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| Fisher Y. — Fractal Image Compression. Theory and Application |
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| Предметный указатель |
Metric, space 25 30 33
Metric, supremum 8 14 32 44 48—52 92
Minimal range size 63 66
Minimal WFA states 243
Minimization 149
Minimization collage 13 41 52 55 92 94 153 181 232
Minimization comparisons 180
Minimization over transforms 93
Minimization search time 180
Minimization square difference 21 43
Minimum quadtree depth 55 (see also “Maximum quadtree depth”)
Minimum range size 66 69
Motion compensation 300
ms see “Metric”
Multiresolution function 245 247 255
Multiresolution image 243—247 254
Negative scaling 58 61 64 66 69 121 127 288
Neighborhood 26 39
Nilpotent 158
Nondeterministic WFA 250
Noniterative decoding 163
Nonlinear kernel 145
Nonlinear operator 141 149
Nonlinear transforms 145
Nonorthogonal basis 160
Nonoverlapping 2 x 2 blocks 22 59 286
Nonoverlapping domains 61 146 156 169
Nonoverlapping IPS 216 293
Nonoverlapping ranges 13 119 141 154 201 298
Norm 46 143 182 187
Norm,  204
Norm,  44
Norm, equivalent 148
Norm, matrix 34 46 146 159 169 294
Norm, operator 143 187
Norm, p 43
Norm, quadratic 149
Norm, quadtratic 143
Normally distributed 256
Normed vector space 229
NullSpace 174
Objective function 183—187
Offset see “Scaling” “Coefficient”
Offset in HV-partition 22 122
Offset, bits 261 263
Offset, vector 46 101
Oien, G. xii 144 150 153 177 192 197
Open interval 33
Optimal basis 203 204 206
Optimal bit allocation 21 261 311
Optimal classification 301
Optimal clusters 179
Optimal codebook 179
Optimal collage 137 149 163 169
Optimal domain 56 122 123 148 159 309
Optimal kernel 149
Optimal number of classes 77
Optimal quantization 153 163
Optimal scaling and offset 20 21 56 77 148 156 157 159 164 307
Optimal transformations 64
Optimization, decoding 123
Optimization, direct altractor 153 171
Optimization, encoding 57 121 127 290 299
Optimization, least-squares 234
Orientation 2 14 22 38 57—59 61 79 85 121 127 136 289 290 293 294 305 308
Orthogonal see “Basis” “Gram “Matrix”
Ortiz, L. 311
Parallel blocks 181—184 189
Parallel matrix rows 189
Parallel vectors 179
Parallelization 309
Parallelogram 38 46
Partition 226
Partition, cluster 186
Partition, curve 2 41
Partition, edge based 301
Partition, hexagonal 308
Partition, HV 17 22 119—120 122 134
Partition, image 10 13 14 19 52 90 96 154 229 298
Partition, polygonal 305
Partition, quadtree 16 21 55—56 59 160 174 259—261 289 298
Partition, range 122 142 160 163—165 168 263 288
Partition, rectangular 119
Partition, signal 141
Partition, triangular 18 22 136
Path 246 250 253
Peitgen, H.-O. 3
Peppers image 165 192 322
Perception 156 245 311
Permutation matrix 53 141
Perron — Frobenius theorem 221
Photocopying machine see “Copy machine”
Photograph 1 138 254
Piece of signal 139
piecewise 105 137 139—147 199
PIFS 25 48 50 52 91 92 96 97 100 104 105 108 112
PIFS as a copying machine 11
PIFS bow tie 47
PIFS code 91 94 96—98 100 102 104—110 113
PIFS code, coding 96
PIFS code, decoding example 96
PIFS code, description 94
PIFS code, example 94
PIFS code, finding 92
PIFS code, hierarchical 102
PIFS code, matrix 106
PIFS code, matrix example 103
PIFS code, zooming 109
PIFS contractive 113
PIFS decoding 12
PIFS early coders 199
PIFS embedded function 104 105 106 110 112
PIFS encoding image with 50
PIFS eventually contractive 52
PIFS example 94
PIFS finding fixed point by matrix inversion 297
PIFS fixed point 11 99 109 114
PIFS fractal dimension 106
PIFS iterating 102
PIFS matrix description 100 (see also “PIFS-code”)
PIFS pyramid of fixed points 99
Pivoting 297
Pixel 1
Pixelization 4
Poinuvise convergence 44 216
Polygonal fit 301
Polygonal partition 305
Postprocessing 59 62 72 76 77 124 128 133 134 262 263 289 290 295 298
PRECISION 168
Primary classes 79
Primary Colors 45
probability 39 69 70 296
Programs, dec.c 278
Programs, enc.c 264
Projection operator 202 204
Pseudo-archetype 90
Pseudo-code 19 55
PSNR 44 62—64 70 75 85 86 128 164 166 170 173 193 240 257 298 311
Pyramid of the PIFS 99—111
Q signal 45
Quadrant 53 55—57 82 85 180 234 238 247—249 256 260 288 308
Quadrant address 244
Quadtree partition see “Partition”
Quadtree scheme 55—77
Quantization 21 56 61—63 76 77 122 153 162 163 172 174 178 181 208 209 240 255 261 263 287 289 299
Rademacher labellings 305
Radon — Nikodym theorem 225
Ramamurthi, B. 177
Ramstad, T. 174 295
Random cluster centers 186 192
| Random fluctuations 1
Random junk 8
Random points 69 296
Random strings 254
Random subset of vectors 80
RANGE 11 19 20 48 49 52 55 59 64 93 139 177 182 302
Range in HV scheme 120
Range in quadtree scheme 160 260
Range, adjacent 11 115
Range, approximation by linear combinations of domains 200 298
Range, boundary 61 124
Range, classification see “Classification” “Domain
Range, comparing see “Comparing”
Range, complexity 201
Range, concatenation 93
Range, contrast 12
Range, covering 14
Range, distance to domain 69
Range, Gram — Schmidt on 206
Range, index block see “Index block”
Range, nonoverlapping 13 119 141 154 201 298
Range, number of 20 95
Range, partition see “Partition”
Range, quadtree 55—56
Range, size 14 19 21 55 56 61 63 66 69 76 82 88 90 93 95 100 103 120—122 134 140 141 154—156 162 178 192 201 202 260 286 287 290
Range, storing 122
Range, using a particular domain 146
Reclassification of domains 57
Rectangle, grid 115
Rectangle, size 19
Rectangle, tiling 233
Rectangular domain 140 302
Rectangular image 287 290
Rectangular image sample 139
Rectangular partition 308
Rectangular partitioning 17 22 119
Rectangular ranges 229
Recurrent iterated function systems see “RIFS”
Recursion depth in quadtree scheme 260 (see also “Maximum” “Mimimum”)
Recursive decoding 241
Recursive function definision 231 238
Recursive generation of Sierpinski Triangle 28
Recursive image partition 16—18 119 260
Recursive inference algorithm 243 250 254 255 257
Reducing complexity see “Complexity”
Reducing dimensionality of data 199 201
Reducing domains 14 57 79 180 207
Reducing the image see “Copy machine”
Redundancy 1 10 137
Regression 14 289
Regular 225 226 227
Resolution 3 43 62 63 91 99 102 107 109 230 231 240 243 244 250 253 254
Resolution m 230—232 235 238 240 241
Resolution, coarser, finer 110
Resolution, grey-scale 43
Resolution, independence 46 59
Resolution, infinite 8 44 245 262 300
Resolution, super 104—107
Restricted self-similarity 10
Restricting  11 48
Restricting, domain range size ratio 122
Restricting, scaling 52 62
Results 10 61 82 126 169 170 192 209 257 311
RGB signal 45
RIFS 39 39 42 49—51 216 218 227 295
Rigor 25
Robust archetypes 88
Rotation 3 10 14 18 21 22 46 57 121 123 293 294
Sampled signal 138 139
Sampling 104 109 110 138
Sampling, resolution 234 239
San Francisco image 18 317
Saturation 45
Saupe, D. 3 302
Scalar multiplication 172 174 189 190
Scalar quantization 163 174 185
Scaling 3 10 20 21 38 52 56 62 63 121—123 145 146 148 155 163 165 174 201 261—263 289 290 294 301 307 “Maximum” “Negative” “Coefficient”)
Scaling, constrained 157
Scaling, histogram 63 163
Scaling, matrix 53 102
Scaling, positive 260 288
Scaling, relationship 26
Scaling, zero 123 289
Search 14 72 79 80 85 88 90 119 120 127 144 149 155 179 180 182 192 197 200 203 204 206 207 260 261 288 297 299
Search class 63 76
Search time 66 122
Self-similarity 9 10 17 18 26 69 70 76 91 136 142 199 229 249 301 308
Self-transformable 137 142 144
SEQUENCE 1 39 44 139 141 163 188 189
Sequence of quantizers 185
Sequence, convergent 33
Series 162 168 171 174
Set 3 4 6—9 26 30—32 37 40 41 232 234 237 238 “Attractor”)
Set of Ap-functions 244
Set of archetypes 79 82 86
Set of cluster centers 178 183 197
Set of domain pixels 171
Set of images 82 85 88
Set of measure zero 44
Set of rationals 33
Set of states 251
Set of teaching vectors 80 90
Set, empty 48
shrink 20 140 141 155 162 178 181
Shuffle 155 178 181
Sierpinski triangle 28 39 216
Signal to noise ratio see “PSNR”
Signal, discrete 138
Signal, piece 137
Similitude 50 293
Simoncelli, E.P. 312
SIZE 19 255 “Domain” “Cluster” “Codebook”)
Size of covering 26
Size of decoding image 4
Size, automaton 254—256
Size, covering 115
Skewing 3 10 46 294
Slow convergence 63 148 157
Slow decoding 263
Slow encoding 261
Slow initialization 197
Smooth motion 300
Smoothing see “Postprocessing”
Smoothing weights see “Weights”
Sorting domains and ranges 56 70 85
Sorting vectors 80 81
source code see “Code”
span 202 207
Sparse matrix 59 254 256 297
Spatial contraction see “Contraction”
Spatial transformation 11 50 53
Speech coding 177
Spiral 38
States, WFA 243 246—248 250 252 255 256
Statistical collage argument 170
Statistical self-similarity 26
Stochastic 116
Storage 1—3 14 21 22 52 56 61 77 80 90 94 119 122 123 199 209 240 241 253 255 256 261 300 301
Stretching 3 10 46 294
Strictly contractive 143 144 156 157 163
String Cheese image 324
Subnodes 55 56
Subsainpling matrix see “Matrix”
Subsaniple 14 19 123 124 140 141 147 148 165 301 305
subspace 158 178 181 201—207 252 “Translation”)
Subtree 254
Superposition 45
Supremum metric see “Metric”
Supremum norm see “Norm”
Tank Farm image 85 86 88 318
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