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3 | (8) |
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11 | (12) |
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2.1 The General Model with a Fixed Light Source |
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11 | (2) |
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13 | (3) |
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2.3 Shade/Shadows and Specularity |
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16 | (2) |
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2.4 Reduction to an Abstract Classification of Local Maps |
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18 | (1) |
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2.5 The Role of Previous Classifications and Geometric Realizations |
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19 | (4) |
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Part II Mathematical Basis for Analysis of Feature-Shade/Shadow-Contours |
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3 Apparent Contours for Projections of Smooth Surfaces |
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23 | (12) |
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3.1 Projections of Smooth Surfaces |
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23 | (1) |
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3.2 A-equivalence and the Classification of Stable Projection Maps |
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24 | (1) |
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3.3 Classification of Singularities of Local Projection Maps Via A-equivalence |
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25 | (3) |
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3.4 Relations Between Projection Singularities and the Geometry of the Surface |
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28 | (7) |
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4 Abstract Classification of Singularities Preserving Features |
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35 | (6) |
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4.1 Abstract Classifications Preserving Geometric Features |
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35 | (1) |
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4.2 Abstract Classification of Boundary Singularities |
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36 | (2) |
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4.3 Classification of Singularities on a Crease |
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38 | (1) |
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4.4 Classification of Singularities on a Corner |
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38 | (1) |
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4.5 Applications of the Classification to Shade/Shadow Curves |
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39 | (2) |
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5 Singularity Equivalence Groups Capturing Interactions |
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41 | (32) |
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5.1 Equivalence of Views Preserving Shade/Shadow and Geometric Features |
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41 | (3) |
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5.2 Geometric Subgroups of A and K |
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44 | (2) |
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5.3 Unfolding and Determinacy Theorems |
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46 | (1) |
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5.4 vA as a Geometric Subgroup of A |
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47 | (7) |
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5.5 Sufficient Conditions for Special Semianalytic Stratifications |
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54 | (3) |
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5.6 Proofs of the Propositions |
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57 | (8) |
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5.7 Geometric Criterion for Finite vA-determinacy |
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65 | (2) |
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5.8 Relation Between vA and vA Equivalences |
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67 | (2) |
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5.9 S-equivalence and Its Reduction to vA-equivalence |
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69 | (4) |
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6 Methods for Classification of Singularities |
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73 | (28) |
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6.1 Classification of Jets Via Lie Group Methods |
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73 | (1) |
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6.2 Unipotent Group Methods for Order of Determinacy |
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74 | (3) |
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6.3 Complete Transversals for Classification of Jets |
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77 | (2) |
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6.4 Statement of Results on Abstract Classifications |
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79 | (3) |
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6.5 Detailed Treatment of Two Examples |
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82 | (3) |
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6.6 The Abstract Models and Abstract Normal Forms |
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85 | (16) |
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7 Methods for Topological Classification of Singularities |
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101 | (16) |
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101 | (1) |
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7.2 Topological Triviality and Versality for vA-equivalence |
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102 | (1) |
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7.3 Sufficient Conditions for Topological Triviality |
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103 | (1) |
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7.4 Sufficient Conditions for Topological Versality |
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104 | (3) |
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7.5 Applications of Topological Methods to Classification for vA-equivalence |
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107 | (3) |
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7.6 Details of the Calculations for Topological vA-equivalence and Versality |
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110 | (2) |
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7.7 Versal Topological Equivalence of the "Semiswallowtail" Germs |
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112 | (5) |
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Part III The Classification of Interactions Involving Feature-Shade/Shadow-Contours |
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8 Stratifications of Genetically Illuminated Surfaces with Geometric Features |
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117 | (18) |
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8.1 Realizations of Stable Map Germs at Geometric Feature Points |
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117 | (7) |
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8.2 Generic Stratifications Resulting from Geometric Features and Shade/Shadow Curves |
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124 | (7) |
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8.3 Stratifications from Cast Shadows via Multilocal Configurations |
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131 | (2) |
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8.4 Summary of the Physical Interpretations of the Stratifications |
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133 | (2) |
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9 Realizations of Abstract Mappings Representing Projection Singularities |
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135 | (22) |
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9.1 Realizations in General |
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135 | (3) |
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9.2 Geometrical Considerations |
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138 | (6) |
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9.3 Examples of Realizations for Particular Stratifications |
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144 | (13) |
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10 Statements of the Main Classification Results |
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157 | (24) |
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10.1 Overview of the Main Results |
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157 | (4) |
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10.2 Classification of Stable Views and Curve Configurations in the Image |
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161 | (3) |
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10.3 Stable Curve Configurations for the Local and Multilocal Cases |
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164 | (3) |
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10.4 Classification of Generic Transitions of View Projection Mappings s |
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167 | (3) |
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10.5 Classification of Transitions on One-Dimensional Strata |
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170 | (1) |
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10.6 Figures Illustrating the Transitions on One Dimensional Strata |
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171 | (3) |
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10.7 Higher Codimension Transitions |
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174 | (7) |
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Part IV Classifications of Interactions of Pairs of Feature-Shade/Shadow-Contours |
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11 Stable View Projections and Transitions Involving Shade/Shadow Curves on a Smooth Surface (SC) |
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181 | (12) |
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11.1 Summary of Results in the SC Case |
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181 | (1) |
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11.2 Realizations of Fold Shade Singularities (SC) |
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182 | (8) |
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11.3 Comparison of the Present Results with Those of Donati and Stolfi |
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190 | (3) |
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12 Transitions Involving Views of Geometric Features (FC) |
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193 | (22) |
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12.1 Statement of Results |
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193 | (2) |
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12.2 Marking Curve Meeting Edge or Across One Sheet of a Crease |
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195 | (1) |
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12.3 Marking Curve Across Both Sheets of a Crease |
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196 | (2) |
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12.4 The Non transverse Semifold |
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198 | (3) |
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12.5 Classification of Generic Transitions for Apparent Contours and Corners (FC) |
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201 | (14) |
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Part V Classifications of Multiple Interactions |
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13 Transitions Involving Geometric Features and Shade/Shadow Curves (SFC) |
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215 | (28) |
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13.1 Classifications of Generic Transitions for Triple Interactions (SFC) |
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215 | (2) |
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13.2 Generic Transitions of Apparent Contours on Marking or Edge Curves with Shade/Shadow Curves or V or C1 Parabola Cast-Shadow Points |
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217 | (5) |
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13.3 Generic Transitions of Apparent Contours on Creases with Shade/Shadow Curves |
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222 | (2) |
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13.4 Ridge Crease with Cast Shadow of Crease or Shade Curve on One Sheet |
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224 | (3) |
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13.5 Valley Crease with Shade Curve on One Sheet and Cast Shadow of the Shade Curve on the Other Sheet |
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227 | (4) |
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13.6 Generic Transitions of Apparent Contours on Corners with Shade/Shadow Curves (SFC) |
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231 | (12) |
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14 Classifications of Stable Multilocal Configurations and Their Generic Transitions |
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243 | (10) |
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14.1 Classifying the vA-Stable Multigerms |
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243 | (3) |
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14.2 Classifying the Stable Multi-View Projections |
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246 | (2) |
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14.3 Classifying the Generic Transitions for Multi-View Projections... |
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248 | (5) |
| References |
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253 | |
Lisainfo e-raamatute kohta