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| Fisher Y. — Fractal Image Compression. Theory and Application |
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| Предметный указатель |
Contractive maps, examples 34
Contractive operator 143 216
Contractive z 50
Contractivity 33 34 36 50
Contractivity of W 34
Contractivity, condition 12 14 46 50 57 62 156 163 230 232
Contractivity, eventual 36 50 52 56 143 149 157 165 230 231 310
Contractivity, factor 143
contrast 10—12 14 21 56 244 252 311
Convergence 28 29 32 33 38 51 145 153 160 185 202
Convergence,  216 218
Convergence, almost everywhere 44 216 223
Convergence, conditions 157
Convergence, exact 153 157
Convergence, pointwise 44 216 223
Convergence, speed of 62 148 157 158 263
Copy machine 2 4 6 7 10 11 28 29 35;
Correlation 204 205
Cost 255
Covariance method 203 206 214
Cover 14
Crocker, L. 311
Culik II, K. x 243
Curve 26 107 301 302
Curves, fractal 2 106
Curves, Hilbert 154
Curves, space of 41
DB 44
DCT 2
Debauchies' wavelets 243
dec.c, explanation 289
dec.c, listing 278—286
Decibel 44
Decimated chrominance 45 312
Decimated domain 150 155 157—160 162 172 201 202 290 305
Decimated image 128 132 286
Decimation 140
Decimation, averaging 98 121 123 140 160 286
Decoder 61
Decoding 12 20 59 96 123 244
Decoding at larger size 4 5 59 262
Decoding by matrix inversion 228 297
Decoding by pixel chasing 305
Decoding in finite number of steps 163
Decoding with pyramid structure 165
Decoding, C code 262
Decoding, complexity 165
Decoding, exact 157 238
Decoding, example 108
Decoding, fast 59 102 123 172 238 253 307
Decoding, hierarchical 103
Decoding, non-iterative 153 172 238
Decoding, PSNR in 62
Decoding, time 123 126 132 133
Decoding, video 300
Detail, artificial 4 60
Deterministic WFA 250
Dimension, box 26
Dimension, fractal 26 50 91 106 107 111 115 293
Dimension, reduction of 197 199 201
Dimension, topological 26
Discrete cosine transform 2
Discrete picture elements 43
Discrete signal 105 110 138
Distance see “Metric”
Distance, domain-range 69
Distributional 64
Divergence 217 218 224—226
Divergence of decoding 62 157
Domain 11 14 48 53 59 77 82 93 123 134 148 155 177 181 302 “Linear” “Comparing”)
Domain in PIFS 48
Domain in quadtree scheme 57
Domain in RIFS 49 295
Domain, adjacent 111 146
Domain, binning 82
Domain, classification 57—58 64 66 79 85 121 122
Domain, coordinate mapping 138
Domain, decimated see “Decimated”
Domain, distance to range 69
Domain, index block see “Index block”
Domain, lattice see “Lattice”
Domain, location matrix 101
Domain, optimal see “Optimal”
Domain, pool 16 17 19 55 58 69—72 75 134 136 201 261 303
Domain, rectangular 140
Domain, reducing search 79 302
Domain, size 16 19 55 57 93 95 119 120 123 127 155 158 160 163 165 260—262 286 287
Domain, storage 61 122
Dudbridge, F. x 229 307
Edge, graph 243 246—249 255 256
Edge, image 14 17 18 22 57 79 82 134 136 177 234 301 308
Eigenvalue 46 50 106 117 146 147 186 187 247 294
Eikseth, H.M. 187 189
Elton, J. 39
enc.c, explanation 286
enc.c, listing 264—277
Encoding by edges 301
Encoding with block coding scheme 232
Encoding with hierarchical scheme 92
Encoding with HV method 119
Encoding with orthogonal basis method 207
Encoding with quadtree 55
Encoding with WFA 250
Encoding, C code 259
Encoding, color 45
Encoding, fast 177
Encoding, images 12 19 25 51 153 178 215
Encoding, optimization 57 121 299 302
Encoding, scan lines 300
Encoding, time 22 57 64 69 70 75 76 79 82 85 86 88 90 121 126 128 134 136 177 261
Encoding, video 300
Entropy coding 21
Ergodic see “Transformation” “Ergodic”
Error 9 52 81 124 202 214 245 255 299 301 “Collage
Ervin,V. 144
Euclidean distance 31
Euclidean norm 143
Eventually contractive 12 36 36 37 56 62 143 144 149 156 157 230—232 309 310
Expanding map 226
Expansive IPS 309
Expansive maps 34 50 52 209
Exponent of eventual contiactivity 36
Falconer, K. 25
Feedback 2 6 7 11 12
Fern 3—5 31 39 293
Fetch operator 140 155
Fidelity, limit 66
Fidelity, targeting 19
Filler, averaging 171
Filler, decimation 141 147
Filler, mask 171
Filler, RGB 45
Finer resolution 62 104 110
Fisher, D. 324
Fisher. Y. x 1 25 55 119 144 150 165 175 177 215 259 293 297 311 312
Fixed basis see “Basis”
Fixed point 7 34 35 36—38 50 52 59 92 96 98 123 215 217 225 228 232 263 294 297 306 307
Fixed-point pyramid 110
Flip 3 14 21 22 57 121 293
Flying start, decoding 165
Fractal 2 25
Fractal, code see “Code”
Fractal, curves 2
Fractal, dimension see “Dimension”
Fractal, example of 3
Fractal, fixed points 37
Fractal, functions 229
Fractal, image format (FIF) 312
Fractal, interpolation 106
Fractal, set 25 26
| Fractal, signal 137
Fractal, signal model 143
Gardner, J. 136
Gentle reader 23 30
Gersho, A. 177
Gladstone, L. 311
Goldberger, J. 312
Gram — Schmidt orthogonalization 158 201 203 204 206—209
Gray, R.M. 80
Grey-scale 7
Grey-scale operator 234 237 240
Growth rate 221 222
Hardin, D. 39 144
Hausdorff metric 7 31 32 34 40 50 310
Hept-tree 308
Hexagonal partitioning 308
Hierarchical decoding 102 104
Hierarchical model 91
Hilbert curve 154
Histogram of classes 64
Histogram of clusters 192
Horizontal partition 17 119
Horizontal sums 120
Hue 45
Huffman coding 76 122 134 312
Hurd, L. 42
Hutchinson, J. 3 6 25 30
I signal 45
IFS 6—7 25 37 28—39 229—232 237 293 308
IFS as copy machine 2
IFS, encoding images with 229
IFS, example 39 294
IFS, non-contractive 309
IFS, partitioned see “PIPS”
IFS, recurrent see “RIFS”
Index block 139—151
Index block, domain 139
Index block, range 139 140 141
Initial basis in WFA 255 256
Initial classification 85
Initial distribution of WFA 246 247 249 253—255
Initial function 49
Initial hexagon 309
Initial image 12 14 20 59 62 162 164 165 208 306 307
Initial image in copying machine 2 11 29
Initial image, choice 163
Initial image, root of quadtree 55
Initial image, size 5
Initial image, translation term 164
Initial LEG code vectors 80
Initial nodes of WFA 253
Initial quadtree partitions 55
Initial state of LEG algorithm 80
Initial vector 96 102 207
Interpolation, fractal 106 115 116
Interval, unit I = [0,1] 8
Invariant function 231 232
Invariant measure 224
Iterated Function Systems see “IFS”
Iterated Systems, Inc. 311
Iterating, to convergence 29 35 59 80 96 208
Iterations, example 2
Iterations, needed to decode 20 62 123 157 162 163 165 208 263 300 306 307
Iterative codebook algorithm 81 185
Iterative search for basis vectors 204
Jacobs, E.W. x 79 144
Jacquin, A. 2 14 19 41 57 145 153—155 160 165 170 175 177 178 181
Juergens, H. 3
Kari, J. xi 243
Karnin, E. xi 91
Kernel 140 141 142 145 148 149 200
Kiel Harbor image 165 166 192 194 321
Kolmogorov complexity 254
Lancaster, J. 144
Lane, T. 311
Lattice 19 57 58 61 70 82 120 261 262 286 287 312
LBG algorithm 185
Lebesgue measure 44 225
Lenna 4 5 7 9 10 16 59—62 64 69 70 73—76 85 86 88 127 132—135 165 170 199 209 257 298 307 312 319
Lepsoy, S. xi 150 153 171 177 295
Limit copy 29
Limit of graphs of functions 50
Limit point 32 33 36
Limit set 7 39
Linde, Y. 80
Linear algebra 138 149 158
Linear combination of domains 200 297
Linear complexity 240 302
Linear interpolation 106 107
Linear operator 34 186 187
Linear subspace 155 156 244
Linear term 145 146 154 155 157 158 162 170—172
Linear transformations 47 145
Lipschitz condition 50
Lipschitz factor 33 36 143—149 157 169
Lipschitz map 33 34 36 39 143 293
Lloyd algorithm 185
Lloyd — Max quantizer 209
Lossless code 96 106 109
Lossy code 94 106
Lossy compression 5
Luminance 45 312
Lundheim, L. xi 137 144 150 156 175
Magnification 4
Major classes 57 58 64 85 260
Malah, D. xii 91
Mallat form 244 255
Mandrill image 234 240 320
Manual dec.c 262
Manual enc.c 259
Matrix  in WFA 246 247 254
Matrix B 202 207—209
Matrix Q 203 208 209
Matrix, averaging 140
Matrix, binary 256
Matrix, block 146
Matrix, block diagonal 146
Matrix, color 45
Matrix, connectivity 50
Matrix, decoding by inversion 297
Matrix, descripiion of PIFS 100
Matrix, norm 146 159 169
Matrix, operator 53
Matrix, orthogonalizing 158 163
Matrix, permutation 53 141
Matrix, positive 221
Matrix, primitive 221
Matrix, projection 159
Matrix, scaling 102
Matrix, stochastic 116
Matrix, storage 122
Matrix, subsampling 140
Matrix, transfer 101
Maximal eignvalue 50
Maximizing, objective function 185 187
Maximum quadtree depth 56 58 61 260 261 287
Maximum range size 61
Maximum scaling 56 58 261 263 287
Measurable function 32 48
Measure, preserving 224
Measure, spaces 42 138
Menlove, S. xii 119
Metric 7 8 30 293 299
Metric,  43 155 156
Metric, 32 44 215
Metric,  44
Metric, Euclidean 31 50 230 231 294
Metric, examples 31
Metric, induced by norm 43
Metric, rms 9 14 20 44
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