Related Works

Neural fuzzy networks are gaining research interest and they have been widely used in fields of pattern recognition, control problems, image processing, and diagnosis. The major benefit of neural fuzzy network is the integration of computation power from neural networks and human-like reasoning from fuzzy systems. Since neural fuzzy networks can bring such benefit, how to train neural fuzzy networks has become a critical issue.

The back-propagation (BP) algorithm [3] is a typical method for training neural fuzzy networks. Although the use of steepest descent technique in BP learning can reach the local minimal much quickly, the global minimal may be never found. Thus, evolutionary algorithms are better ones than BP due to their parallel search techniques. Recently, evolutionary fuzzy models have become a popular research field [16]-[24]. The evolutionary fuzzy model is a learning process using evolutionary learning procedures to generate a fuzzy system automatically. Among these evolutionary fuzzy models, the well-known algorithms are the genetic fuzzy models, which are augmented by incorporating genetic algorithms (GAs).

There are several genetic fuzzy models have been proposed [16]-[18]. In [16], Karr adopted GAs to adjust membership functions for designing a fuzzy controller where its fuzzy rule set must be predetermined. Lin and Jou [17] applied GAs to fuzzy reinforcement learning to control a magnetic bearing system. In [18], Juang et al. proposed symbiotic evolution based genetic reinforcement learning for designing fuzzy controllers. In their work, the symbiotic-evolution-based fuzzy controller required fewer trail and less CPU time than the traditional GA-based fuzzy controller.

Although the genetic fuzzy models can be used to search for the optimal solution, they may have some limitations, such as the same lengths of chromosomes, predefined parameters, and so on. Thus, there are several improved evolutionary algorithms [19]-[22] to take into account these limitations. In [19], Carse et al. used the fusion of genetic algorithms and fuzzy

logic to evolve variable length fuzzy rule-sets. In [20], Bandyopadhyay et al. proposed variable-length genetic algorithm (VGA) to encode different length of chromosomes in the same population. Tang [21] proposed a hierarchical genetic algorithm to enable the optimization of designing a fuzzy system for particular applications. Juang [22] proposed a combination of online clustering and Q-value based GA learning for fuzzy system design (CQGAF) to generate fuzzy rules automatically and free parameters in a fuzzy system. In addition, Gomez and Schmidhuber [14] proposed enforced subpopulations (ESP) to provide several subpopulations to evaluate each partial solution. The subpopulations that are used to evaluate the solution locally can obtain better performance than those methods that only use one population for evaluating the solution. In [15], Hsu and Lin proposed a multi-groups cooperation based symbiotic evolution (MGCSE) to train a TSK-type neuro-fuzzy network (TNFN). They develop a novel symbiotic evolution to let each sub population can cooperate to generate better offspring.

In spite of the above evolutionary learning algorithms improving genetic fuzzy models, these algorithms may conduct one or more of the following problems: (1) the random group selection of fuzzy rules, (2) low convergence rate as the problem becomes complex, and (3) potential fuzzy rules combinations are lost.

Recently, hierarchical enforced sub-populations (HESP) [23] provided a hierarchical evolutionary for preserving the potential neuron combinations. In their work, in spite of keeping useful networks, HESP still suffer from: the lengths of chromosomes must be the

the number of fuzzy rules automatically.

In addition, to consider 2D image alignment application, the problem of precise image alignment has been well-studied in several fields. In [30], Liu et al. point out that image alignment techniques are broadly classified as feature-based[31] and [32] and area-based matching approaches[33-35]. Amintoosi et al. pointed out that area-based methods produce better results than results with low signal-to-noise ratio (SNR) from feature-based methods.

Moreover, Zitova and Flusser indicated[39] that area-based methods are preferably applied to less detailed images. In this study, we assume that our proposed image alignment system is developed for industrial inspection tasks such that the captured images usually have less detail.

Thus area-based methods that adopt global descriptors are recommended in this paper.

In recent years, the neural network-based image alignment utilizing global features have been a relatively new research subject[40-44]. In [40-43], the alignment scheme is to estimate the affine parameters by a feedforward neural network (FNN). Although FNN is helpful to improve the alignment efficiency, such methods must take a large number of iterations to minimize the error function and several training attempts are needed to provide the robust FNN. In addition to FNN-based methods, Sarnel et al.[44] used a radial basis function neural network (RBFNN) to align images. According to their results, the training time of a RBFNN has been reduced, and the alignment accuracy and robustness against noise are better than those of FNN-based methods. However, a major drawback of the existing neural network-based methods is the difficulty in applying to align images on a large range of affine transformation. The reason is that a large range of affine parameters would lead to a large amount of training data such that the mapping surface becomes more complex and applying one-stage neural network to estimate a large range of affine parameters accurately is almost impossible. In this dissertation, a scheme of multi-stage neural network is proposed to overcome the problem produced by the one-stage neural network. The notion of this approach is to divide a large size of the network into several small networks, aiming to gradually reduce

the image alignment error and finally obtain the desired accuracy. Such phenomenon can be considered a coarse-to-fine alignment of the sensed image with the reference image.

Regarding the 3D image alignment application, the problem of 3D image alignment has been implemented by several methods [45-50]. Among them, a coarse-to-fine technique is a useful way for performing 3D image alignment [45] and [46]. Coarse alignment provides an approximate transformation for aligning two images. Such alignment must be efficient and accurate. Fine alignment uses the initial gauss of a transformation given by a coarse alignment as a starting point to iteratively minimize the distance between the input and the destination images. Specifically, in consideration of coarse image alignment, common methods [45] and [46] utilized principal component analysis (PCA) [51] for coarsely aligning two images due to its high-speed performance. However, PCA cannot ensure that the laser scanned point clouds have the same orientation of principal axes as the reference model. This phenomenon would cause a high alignment error in the coarse alignment phase. In consideration of fine alignment method, iterative closest point (ICP) [52] is a typical method to iteratively calculate the rigid-body transformation to minimize the cost function. Although ICP can provide highly accurate 3D image alignment, its heavy computational cost in searching corresponding points has been criticized by many researchers [45, 46, 53-55]. To this end, this dissertation intends to propose a coarse-to-fine 3D image alignment scheme to improve the drawback generated by PCA and ICP.