Preface |
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xv | |
Acknowledgments |
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xix | |
Author |
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xxi | |
1 Introduction to Mathematical Morphology |
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1 | |
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1.1 Basic Concept in Digital Image Processing |
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2 | |
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1.2 Brief History of Mathematical Morphology |
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5 | |
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1.3 Essential Morphological Approach to Image Analysis |
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5 | |
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7 | |
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7 | |
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Appendix: Selected List of Books on Image Processing and Mathematical Morphology |
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9 | |
2 Binary Morphology |
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11 | |
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2.1 Set Operations on Binary Images |
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11 | |
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2.2 Logical Operations on Binary Images |
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13 | |
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15 | |
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2.3.1 Properties of Dilation |
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17 | |
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17 | |
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2.4.1 Properties of Erosion |
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18 | |
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20 | |
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2.5.1 Properties of Opening and Closing |
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21 | |
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2.6 Hit-or-Miss Transformation |
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22 | |
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24 | |
3 Grayscale Morphology |
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25 | |
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3.1 Grayscale Dilation and Erosion |
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26 | |
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3.2 Grayscale Dilation Erosion Duality Theorem |
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32 | |
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3.3 Grayscale Opening and Closing |
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33 | |
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35 | |
4 Basic Morphological Algorithms |
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37 | |
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37 | |
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39 | |
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4.3 Extraction of Connected Components |
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41 | |
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43 | |
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45 | |
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4.9 Morphological Edge Operator |
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4.9.1 Simple Morphological Edge Operators |
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48 | |
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4.9.2 Blur-Minimum Morphological Edge Operators |
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51 | |
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52 | |
5 Basic Morphological Filters |
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55 | |
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5.1 Alternating Sequential Filters |
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56 | |
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5.1.1 Morphological Adjunction |
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57 | |
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5.1.2 Redundancy Removal in ASFs |
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58 | |
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5.1.3 Definitions of the New Class of ASFs |
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59 | |
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5.1.4 Properties of the New Class of ASFs |
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61 | |
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5.2 Recursive Morphological Filters |
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67 | |
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5.3 Soft Morphological Filters |
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5.3.1 Properties of Soft Morphological Operations |
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5.3.2 Idempotent Soft Morphological Filters |
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78 | |
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5.4.1 One-Dimensional Filtering Analysis |
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5.4.2 Two-Dimensional Filtering Analysis |
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5.4.3 Relationship between the OSSM Dilation and Erosion |
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86 | |
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5.4.4 Properties of OSSM Filters and Relationship to Other Nonlinear Filters |
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86 | |
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5.4.5 Experimental Results |
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90 | |
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5.4.6 Extensive Applications |
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92 | |
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5.5.1 Properties of RSMFs |
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103 | |
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105 | |
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106 | |
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107 | |
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5.7 Regulated Morphological Filters |
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111 | |
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5.8 Fuzzy Morphological Filters |
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116 | |
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123 | |
6 Distance Transformation |
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127 | |
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6.1 DT by Iterative Operations |
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128 | |
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6.2 DT by Mathematical Morphology |
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133 | |
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6.3 Approximation of Euclidean Distances |
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136 | |
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6.4 Decomposition of Distance SEs |
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139 | |
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6.4.1 Decomposition of City-Block and Chessboard Distance SEs |
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6.4.2 Decomposition of the Euclidean Distance Structuring Element |
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6.4.2.1 Construction Procedure |
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141 | |
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6.4.2.2 Computational Complexity |
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143 | |
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6.5 Iterative Erosion Algorithm |
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144 | |
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6.5.1 Redundant Calculations in the IEA |
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147 | |
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6.5.2 An Improved Iterative Erosion Algorithm |
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147 | |
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6.5.3 An Example of Improved Iterative Erosion Algorithm |
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150 | |
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6.6 Two Scan-Based Algorithm |
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152 | |
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6.6.1 Double Two-Scan Algorithm |
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6.6.2 Basic Ideas of Two-Scan Algorithms |
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6.6.4 TS1—A Two Scan-Based EDT Algorithm for General Images |
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161 | |
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6.6.5 TSinfinity—A Two Scan-Based EDT Algorithm for Images with Obstacles |
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164 | |
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6.6.6 Computational Complexity |
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165 | |
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6.7 Three-Dimensional Euclidean Distance |
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168 | |
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6.7.1 Three-Dimensional Image Representation |
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6.7.2 Distance Definition Functions in the Three-Dimensional Domain |
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6.7.3 A Three-Dimensional Neighborhood in the EDT |
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6.8.1 Acquiring Approaches for City-Block and Chessboard DT |
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6.8.2 Acquiring Approaches for EDT |
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6.9.2 Two Scan-Based Algorithm for Three-Dimensional EDT |
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6.9.3 Complexity of the Two-Scan-Based Algorithm |
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7 Feature Extraction |
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183 | |
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184 | |
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7.1.2 Adaptive Morphological Edge-Linking Algorithm |
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185 | |
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7.1.3 Experimental Results |
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187 | |
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7.2 Corner Detection by Regulated Morphology |
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192 | |
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7.2.1 A Modified Laganiere's Operator |
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194 | |
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7.2.2 Modified Regulated Morphology for Corner Detection |
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7.2.3 Experimental Results |
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197 | |
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7.3 Shape Database with Hierarchical Features |
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7.3.1 Shape Number from DT |
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7.3.2 Significant Points Radius and Coordinates |
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7.3.3 Recognition by Matching Database |
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7.3.4 Localization by Hierarchical Morphological Band-Pass Filter |
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7.4 Corner and Circle Detection |
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8 Object Representation |
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213 | |
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8.1 Object Representation and Tolerances |
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8.1.1 Representation Framework: Formal Languages and MM |
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214 | |
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8.1.2 Dimensional Attributes |
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8.1.2.1 The Two-Dimensional Attributes |
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8.1.2.2 The Three-Dimensional Attributes |
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216 | |
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8.1.2.3 Tolerancing Expression |
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218 | |
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8.2 Skeletonization or MA Transformation |
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219 | |
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8.2.1 Medial Axis Transformation by Morphological Dilations |
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221 | |
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8.2.2 Thick Skeleton Generation |
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8.2.2.1 The Skeleton from Distance Function |
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8.2.2.2 Detection of Ridge Points |
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223 | |
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8.2.2.3 Trivial Uphill Generation |
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8.2.3.3 Directional-Uphill Generation |
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8.2.3.4 Directional-Downhill Generation |
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226 | |
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8.2.4 The Skeletonization Algorithm and Connectivity Properties |
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8.2.5 A Modified Algorithm |
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230 | |
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8.3 Morphological Shape Description |
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231 | |
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8.3.3 The Properties of G-Spectrum |
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242 | |
9 Decomposition of Morphological Structuring Elements |
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9.1 Decomposition of Geometric-Shaped SEs |
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9.1.1 Definitions of Types of SEs |
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246 | |
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9.1.2 Decomposition Properties |
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249 | |
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9.1.3 One-Dimensional Geometric-Shaped SEs |
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252 | |
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9.1.3.1 Semicircle, Semiellipse, Gaussian, Parabola, Semihyperbola, Cosine, and Sine |
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252 | |
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9.1.3.2 Decomposition Strategy |
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252 | |
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9.1.4 Two-Dimensional Geometric-Shaped SEs |
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257 | |
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9.1.4.1 Hemisphere, Hemiellipsoid, Gaussian, Elliptic Paraboloid, and Hemihyperboloid |
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257 | |
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9.1.4.2 Decomposition Strategy |
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258 | |
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9.1.5 Decomposition of a Large Transformed Cyclic Cosine Structuring Element |
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260 | |
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9.1.6 Decomposition of Two-Dimensional SEs into One-Dimensional Elements |
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263 | |
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9.2 Decomposition of Binary SEs |
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263 | |
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9.2.1 Overview of Decomposition Using GAs |
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264 | |
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9.2.2 Advantages of Structuring Element Decomposition |
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9.2.3 The Decomposition Technique Using GAs |
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266 | |
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9.2.4 Experimental Results |
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270 | |
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9.3 Decomposition of Grayscale SEs |
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272 | |
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9.3.1 General Properties of Structuring Element Decomposition |
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275 | |
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9.3.2 The One-Dimensional Arbitrary Grayscale Structuring Element Decomposition |
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275 | |
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9.3.3 The Two-Dimensional Arbitrary Grayscale Structuring Element Decomposition |
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280 | |
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9.3.4 Complexity Analysis |
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283 | |
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286 | |
10 Architectures for Mathematical Morphology |
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289 | |
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10.1 Threshold Decomposition of Grayscale Morphology into Binary Morphology |
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290 | |
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10.1.1 Threshold Decomposition Algorithm for Grayscale Dilation |
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290 | |
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10.1.1.1 Notations and Definitions |
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291 | |
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10.1.1.2 Formulas' Derivation |
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293 | |
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10.1.1.3 Algorithm Description |
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295 | |
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10.1.1.4 Computational Complexity |
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298 | |
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10.1.2 A Simple Logic Implementation of Grayscale Morphological Operations |
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300 | |
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10.1.2.1 Binary Morphological Operations |
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10.1.2.2 Grayscale Morphological Operations |
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301 | |
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10.1.2.3 Additional Simplification |
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304 | |
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10.1.2.4 Implementation Complexity |
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304 | |
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10.2 Implementing Morphological Operations Using Programmable Neural Networks |
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306 | |
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10.2.1 Programmable Logic Neural Networks |
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10.2.2 Pyramid Neural Network Structure |
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311 | |
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10.2.3 Binary Morphological Operations by Logic Modules |
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312 | |
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10.2.4 Grayscale Morphological Operations by Tree Models |
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10.2.5 Improvement by Tri-Comparators |
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316 | |
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10.2.6 Another Improvement |
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10.2.7 Application of Morphological Operations on Neocognitron |
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320 | |
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10.3 MLP as Processing Modules |
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321 | |
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10.4 A Systolic Array Architecture |
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329 | |
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10.4.1 Basic Array Design |
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329 | |
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10.4.2 A Systolic Array for Processing One Scan of the Whole Image |
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332 | |
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10.4.3 The Complete Systolic Array for Processing Two Scans of the Whole Image |
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333 | |
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10.5 Implementation on Multicomputers |
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333 | |
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10.5.1 Characteristics of Multicomputers |
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334 | |
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10.5.2 Implementation of the Two-Scan Algorithm |
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335 | |
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10.5.3 Implementation of the Blocked Two-Scan Algorithm |
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336 | |
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10.5.4 Performance of Two-Scan Algorithms |
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11 General Sweep Mathematical Morphology |
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341 | |
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342 | |
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11.2 Theoretical Development of General Sweep MM |
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343 | |
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11.2.1 Computation of Traditional Morphology |
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344 | |
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11.2.3 Properties of Sweep Morphological Operations |
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348 | |
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11.3 Blending of Sweep Surfaces with Deformations |
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350 | |
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354 | |
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11.6 Geometric Modeling and Sweep MM |
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357 | |
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11.6.1 Tolerance Expression |
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360 | |
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11.6.2 Sweep Surface Modeling |
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361 | |
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11.7 Formal Language and Sweep Morphology |
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361 | |
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11.7.1 Two-Dimensional Attributes |
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363 | |
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11.7.2 Three-Dimensional Attributes |
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364 | |
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366 | |
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11.8.1 Two-Dimensional Attributes |
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366 | |
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11.8.2 Three-Dimensional Attributes |
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369 | |
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370 | |
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373 | |
12 Morphological Approach to Shortest Path Planning |
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377 | |
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378 | |
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12.2 Relationships between Shortest Path Finding and MM |
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379 | |
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380 | |
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380 | |
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382 | |
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12.4 The Shortest Path—Finding Algorithm |
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383 | |
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12.4.1 Distance Transform |
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383 | |
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12.4.2 Describing the Algorithm |
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384 | |
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12.5 Experimental Results and Discussions |
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386 | |
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12.6 Dynamic Rotational MM |
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391 | |
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12.7 The Rule of Distance Functions in Shortest Path Planning |
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397 | |
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397 | |
Index |
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399 | |