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Adaptive wavelets and their applications to image fusion and compression
Piella, G.
Publication date
2003
Link to publication
Citation for published version (APA):
Piella, G. (2003). Adaptive wavelets and their applications to image fusion and compression.
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Contents
1 I n t r o d u c t i o n t o m u l t i r e s o l u t i o n s i g n a l p r o c e s s i n g 1 1.1 The need for multiresolution representations 1
1.1.1 Classical approaches 1 1.1.2 Time-frequency trade-off 2 1.1.3 Multiresolution: what is it good for? 5
1.2 Multiresolution approaches 6 1.2.1 Continuity versus discreteness, redundancy versus non-redundancy . . . . 6
1.2.2 Examples of multiresolution representations and methods 7
1.2.3 Applications of multiresolution representations 8
1.3 A case study: the Burt-Adelson pyramid 10
1.4 Wavelets \\ 1.4.1 The continuous wavelet transform 11
1.4.2 Mallat's multiresolution analysis 14 1.4.3 Wavelets and filter banks 15 1.4.4 How to choose a wavelet? 17 1.4.5 The need for adaptive wavelets 18
1.5 Application to image fusion 20 1.6 Outline of the thesis 20 2 M u l t i r e s o l u t i o n d e c o m p o s i t i o n s y s t e m s 2 3
2.1 Decomposition systems with perfect reconstruction 23
2.2 Lifting 25 2.3 T h e pyramid transform 27 2.3.1 Axiomatics 27 2.3.2 Pyramid condition 29 2.3.3 Lifting pyramids 31 2.4 T h e wavelet transform 32 2.4.1 Axiomatics 32 2.4.2 Pyramid condition 33 vn
2.4.3 Lifting wavelets 34 2.5 Other multiresolution decompositions 34
2.5.1 Wavelet packets 35 2.5.2 Local basis 35 2.5.3 Multiwavelets 36 2.5.4 Steerable pyramid 38 2.5.5 Gradient pyramid 41 3 A d a p t i v e u p d a t e lifting: t h e a x i o m a t i c f r a m e w o r k 4 3
3.1 Adaptive wavelets: existing approaches 44 3.2 General framework for update lifting 46
3.3 Intermezzo: seminorms 48 3.4 Choice of decision m a p and update filters 51
3.5 When do we have perfect reconstruction? 55 4 A d a p t i v e u p d a t e lifting: specific c a s e s 59
4.1 Weighted gradient seminorm 60 4.1.1 Perfect reconstruction conditions 60
4.1.2 Simulations 66 4.2 Quadratic seminorm 73
4.2.1 Perfect reconstruction conditions "3
4.2.2 Simulations 79
4.3 /1-norm and l^-novm 85
4.3.1 Perfect reconstruction conditions 85
4.3.2 Simulations 88 4.4 Continuous decision map 89
4.4.1 Perfect reconstruction conditions 89
4.4.2 Simulations 95 4.5 Other cases 95
4.5.1 Ranking-based updating 96 4.5.2 Switching between horizontal and vertical filters 100
5 A d a p t i v e w a v e l e t s i n i m a g e c o m p r e s s i o n 105
5.1 Preliminaries 105 5.2 Wavelets in image compression 107
5.3 Adaptive wavelets in image compression 108 5.4 Computing the empirical entropy 109
5.5 Adding quantization 112 5.6 A case study H ' 5.7 Discussion 126
6 M u l t i r e s o l u t i o n i m a g e fusion 1 2 7
6.1 Image fusion 127 6.1.1 Concept of image fusion 128
6.1.2 Objectives, requirements and challenges of image fusion 129
6.1.3 Application fields 130 6.1.4 Fusion techniques 133 6.2 A general pixel-based MR fusion scheme 134
6.2.1 Notation 135 6.2.2 T h e general framework 136
6.2.3 MR analysis and synthesis 137
6.2.4 Activity measure 138 6.2.5 Match measure 139 6.2.6 Combination map 139 6.2.7 Decision map 140 6.3 Overview of some existing fusion schemes 143
6.4 Examples 146 6.5 Adaptive MR schemes for image fusion 147
6.5.1 Case studies 150 6.5.2 Discussion 152 7 R e g i o n - b a s e d m u l t i r e s o l u t i o n i m a g e fusion 1 5 7
7.1 The overall scheme: from pixels to regions 158
7.1.1 Introduction 158 7.1.2 M R / M S segmentation 158
7.1.3 Combination algorithm 159 7.2 M R / M S segmentation based on pyramid linking 160
7.2.1 The linked pyramid 160 7.2.2 MR segmentation algorithm using linking 161
7.2.3 M R / M S segmentation algorithm using linking 163
7.3 Experimental results 165 7.3.1 Casestudies 165 7.3.2 Discussion 167 8 P e r f o r m a n c e a s s e s s m e n t in i m a g e fusion 171
8.1 Existing approaches to image fusion performance 171
8.2 A new quality measure for image fusion 173 8.2.1 T h e image quality index of Wang and Bovik 173
8.2.2 A new fusion quality measure 175
8.3 Experimental results 176 8.3.1 Case studies 176 8.3.2 Discussion 178
9 C o n c l u s i o n s 1 8 3 ix
