Results

The MOGA applied to the dinosaur data of Figure  7 consisted of 10 sets of 58 individuals and was run for 100 generations. Figure  9(a) shows a distribution of match scores for an initial and final population of PGHs. These data were generated by calculating the match scores between all histograms having a similar type and then binning the results. The data distribution for the initial population shown in Figure  9(a) has mean = 0.415 and variance = 0.013. Similarly, the rightmost histogram shown in Figure  9(a) shows a typical distribution of match scores for a final population, this distribution has mean = 0.275 and variance = 0.015. The first plot of Figure  10 shows how for each of the 10 populations, the histogram representation has become more distinct as is evident by the reduced means of the final populations.

The MOGA applied to the data of Figure  8 consisted of 10 populations containing 107 lines. An example initial and final histogram is shown in Figure  9(b) . As for the dinosaur data, the second plot of Figure  10 shows how for each of the 10 populations the histogram representation has become more distinct by the reduced means and greater compactness of the final populations.

     
Figure 9: Example Initial and Final Distributions

By comparing the means of the initial and final populations shown in Figure  10 we can see that the effect of the MOGA is to produce histograms that have, on average, a lower match score across their associated populations, confirmed by the lower means of the final populations. This is due to the first objective function optimising on histogram distinctiveness, and thus the MOGA has produced sets of PGHs containing less redundant information than the initial populations. It can also be seen by comparing the initial and final population distributions of Figure  9(a) and Figure  9(b) , that the MOGA has reduced the number of PGHs having high match scores, another indication of how the amount of redundancy in the representation has been reduced and the distinctiveness increased. The overall effect of the MOGA is that it produces sets of PGHs, (consisting of individuals with associated pairwise parameters), that represent the line data more efficiently.

Thus the three separate objective criteria are jointly optimised as required. Also, an examination of the histograms (line fragments) selected for inclusion in the database shows that:

• histograms are selected from those with the lowest quantity of noise, (as these are the most reliable and on average give the best match scores).
• histograms are constructed from the most complete versions of objects within the variant sets (as these are the most discriminable).
• histograms are selected with the requisite degree of invariance (as these are the representations which have the best recognition repeatability). For example, using mirror symmetric PGHs for objects with mirror symmetry.