Chapter Conclusions

Table 2.4: Comparison results for the Bull image (bold indicates best result).

Error method SAD NCC BTO GP

Mean of Abs. Differences 1.785469 1.378297 2.030898 1.330506

Bad Pixel Percentage 1.186709 0.703539 1.422414 0.675807

50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (a) SAD 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (b) NCC 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (c) BTO 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (d) GP 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350

(e) Ground Truth

Figure 2.11: Disparity maps comparison for the Bull image.

method achieves the best performance. Figures 2-6 present a compar- ative visual analysis of the best GP individual and the three standard methods, compared with the ground truth. Visually, we can detect the improvement provided by the GP operator K over the standard meth- ods.

2.6 Chapter Conclusions

In this chapter a background about GP is presented, focusing on the fitness function as well as in the search spaces. Here, is highlighted that

Table 2.5: Comparison results for the Poster image (bold indicates best result).

Error method SAD NCC BTO GP

Mean of Abs. Differences 2.432111 1.988050 3.010154 1.945446

Bad Pixel Percentage 1.57552 1.218279 1.985391 1.202187

50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (a) SAD 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (b) NCC 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (c) BTO 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (d) GP 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350

(e) Ground Truth

Figure 2.12: Disparity maps comparison for the Poster image. we can use a different approach to implement a fitness function. The traditional approach is to reward solutions which are closer to the ob- jective. Different approaches to the customary objective-based fitness function has been proposed, one interesting approach will be presented in the Chapter 4.

Furthermore, this chapter studies the problem of dense stereo corre- spondence using GP. The proposed approach is to combine three well- known similarity measures and derive a composed estimation of the disparity map for a stereo image pair. This task is posed a search and optimization problem and solved with GP. The terminal elements for the GP search is composed by the cost volumes produced by the three

2.6 chapter conclusions

Table 2.6: Comparison results for the Sawtooth image (bold indicates best result).

Error method SAD NCC BTO GP

Mean of Abs. Differences 1.532218 1.433264 1.727435 1.374315

Bad Pixel Percentage 1.073662 0.859555 1.169753 1.202187

50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (a) SAD 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (b) NCC 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (c) BTO 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (d) GP 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350

(e) Ground Truth

Figure 2.13: Disparity maps comparison for the Sawtooth image.

correspondence methods; SAD, NCC, and BTO. Fitness is based on the error between the estimated disparity map and the ground truth dis- parity.

Experimental results for this case study show that the evolved GP operator achieves better performance that the standard methods based on well-known benchmark problems. These results are validated with a set of test cases and an additional performance metric. While these results are an encouraging first step, further work is considering follow- ing this topic. For instance, we can add other standard approaches as input to the GP search, such as non-parametric correspondence meth- ods. Moreover, we can use the raw disparity map generated by the GP

Table 2.7: Comparison results for the Venus image (bold indicates best result).

Error method SAD NCC BTO GP

Mean of Abs. Differences 2.281053 1.916733 2.704778 1.880739

Bad Pixel Percentage 1.617716 1.285286 1.804815 1.267094

. 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (a) SAD 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (b) NCC 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (c) BTO 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 (d) GP 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350

(e) Ground Truth

Figure 2.14: Disparity maps comparison for the Venus image.

operators as raw input for global optimization methods which could allow us to define a higher level fitness evaluation.

3

Deception

a b s t r a c t — Since the very introduction of genetic algorithms (GAs), it was noted by Goldberg that there is a certain kind of prob- lem which deceives a search process. Rewarding solutions closer to the objective in these deceptive problems, the search will be lead away from the global optimum, getting trapped into regions of local optima. The notion of deception is related with problem complexity. The more complex the problem is, the higher the possibilities that it is a decep- tive problem. Most deceptive problems found in the evolutionary com- putation literature are toy problems, particularly applied on binary representations, and more recently in evolutionary robotics. In this chapter, our intent is to design a set of deceptive classification prob- lems which hopefully could serve as benchmark to test evolutionary or search-based classification strategies.

3.1 Introduction

EAs in general have shown good performance when solving com- plex problems, but a central issue is the characterization of problems that are difficult to solve, particularly by GAs. A noteworthy attempt was made by (Goldberg, 1989) to explain the ability of GAs in fre- quently succeeding at finding good solutions; what is called the build-

ing block hypothesis (BBH). In this hypothesis Goldberg states that GAs can identify segments (blocks) of the optimal solution contained in the current solution. Furthermore, Goldberg hypothesises that GAs use these blocks to generate new and better solutions by recombining them or by mutating them, which at the end (mostly) build-up the complete optimal solution.

There are a wide range of benchmark problems to test the per- formance of EAs, which can be ranked from easy to hard problems. Among the efforts to characterize GA-hard problems some have fo- cused particularly on the notion of deception. Since the introduction of the GAs, many deceptive problems have been proposed for binary- coded GAs.

More recently, (Lehman and Stanley, 2008) have proposed several deceptive navigation robotic tasks. But, to the best of our knowledge, there are not deceptive benchmark problems for pattern recognition, particularly deceptive classification problems.

This work introduces a first attempt to design a deceptive classi- fication problem that can be used for benchmarking. The following sections address the notion of deception.

3.2 Deception in the Artificial Evolution

Finding the factors that affect the performance of GAs to solve opti- mization problems, has been a major interest in the theoretical commu- nity (Jones and Forrest, 1995). In general, the performance is measured in terms of their ability to find the closest solution to the global opti- mum of a given problem. So, according with the BBH, if a GA finds the global optimum, particularly on problems with a binary representation, it is because in fact it correctly identified the correct building blocks for the problem, classifying those problems as easy-GA problems. On the other hand, it is a hard-GA problem if a GA fails to find the global opti- mum for that particular problem and this means it did not identify the correct building blocks.