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Fisher Y. — Fractal Image Compression. Theory and Application
Fisher Y. — Fractal Image Compression. Theory and Application

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Название: Fractal Image Compression. Theory and Application

Автор: Fisher Y.

Аннотация:

This book presents the theory and application of new methods of image compression based on self-transformations of an image. These methods lead to a representation of an image as a fractal, an object with detail at all scales. Very practical and completely up-to-date, this book will serve as a useful reference for those working in image processing and encoding and as a great introduction for those unfamiliar with fractals. The book begins with an elementary introduction to the concept of fractal image compression and contains a rigorous description of all the relevant mathemtics of the subjects.


Язык: en

Рубрика: Математика/Численные методы/Вейвлеты, обработка сигналов/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 341

Добавлена в каталог: 14.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adaptive bit allocation      63
Adaptive block classification      177
Adaptive classes      197
Adaptive cluster centers      197
Adaptive coding      61 63 69 76 77
Adaptive partitioning      19 134 136
Adaptive smoothing      298
Adelson, E.H.      312
Adjacent domains      111 146
Adjacent hexagons      308
Adjacent pixels      95 98 102
Adjacent pyramid levels      99 106
Adjacent range boundary      290
Adjacent ranges      11 49 115
Adjacent signal samples      139
Adjusting pixels on range boundary      298
Affine image mapping      157
Affine maps      153 154 172 201 216 299
Affine maps in $R^4$      299
Affine matrix operator      53
Affine operator      137 146 149 230
Affine operator, example      149
Affine operator, Lipschitz factor of      146 147
Affine transformation      3 9 37 46 145 148 150 232 299
Affine transformation in PIFS      11
Affine transformation of pixel values      56 120 240 261 263 308
Affine transformation, fern      3
Affine transformation, local      9
Affine transformation, minimizing rms      21
Algorithm, adaptive      19
Algorithm, decoding      243 244 301
Algorithm, encoding      16 20 243 250
Algorithm, encoding, targeting fidelity      19
Algorithm, inference      243 244 248 250 250 255—257
Algorithm, quadtree parameters      58
Algorithm, relating pyramid levels      106
Algorithm, termination      251
Algorithm, unstable      240
Algorithm, VQ      81
Algorithm, zoom-in      102 106
Algorithmic description of fractals      26
Alphabet $\Sigma$      244 246
Ap-function      244 244 250—252
Ap-WFA      247 247 249 251
Approximating an image      232 243
Approximating contour pieces      41
Approximating fixed point      20 59 94 102 143
Approximating fixed point in lower-dimensional space      123
Approximating image in lower-dimensional space      59
Approximating image pieces      13
Approximating original image block      178
Approximating pieces of a signal      137
Approximating range block      181 184
Approximating signal      105
Archetype      81
Archetypes      79—81 82 83 90
Archetypes in iterated transformation encoder      82
Archetypes, comparison with conventional scheme      85 86 88
Archetypes, comparison with different teaching images      88
Archetypes, determining      81
Archetypes, dissimilar      85
Archetypes, diverse images to generate      86
Archetypes, encoding time      85
Archetypes, example      84
Archetypes, flow chart      82
Archetypes, number of      83
Archetypes, similarity to VQ      81
Archetypes, variable number of      296
Arcs      301
Arithmetic coding      76
Arithmetic operations      168 189
Arithmetic shift      126
Artifacts      128 134
Artifacts in Orthogonal Basis scheme      209
Artifacts in quadtree scheme      59
Artifacts in triangular partitioning      18
Artifacts, blocky      59 124 262
Artifacts, minimizing      308
Attractive mappings      231
Attractive operator      237
Attractiveness condition      240
Attractor      2 3 35 37—39 46 49 50 138 143 144 153 157 158 161—163 168—171 177 216 229 231 232 293 308
Attractor for copy machine      2 7
Attractor for non-contractive IFS      2
Attractor for operator      143
Attractor for P1FS      11
Attractor for RIFS      39
Attractor for RIFS, example      40
Attractor for RIFS, fractal dimension of      50
Attractor, $X_T$      161 162 172
Attractor, ${\chi}_T$      153
Attractor, ${\chi}_W$      7 38 51
Attractor, affect of grey-tone scaling.s on      157
Attractor, contrast in      12
Attractor, detail in      12
Attractor, direct optimization      153 171
Attractor, error      161 162 171
Attractor, example      5 39 294
Attractor, fractal dimension of      293
Attractor, identical to collage      171
Attractor, nonoverlapping      233
Attractor, quality with orthogonalization      162
Attractor, scaling      4
Attractor, unbounded      310
Audio signal      138
Automata      see “WFA”
Average of quadrants      121
Average preserving, function      see “Ap-function”
Average preserving, image      247
Average preserving, WFA      see “Ap-WFA”
Averaging decimation      14 19 22 56 98 121 123 140 160 286
Averaging pixels      61 124
Baharav, Z.      ix 91 175
Barnsley, M.      2 3 25 39 41 42 144
Basis      148 155 158—160 172 178 184 199 201—204 206—209 214 256 296;
Basis, a priori      202 203 209
Basis, additional      205 206
Basis, block      178
Basis, initial in WFA      255 256
Bielefeld, B.      ix 215
Bilinear interpolation      59
Bin search      85 88 90
Binary matrices      256
Binary subsquare      243 254
Birkhoff's Ergodic Theorem      224
Bit      1 22 122 123 305
Bit, allocation      63 69
Bit, allocation in comparison of results      311
Bit, allocation in quadtree      61
Bit, allocation in simple example      14
Bit, allocation in WFA      256
Bit, encoding      76
Bit, quantization      174 240
Bit, rate      45
Bit, rate in FIF      312
Bit, rate of block coding method      240
bits      3 5 21 22 76 122 123
Bits, per transform      19 22 134
Block      139
Block, 8 x 8      235 240 307
Block, classification      177
Block, codebook      178
Block, collage      178
Block, comparisons      179 180
Block, diagonal matrix      102 146
Block, diagonal structure      146
Block, edges      134
Block, image      232 234 240
Block, index      139 139—151
Block, matrix      101
Block, structure      145
BLOCKS      79 92; “Domains”
Blocks, 2 x 2      22
Blocks, 3-dimensional      300
Blocks, constant      164 165
Blocks, independent      229
Blocks, nonoverlapping      141 169
Blocks, orthogonal      181
Blocks, parallel      181
Blocks, texture      301
Blockwise, constant      155
Blockwise, mapping      153
Blockwise, orthogonal      171
Blockwise, scalar multiplication      174
Blockwise, transformation      94 94
Blocky artifacts      59 124 262
blue      45
Blurred texture      107
Blurring      124 133 134
Boat image      173 174 312 314 323
Border      124 126
Boss, R.D.      ix 2 14 42 79 144
Bound      52 94 110 143 157 169 172 183 184 232 240
Boundary of point      26
Boundary, block      59
Boundary, pixels      124 295
Boundary, political      2
Boundary, range      49 124 134 290 298 308
Bounded      6 7 30 189 216 223 224 299 310
Bounds on operations      297
Bow tie, example      48
Bow tie, figure      295
bpp      see “Bits per pixel”
Brain      45
Bright      22
Brightest      85 121
Brightness      10—12 14 21 56 58 79 82 85
Buzo, A.      80
BYTE      14 259 260 262 263
canonical ensemble      83
Canonical form      79
Canonical group      121
Canonical orientations      121
Canonical pieces      2
Canonical position      58 287
Cartesian pair      232
Cartesian product      48 92
Cauchy sequence      32 33 36
Cauchy — Schwarz inequality      189
cell      4 123
Center      178 182 183;
Center of quadrant      234
Centroid condition      185
Channels      45 312
Characteristic functions      216
Chasing pixels      306
Children      244 254
Chrominance      45 312
circle      28 38
class      63 64 66 69 75 76 79 127 261 287 288
Class, comparison      66
Class, first and second      287
Class, search      59 66 85
Classes      58 61 64 66 68 69 72 75 76 79 81 82 85 127 177 197 261 288 296
Classes, 24 subclasses      58 85 260
Classes, 3 major      58 260
Classes, optimal number      77
Classes, three major      85
Classification      57 64 79 82 85 88 121 122 127 128 177 197 287 290 301 302
Classification by archtypes      79—90
Classification in HV method      121
Classification in Jacquin's scheme      57 177
Classification in quadtree scheme      57 58
Classification of curves      42
Classification, block      177
Classification, conventional      79 82 85 86 90
Classification, near      57
Classification, sets      86
Classified VQ      177
Clipping      63 289
Cluster, center      181—184 187—191
Cluster, center, computation of      188
Cluster, centers      178 179 182—187 190 192
Cluster, centers, adaptive      197
Cluster, centers, finding      186
Cluster, centers, fixed      197
Cluster, centers, precomputed initial      197
Cluster, size      180 186 190 192
Cluster, size, adjusting      180
Clustering, a rationale for      182
Clustering, K-means      205
Clusters      178 205
Coarser resolution      104 110
Coarsest resolution      99
Cocurullo. F.      197
Code      18 19 301 311
Code C      259—291
Code, fractal      229 232 237 239—241
Code, PIFS      see “PIFS-code”
Code, vectors      80—82
Codebook      80 81 82 90 178—197 255
Codebook, size      179
Coder      153 199 203
Codewords      256
Coding by projection      201
Coefficients      21 61 134 148 155 156 159 160 163 178 240 241 250 260 262 298 299
Coefficients, $l^2$-optimal      157 164
Coefficients, distribution      63
Coefficients, Fourier      2
Coefficients, of PIFS      21
Coefficients, quantization      162 163 181 255
Coefficients, quantized      172 178
Coefficients, scaling      64 76 157 158 163 170
Coefficients, scaling and offset      61
Coefficients, wavelet      243 255
Collage      38 110 137 144 148 149 153 153 155—157 161 162 163 169—172 180 307
Collage theorem      36 37 52 94 110 137 143—145 148 153 157 168 169 171 172 232 307
Collage Theorem, Generalized      36
Collage Theorem, new      169
Collage, approximation      159
Collage, block      178
Collage, error      161 162 170 171 180—184 186 189 298
Collage, subspace      159
Collage, subspace basis      158 159
Collie image      16 134 135 318
Color encoding      45
Color images      42 312
Color television      45
Compact      32 33 40 50 138 216
Comparing domains and ranges      20 42 55—58 61 69 70 119—123 127 163 165 177—197 260 288 309
Comparison of results      199 311
Complete metric space      32 33 35—37 39—41 48 92 143 215 229
complexity      157 158 165 168 174 177 179 180 182 189 192 197 240 302
Compression ratio      5
Computational cost      103
Condensation      216
Condition, attractiveness      240
Condition, centroid      185
Condition, contractivity      12 50 52 156 230 232
Condition, fast decoding      172
Condition, nearest neighbor      185
Condition, orthogonalized codebook blocks      181
Condition, tiling      51
Constraint on cluster centers      184
Continuous functions      34 36 37 104 105 113 138
Continuous signal      110
contours      14 41 42
Contraction, spatial      50 93 95 101 102 300
Contractive Mapping Fixed-Point Theorem      7 11 12 25 30 35 36—38 41 48 49 51 92 143 215—217
Contractive maps      2 33 34 37 48 92 156 202 203 215 230
1 2 3 4
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