||Study on Non-Uniform Rational B-Splines Neural Networks and their Applications
||Department of Electrical Engineering
Non-uniform B-splines (NURBS)
digital image process
traveling wave ultrasonic motor (TWUSM)
An in-depth study on the Non-Uniform B-splines (NURBS) neural networks and their applications is conducted in this dissertation. Firstly, based on the concept of the NURBS curve, the NURBS Curve Neural Network (NURBSCNN) is proposed. Since the characteristic curve that describes the relationship between the input voltage and the output speed for the traveling wave ultrasonic motor (TWUSM) is highly complex and nonlinear, the proposed NURBSCNN is applied to implement the feedforward compensator and speed controller for the TWUSM. Secondly, exploiting the idea of NURBS surface, the NURBS Surface Neural Network (NURBSSNN) is proposed. Since a digital image can be represented by a NURBS surface, the proposed NURBSSNN is employed to cope with the image compression and image restoration problems in this dissertation. Both the proposed NURBSCNN and NURBSSNN belong to the category of feedforward neural networks. Compared with other commonly used neural networks, the most significant difference is that the activation functions of the first hidden layers in the proposed neural networks are blending functions rather than the commonly used sigmoid functions. The back-propagation algorithm is exploited to learn appropriate values of the control points and weights in the proposed NURBSCNN and NURBSSNN. Moreover, the selection methods for the values of the corresponding parameter and knot vector in the NURBSCNN and NURBSSNN, as well as their application flowcharts, are elaborated upon and discussed in detail. The feasibility and effectiveness of the proposed approaches are demonstrated by several illustrative examples in this dissertation.
Abstract (Chinese) i
Abstract (English) ii
List of Tables viii
List of Figures ix
Symbols and Abbreviations xiv
Chapter 1 Introduction 1
1.1 Motivation 2
1.2 Literature review 4
1.2.1 The application of NURBS on the control of TWUSM 4
1.2.2 The application of NURBS on image compression and restoration 6
1.3 Dissertation contributions 9
1.4 Dissertation organization 10
Chapter 2 Background of B-Splines Curves and Surfaces 11
2.1 Introduction 11
2.2 B-spline curves 12
2.3 Degree of a B-spline curve 14
2.4 Control points 15
2.5 Parameterization and knot vectors 16
2.5.1 Parameterization 16
2.5.2 Knot vectors 21
2.6 B-spline basis functions 25
2.7 B-spline surfaces 31
2.8 Rational B-spline curves and surfaces 32
2.9 Summary 35
Chapter 3 NURBS Curve Neural Networks and NURBS Surface Neural Networks 36
3.1 Introduction 36
3.2 The proposed NURBSCNN 38
3.2.1 Derivation of NURBSCNN 38
3.2.2 Learning rules for updating the control points and weights of NURBSCNN 40
3.3 The proposed NURBSSNN 42
3.3.1 Derivation of NURBSSNN 42
3.3.2 Learning rules for control points and weights of NURBSSNN 44
3.4 Summary 46
Chapter 4 Design of Feedforward Compensator and Speed Controller for TWUSM Using NURBSCNN 47
4.1 Introduction 47
4.2 Feedforward compensator design for TWUSM using NURBSCNN 49
4.2.1 Parameterization for feedforward compensator 52
4.2.2 Determination of knot vectors for feedforward compensator 53
4.3 Speed feedback controller design for TWUSM using NURBSCNN 56
4.3.1 Parameterization for speed feedback controller 57
4.3.2 Determination of knot vectors for speed feedback controller 58
4.4 Speed control architecture for TWUSM 61
4.5 Simulation and experimental results 63
4.5.1 Simulation results of feedforward compensator 63
4.5.2 Experimental results of speed control 65
4.6 Summary 97
Chapter 5 Application of NURBS Surface Neural Networks to Digital Image Processing 98
5.1 Introduction 98
5.2 NURBS surface representation of a digital image 100
5.3 Image compression using NURBSSNN 102
5.3.1 Parameterization and knot vectors determination for image compression 103
5.3.2 Selection of compression ratio 104
5.4 Corrupted image restoration using NURBSSNNs 106
5.4.1 Parameterization for image restoration 107
5.4.2 Determination of knot vectors for image restoration 108
5.5 Experimental results 109
5.5.1 Experimental results of image compression 109
5.5.2 Experimental results of corrupted image restoration 111
5.6 Summary 112
Chapter 6 Conclusions 114
6.1 Conclusions 114
6.2 Further work 115
Publication List 122
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