Radial Basis Function Network Robust Learning Algorithms in Computer Vision Applications

This thesis introduces new learning algorithms for Radial Basis Function (RBF) networks. RBF networks is a feed-forward two-layer neural network used for functional approximation or pattern classification applications. The proposed training algorithms are based on robust statistics. Their theoretical performance has been assessed and compared with that of classical algorithms for training RBF networks. The applications of RBF networks described in this thesis consist of simultaneously modeling moving object segmentation and optical flow estimation in image sequences and 3-D image modeling and segmentation. A Bayesian classifier model is used for the representation of the image sequence and 3-D images. This employs an energy based description of the probability functions involved. The energy functions are represented by RBF networks whose inputs are various features drawn from the images and whose outputs are objects. The hidden units embed kernel functions. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. In this thesis the hidden unit activation functions are considered Gaussians while the output unit activation functions are Perceptron-like. The first chapter describes the state-of-the art in the RBF networks. A short history of the RBF networks as well as their relation to other pattern recognition techniques are presented in this chapter. Various functions used as hidden unit activation functions, weight interpretation and various properties of the RBF networks are described. Different training algorithms employed for training RBF networks are presented. Many and diverse applications of RBF Networks have been considered in the literature. The main application fields have been speech processing, telecommunication systems, image processing, time-series modeling and prediction, computer vision, computer graphics, etc. In order to find the parameters of an RBF neural network in chapter 2 we take into consideration two different statistical approaches. The first approach uses classical statistical estimators in the learning stage and it is based on the second order statistics extension for the learning vector quantization algorithm. After the presentation of this approach, we introduce the Median Radial Basis Function (MRBF) algorithm based on the robust estimation of the hidden unit parameters. Marginal median and median of the absolute deviations from the median (MAD) estimators are employed for estimating the basis function parameters. Both algorithms are implemented on-line. The theoretical performance is evaluated for an one-dimensional model consisting of the analysis of the expected bias for the parameters in the case of mixture of Gaussians distributions. A fast implementation for the proposed algorithm based on histogram modeling is presented in this chapter. The algorithms for training the networks are applied in two-dimensional distribution estimation problems and for optical flow segmentation from a real image sequence. Various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences. In chapter 3 the moving scene is decomposed into different regions with respect to their motion, by means of a pattern recognition scheme. The inputs of the proposed scheme are the feature vectors representing still image and motion information. Each class corresponds to a moving object. The classifier employed is the Median Radial Basis Function (MRBF) neural network which has been introduced in chapter2. An error criterion function derived from the probability estimation theory and expressed as a function of the moving scene model is used as cost function. Each basis function is activated by a certain image region. The image regions associated with the basis functions are merged by the output units in order to identify moving objects. A prediction model for moving object velocity and location estimation derived from Bayesian theory is provided in chapter 4. The optical flow of a certain moving object depends on the history of its previous values. The joint optical flow estimation and moving object segmentation algorithm described in chapter 3 is used for the initialization of the tracking algorithm. The segmentation of the moving objects is determined by appropriately classifying the unlabeled regions. Segmentation and optical flow tracking is used in order to predict future frames. In chapter 5 a pattern classification based approach for simultaneous 3-D object modeling and segmentation in image volumes is proposed. The 3-D objects are described as a set of overlapping ellipsoids. The segmentation relies on the geometrical model and graylevel statistics. The characteristic parameters of the ellipsoids and of the graylevel statistics are embedded in a Radial Basis Function (RBF) network and they are found by means of unsupervised training. A new robust training algorithm for RBF networks based on α-trimmed Mean statistics is employed in this chapter. The extension of the Hough Transform algorithm in the 3-D space by employing spherical coordinate system is used for ellipsoidal center estimation. The performance of the proposed algorithm when estimating the parameters of ideal ellipsoids and for segmenting a stack of microscopy images is anlysed.