Mathematical Optimization in Graphics and Vision - Luiz Velho - Impa

More documents

Recommendations

Info

xii LIST OF FIGURES 3.8 Edge detection using snakes: (a) initial curve; (b) final edge curve (P. Brigger & Unser, 1998). . . . . . . . . . . . . . . . . . . . . . 52 4.1 Minimum-length path on a surface . . . . . . . . . . . . . . . . . 56 4.2 Detecting a boundary segment . . . . . . . . . . . . . . . . . . . 57 4.3 Discretizing a variational problem . . . . . . . . . . . . . . . . . 59 4.4 Attractors: punctual (a) and directional (b). . . . . . . . . . . . . 62 4.5 Basis of B-spline curves. . . . . . . . . . . . . . . . . . . . . . . 64 4.6 Control points and B-spline curves. . . . . . . . . . . . . . . . . . 64 4.7 Interactive variational modeling. . . . . . . . . . . . . . . . . . . 67 5.1 Descent directions. . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 Quadratic function with a unique local minimum. . . . . . . . . . 75 5.3 Quadratic function without local extrema. . . . . . . . . . . . . . 76 5.4 Quadratic function without local extrema. . . . . . . . . . . . . . 77 5.5 Quadratic function with an infinite number of local extrema. . . . 78 5.6 Linear regression. . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.7 Geometric interpretation of the pseudo-inverse. . . . . . . . . . . 81 5.8 Gradient descent. . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.9 d e d ′ are conjugate directions. . . . . . . . . . . . . . . . . . . . 87 5.10 Equality constraint. . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.11 Inequality constraint. . . . . . . . . . . . . . . . . . . . . . . . . 90 5.12 Projected gradient algorithm. . . . . . . . . . . . . . . . . . . . . 95 5.13 Optimal solutions of linear programs. . . . . . . . . . . . . . . . 98 5.14 The pinhole camera. . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.15 Camera coordinate systems. . . . . . . . . . . . . . . . . . . . . 103 5.16 A panoramic image. . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.17 Image sequence with overlapping. . . . . . . . . . . . . . . . . . 107 5.18 Visualization of building enviroments. . . . . . . . . . . . . . . . 110 6.1 Network of connections between A and B . . . . . . . . . . . . . 115 6.2 Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.3 Oriented graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.4 Network of connections between A and B . . . . . . . . . . . . . 121 6.5 State variable of the problem. . . . . . . . . . . . . . . . . . . . . 122
LIST OF FIGURES xiii 6.6 Monocromatic discrete image. . . . . . . . . . . . . . . . . . . . 134 6.7 Quantization levels and graph of a one-dimensional quantization map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.8 Quantization from 256 (a) to 4 (b) gray levels. . . . . . . . . . . . 139 6.9 Spock represented with 3 levels of detail. . . . . . . . . . . . . . 141 6.10 Human body with three levels of clustering. . . . . . . . . . . . . 143 6.11 Visualization process in two stages. . . . . . . . . . . . . . . . . 145 6.12 Neighborhoods of a pixel. . . . . . . . . . . . . . . . . . . . . . . 149 6.13 Elementary triangle. . . . . . . . . . . . . . . . . . . . . . . . . . 152 6.14 Toroidal graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.1 Local maxima × global maxima in hill climbing (Beasley et al. , 1993). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.2 Sexual reproduction by cromossomial crossover (Beasley et al. , 1993). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.3 Graph of f(x) = x sin(10πx) + 1 on [−1, 2]. . . . . . . . . . . . 164 7.4 Domain decomposition performed by branch-and-bound. . . . . . 168 7.5 Genetic formulation for the design of a stable table (Bentley, 1999).177 7.6 Crossed reproduction of algebraic expressions. . . . . . . . . . . 179 7.7 Curve fitting by evolution. . . . . . . . . . . . . . . . . . . . . . 180 7.8 Intersection of parametric surfaces (Snyder, 1991). . . . . . . . . 182 7.9 Trimming curves (Snyder, 1991). . . . . . . . . . . . . . . . . . . 182 7.10 Intersection of parametric surfaces. . . . . . . . . . . . . . . . . . 183 7.11 Intersection curves computed with interval arithmetic and affine arithmetic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 7.12 Approximating an implicit curve (Snyder, 1991). . . . . . . . . . 185 7.13 Approximating an implicit curve with interval arithmetic and affine arithmetic. . . . . . . . . . . . . . . . . . . . . . . . . . . 186 7.14 Approximating parametric surfaces (Snyder, 1991). . . . . . . . . 187 8.1 Decomposition from the choice of three possibilities. . . . . . . . 194 8.2 Graph of S = −p log 2 p − (1 − p) log 2 (1 − p) . . . . . . . . . . . 195 8.3 Codification trees (a) α (b) β. . . . . . . . . . . . . . . . . . . . . 198 8.4 Trees for schemes (a) and (b) . . . . . . . . . . . . . . . . . . . . 199
Page 1 and 2: Mathematical Optimization in Graphi
Page 3: The book is conceptually divided in
Page 6 and 7: vi CONTENTS 2.7 The problem of posi
Page 8 and 9: viii CONTENTS 6.5.1 Linear and Inte
Page 10 and 11: x CONTENTS
Page 14 and 15: xiv LIST OF FIGURES
Page 16 and 17: 2 CHAPTER 1. COMPUTER GRAPHICS the
Page 18 and 19: 4 CHAPTER 1. COMPUTER GRAPHICS tech
Page 20 and 21: 6 CHAPTER 1. COMPUTER GRAPHICS (Fig
Page 22 and 23: 8 CHAPTER 1. COMPUTER GRAPHICS devi
Page 24 and 25: 10 CHAPTER 1. COMPUTER GRAPHICS We
Page 26 and 27: 12 CHAPTER 1. COMPUTER GRAPHICS Exa
Page 28 and 29: 14 CHAPTER 1. COMPUTER GRAPHICS obj
Page 30 and 31: 16 CHAPTER 1. COMPUTER GRAPHICS onl
Page 32 and 33: 18 CHAPTER 1. COMPUTER GRAPHICS For
Page 34 and 35: 20 CHAPTER 1. COMPUTER GRAPHICS
Page 36 and 37: 22 CHAPTER 2. OPTIMIZATION: AN OVER
Page 52 and 53: 38 CHAPTER 3. OPTIMIZATION AND COMP
Page 62 and 63:
48 CHAPTER 3. OPTIMIZATION AND COMP
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
56 CHAPTER 4. VARIATIONAL OPTIMIZAT
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
P 0 P 5 64 CHAPTER 4. VARIATIONAL O
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
70 CHAPTER 5. CONTINUOUS OPTIMIZATI
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
100 CHAPTER 5. CONTINUOUS OPTIMIZAT
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
114 CHAPTER 6. COMBINATORIAL OPTIMI
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
158 CHAPTER 7. GLOBAL OPTIMIZATION
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
190 CHAPTER 8. PROBABILITY AND OPTI
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
210 BIBLIOGRAPHY Bibliography Atall
Page 226 and 227:
212 BIBLIOGRAPHY Hansen, E. 1988. G
Page 228 and 229:
214 BIBLIOGRAPHY Ratschek, H., & Ro
Page 230 and 231:
Index abstraction paradigm, 5 accum
Page 232 and 233:
218 INDEX analysis, 45 coordinate s
Page 234:
220 INDEX reconstruction, 16 repres
show all

Mathematical Optimization in Graphics and Vision - Luiz Velho - Impa

Create successful ePaper yourself

Delete template?

Save as template?