CHAPTER ONE: Introduction                                                                              1 

1.1      Background to the Study                                                                            1 

1.2      Statement of the Problem                                                                           9 

1.3      Objective of the Study                                                                                9 

1.4      Organisation of the Project                                                                         10 

CHAPTER TWO: Literature Review                                                                    11 

CHAPTER THREE: Methodology                                                                        23 

3.1      Artificial Neural Network                                                                           23 

3.2      Description of the Method                                                                          24 

3.3      Computation of the Gradient                                                                      26 

3.4      Solution of Partial Differential Equations                                                    29 

CHAPTER FOUR: Relating Image Observables to Object Models                              37 

4.1      Principle of the Method                                                                              37 

4.2      Notations                                                                                                   38 

4.3      Range Data                                                                                                39 

CHAPTER FIVE: Discussion and Future Work                                                     61 

References                                                                                                           63 

Artificial intelligence is a branch of computer science that involved in the research, design, and application of intelligent computer. Traditional methods for modeling and optimizing complex structure systems require huge amounts of computing resources, and artificial-intelligence-based solutions can often provide valuable alternatives for efficiently solving problems. The study was carried out to adopt the method of numerical analysis for artificial intelligence to compute. 

          An approach was presented for explicitly relating image observables to models of curved three-dimensional objects. This relationship was used for object recognition and positioning. Object models consist of collections of parametric surface patches. The image observables considered were raw range data, surface normal and Gaussian curvature, raw image contours, contour orientation and curvature, raw image intensity, and intensity gradient. Elimination theory was used to provide a method for constructing an implicit equation that relates these observables to the three-dimensional position and orientation of object models. Determining the unknown pose parameters was reduced to a fitting problem between the implicit equation and the observed data points.          The proposed approach has been implemented and successfully tested on real images. Also, an algorithm for recognizing solids of revolution in raw contour data was presented. Once the pose of candidate object models was determined, recognition was achieved by computing the distance between the actual data points and the surface defined by the observables' equation. 

          Further studies can investigate strategies suited to the positioning approach, in the same way as interpretation trees have been used in conjunction with so-called “rigidity constraints”.