Front-End Vision and Multi-Scale Image Analysis |
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xiii | |
The purpose of this book |
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xiii | |
Scale-space theory is biologically motivated computer vision |
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xiv | |
This book has been written in Mathematica |
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xvi | |
Acknowledgements |
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xviii | |
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Apertures and the notion of scale |
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1 | (12) |
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Observations and the size of apertures |
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1 | (1) |
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Mathematics, physics, and vision |
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2 | (3) |
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5 | (4) |
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A critical view on observations |
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9 | (3) |
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12 | (1) |
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Foundations of scale-space |
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13 | (24) |
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Constraints for an uncommited front-end |
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13 | (2) |
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Axioms of a visual front-end |
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15 | (6) |
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15 | (1) |
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16 | (2) |
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18 | (1) |
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Rowing: more oarsmen, higher speed? |
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19 | (2) |
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Axiomatic derivation of the Gaussian kernel |
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21 | (2) |
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Scale-space from causality |
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23 | (2) |
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Scale-space from entropy maximization |
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25 | (2) |
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Dervatives of sampled, observed data |
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27 | (4) |
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31 | (1) |
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32 | (3) |
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35 | (2) |
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37 | (16) |
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37 | (1) |
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38 | (1) |
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Cascade property, selfsimilarity |
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39 | (1) |
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40 | (1) |
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Relation to generalized functions |
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40 | (3) |
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43 | (1) |
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Relation to binomial coefficients |
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43 | (1) |
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The Fourier transform of the Gaussian kernel |
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44 | (2) |
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46 | (2) |
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48 | (1) |
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49 | (1) |
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50 | (3) |
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53 | (18) |
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53 | (1) |
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Shape and algebraic structure |
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53 | (4) |
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Gaussian derivatives in the Fourier domain |
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57 | (2) |
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Zero crossings of Gaussian derivative functions |
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59 | (1) |
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The correlation between Gaussian derivatives |
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60 | (4) |
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Discrete Gaussian kernels |
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64 | (1) |
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Other families of kernels |
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65 | (2) |
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Higher dimensions and separability |
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67 | (2) |
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69 | (2) |
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Multi-scale derivatives: implementations |
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71 | (20) |
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Implementation in the spatial domain |
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71 | (2) |
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73 | (1) |
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74 | (4) |
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N-dim Gaussian derivative operator implementation |
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78 | (1) |
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Implementation in the Fourier domain |
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79 | (4) |
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83 | (2) |
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Advanced topic: speed concerns in Mathematica |
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85 | (4) |
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89 | (2) |
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Differential structure of images |
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91 | (46) |
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The differential structure of images |
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91 | (1) |
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92 | (4) |
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Coordinate systems and transformations |
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96 | (6) |
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102 | (1) |
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First order gauge coordinates |
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103 | (5) |
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Gauge coordinate invariants: examples |
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108 | (7) |
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108 | (2) |
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Isophote and flowline curvature in gauge coord |
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110 | (3) |
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Affine invariant corner detection |
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113 | (2) |
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115 | (2) |
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117 | (10) |
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The Hessian matrix and principal curvatures |
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119 | (1) |
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120 | (2) |
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122 | (1) |
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Gaussian and mean curvature |
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123 | (3) |
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Minimal and zero Gaussian curvature surfaces |
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126 | (1) |
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Third order image structure. T-junction detection |
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127 | (4) |
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Fourth order image structure: junction detection |
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131 | (1) |
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Scale invariance and natural coordinates |
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132 | (2) |
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134 | (2) |
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Intermezzo: Tensor notation |
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135 | (1) |
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136 | (1) |
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Natural limits on observations |
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137 | (6) |
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Limits on differentiation: scale, accuracy and order |
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137 | (4) |
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141 | (2) |
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Differentiation and regularization |
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143 | (10) |
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143 | (1) |
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Regular tempered distributions and test functions |
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144 | (3) |
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An example of regularization |
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147 | (1) |
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Relation regularization Gaussian scale-space |
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148 | (4) |
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152 | (1) |
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The front-end visual system-the retina |
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153 | (14) |
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153 | (1) |
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154 | (2) |
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156 | (1) |
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157 | (3) |
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160 | (2) |
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Sensitivity profile measurement of a receptive field |
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162 | (3) |
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165 | (2) |
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A scale-space model for the retinal sampling |
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167 | (12) |
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The size and spatial distribution of receptive fields |
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167 | (5) |
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A scale-space model for the retinal receptive fields |
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172 | (5) |
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177 | (2) |
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The front-end visual system - LGN and cortex |
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179 | (18) |
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179 | (2) |
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The lateral geniculate nucleus (LGN) |
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181 | (2) |
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Corticofugal connections to the LGN |
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183 | (2) |
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The primary visual cortex |
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185 | (6) |
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187 | (1) |
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188 | (1) |
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189 | (2) |
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Intermezzo: Measurement of neural activity in the brain |
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191 | (4) |
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Electro-Encephalography (EEG) |
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191 | (1) |
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Magneto-Encephalography (MEG) |
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192 | (1) |
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193 | (1) |
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Optical imaging with voltage sensitive dyes |
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194 | (1) |
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Positron Emission Tomography (PET) |
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194 | (1) |
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195 | (2) |
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The front-end visual system - cortical columns |
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197 | (18) |
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Hypercolumns and orientation structure |
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197 | (3) |
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Stabilized retinal images |
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200 | (2) |
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The concept of local sign |
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202 | (2) |
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Gaussian derivatives and Eigen-images |
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204 | (4) |
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Plasticity and self-organization |
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208 | (2) |
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Higher cortical visual areas |
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210 | (1) |
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211 | (1) |
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211 | (4) |
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Further reading on the web |
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212 | (3) |
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Deep structure I. watershed segmentation |
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215 | (26) |
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215 | (1) |
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216 | (2) |
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Normalized feature detection |
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218 | (1) |
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Automatic scale selection |
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219 | (2) |
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λ-Normalized scale selection |
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220 | (1) |
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Is this really deep structure? |
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220 | (1) |
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221 | (4) |
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Simplification followed by focusing |
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221 | (1) |
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222 | (3) |
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Follicle detection in 3D ultrasound |
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225 | (6) |
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Fitting spherical harmonics to 3D points |
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229 | (2) |
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231 | (8) |
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Dissimilarity measure in scale-space |
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231 | (1) |
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232 | (2) |
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234 | (3) |
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The multi-scale watershed segmentation |
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237 | (2) |
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Deep structure and nonlinear diffusion |
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239 | (2) |
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Non-linear diffusion watershed segmentation |
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239 | (2) |
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Deep structure II. catastrophe theory |
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241 | (16) |
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Catastrophes and singularities |
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241 | (1) |
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Evolution of image singularities in scale-space |
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242 | (1) |
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Catastrophe theory basics |
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243 | (7) |
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243 | (1) |
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Characterization of points |
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243 | (1) |
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244 | (1) |
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Local characterization of functions |
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244 | (1) |
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245 | (1) |
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246 | (1) |
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246 | (1) |
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Illustration of the concepts |
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247 | (3) |
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Catastrophe theory in scale-space |
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250 | (6) |
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Generic events for differential operators |
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251 | (3) |
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Generic events for other differential operators |
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254 | (1) |
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Annihilations and creations |
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255 | (1) |
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256 | (1) |
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Deep structure III. topological numbers |
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257 | (20) |
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257 | (6) |
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Topological numbers in scale-space |
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258 | (1) |
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Topological number for a signal |
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259 | (1) |
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Topological number for an image |
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259 | (1) |
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The winding number on 2D images |
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260 | (3) |
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Topological numbers and catastrophes |
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263 | (2) |
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The deep structure toolbox |
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265 | (6) |
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Detection of singularities |
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265 | (1) |
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265 | (3) |
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268 | (1) |
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Detection of catastrophes |
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268 | (1) |
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General discrete geometry approach |
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269 | (2) |
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From deep structure to global structure |
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271 | (4) |
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271 | (1) |
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Hierarchical pre-segmentation |
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272 | (1) |
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273 | (1) |
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Matching and registration |
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274 | (1) |
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274 | (1) |
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275 | (1) |
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275 | (2) |
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277 | (8) |
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277 | (1) |
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Deblurring with a scale-space approach |
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277 | (4) |
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Less accurate representation, noise and holes |
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281 | (3) |
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284 | (1) |
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285 | (26) |
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285 | (1) |
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Motion detection with pairs of receptive fields |
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286 | (3) |
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Image deformation by a discrete vectorfield |
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289 | (1) |
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The optic flow constraint equation |
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290 | (2) |
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Scalar and density images |
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292 | (1) |
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Derivation of multi-scale optic flow constraint equation |
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292 | (11) |
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Scalar images, normal flow |
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296 | (5) |
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Density images, normal flow |
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301 | (2) |
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Testing the optic flow constraint equations |
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303 | (2) |
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Cleaning up the vector field |
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305 | (2) |
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307 | (2) |
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309 | (1) |
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310 | (1) |
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Color differential structure |
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311 | (18) |
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311 | (1) |
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Color image formation and color invariants |
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311 | (3) |
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Koenderink's Gaussian derivative color model |
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314 | (6) |
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320 | (5) |
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Combination with spatial constraints |
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325 | (2) |
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327 | (2) |
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329 | (16) |
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329 | (1) |
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330 | (1) |
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Orientation analysis with Gaussian derivatives |
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331 | (1) |
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Steering with self-similar functions |
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332 | (4) |
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Steering with Cartesian partial derivatives |
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336 | (2) |
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Detection of stellate tumors |
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338 | (4) |
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Classical papers and student tasks |
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342 | (1) |
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343 | (2) |
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345 | (16) |
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345 | (1) |
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Analysis of prerecorded time-sequences |
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346 | (3) |
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Causal time-scale is logarithmic |
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349 | (2) |
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Other derivations of logarithmic scale-time |
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351 | (2) |
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Real-time receptive fields |
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353 | (1) |
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A scale-space model for time-causal receptive fields |
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354 | (5) |
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359 | (1) |
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360 | (1) |
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Geometry-driven diffusion |
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361 | (32) |
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Adaptive Smoothing and Image Evolution |
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361 | (1) |
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Nonlinear Diffusion Equations |
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362 | (2) |
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The Perona & Malik Equation |
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364 | (2) |
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Scale-space implementation of the P&M equation |
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366 | (4) |
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The P&M equation is ill-posed |
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370 | (2) |
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Von Neumann stability of numerical PDE's |
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372 | (1) |
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Stability of Gaussian linear diffusion |
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373 | (3) |
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A practical example of numerical stability |
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376 | (2) |
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Euclidean shortening flow |
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378 | (1) |
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379 | (1) |
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Numerical examples shortening flow |
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379 | (3) |
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382 | (1) |
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Duality between PDE-and curve evolution |
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383 | (3) |
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386 | (3) |
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Mathematical morphology on grayvalued images |
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389 | (1) |
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Mathematical morphology versus scale-space |
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390 | (1) |
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390 | (3) |
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393 | (2) |
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A. Introduction to Mathematica |
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395 | (18) |
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Quick overview of using Mathematica |
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395 | (2) |
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Quick overview of the most useful commands |
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397 | (4) |
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401 | (1) |
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401 | (3) |
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404 | (1) |
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A faster way to read binary 3D data |
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405 | (2) |
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407 | (3) |
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410 | (2) |
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412 | (1) |
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B. The concept of convolution |
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413 | (6) |
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413 | (3) |
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Convolution is a product in the Fourier domain |
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416 | (3) |
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C. Installing the book and packages |
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419 | (4) |
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419 | (1) |
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Installation for all systems |
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420 | (1) |
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Viewing the book in the Help Browser |
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420 | (1) |
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Sources of additional applications |
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421 | (2) |
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D. First Start with Mathematica: Tips & Tricks |
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423 | (2) |
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423 | (1) |
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423 | (1) |
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424 | (1) |
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424 | (1) |
References |
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425 | (30) |
Index |
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455 | |