothed estimation of the homography ve-
locity, as illustrated on Figure 8.7.