Shih_Image_Processing_and_Mathematical_Morpholo.pdf

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Contents ix 6 Distance Transformation .......................................................................... 127 6.1 DT by Iterative Operations .................................................................. 128 6.2 DT by Mathematical Morphology ...................................................... 133 6.3 Approximation of Euclidean Distances ............................................. 136 6.4 Decomposition of Distance SEs........................................................... 139 6.4.1 Decomposition of City-Block and Chessboard Distance SEs ........................................................... 139 6.4.2 Decomposition of the Euclidean Distance Structuring Element ................................................................... 141 6.4.2.1 Construction Procedure ................................................ 141 6.4.2.2 Computational Complexity .......................................... 143 6.5 Iterative Erosion Algorithm ................................................................. 144 6.5.1 Redundant Calculations in the IEA .......................................... 147 6.5.2 An Improved Iterative Erosion Algorithm .............................. 147 6.5.3 An Example of Improved Iterative Erosion Algorithm ............. 150 6.6 Two Scan–Based Algorithm ................................................................ 152 6.6.1 Double Two-Scan Algorithm ..................................................... 152 6.6.2 Basic Ideas of Two-Scan Algorithms ........................................ 157 6.6.3 Fundamental Lemmas ................................................................ 158 6.6.4 TS 1—A Two Scan–Based EDT Algorithm for General Images ...................................................................... 161 6.6.5 TS •—A Two Scan–Based EDT Algorithm for Images with Obstacles .......................................................... 164 6.6.6 Computational Complexity ....................................................... 165 6.7 Three-Dimensional Euclidean Distance ............................................ 168 6.7.1 Three-Dimensional Image Representation .............................. 168 6.7.2 Distance Defi nition Functions in the Three-Dimensional Domain...................................................... 168 6.7.3 A Three-Dimensional Neighborhood in the EDT .................. 169 6.8 Acquiring Approaches ......................................................................... 170 6.8.1 Acquiring Approaches for City-Block and Chessboard DT ............................................................................ 170 6.8.2 Acquiring Approaches for EDT ................................................ 171 6.9 Deriving Approaches ........................................................................... 173 6.9.1 Fundamental Lemmas ................................................................ 174 6.9.2 Two Scan–Based Algorithm for Three-Dimensional EDT ............................................................ 176 6.9.3 Complexity of the Two-Scan-Based Algorithm....................... 179 References ..................................................................................................... 179 7 Feature Extraction ....................................................................................... 183 7.1 Edge Linking by MM ............................................................................ 183 7.1.1 Adaptive MM ................................................................................ 184 7.1.2 Adaptive Morphological Edge-Linking Algorithm ................ 185 7.1.3 Experimental Results .................................................................. 187
x Contents 7.2 Corner Detection by Regulated Morphology .................................... 192 7.2.1 A Modifi ed Laganiere’s Operator .............................................. 194 7.2.2 Modifi ed Regulated Morphology for Corner Detection ......................................................................... 195 7.2.3 Experimental Results .................................................................. 197 7.3 Shape Database with Hierarchical Features ...................................... 199 7.3.1 Shape Number from DT .............................................................200 7.3.2 Signifi cant Points Radius and Coordinates ............................. 202 7.3.3 Recognition by Matching Database .......................................... 202 7.3.4 Localization by Hierarchical Morphological Band-Pass Filter ...........................................................................203 7.4 Corner and Circle Detection ................................................................204 7.5 Size Histogram ......................................................................................206 References ..................................................................................................... 211 8 Object Representation ........................................................................... 213 8.1 Object Representation and Tolerances ........................................... 213 8.1.1 Representation Framework: Formal Languages and MM ................................................................ 214 8.1.2 Dimensional Attributes .......................................................... 215 8.1.2.1 The Two-Dimensional Attributes ............................. 215 8.1.2.2 The Three-Dimensional Attributes .......................... 216 8.1.2.3 Tolerancing Expression .............................................. 218 8.2 Skeletonization or MA Transformation ......................................... 219 8.2.1 Medial Axis Transformation by Morphological Dilations ........................................................ 221 8.2.2 Thick Skeleton Generation ..................................................... 222 8.2.2.1 The Skeleton from Distance Function ...................................................................... 222 8.2.2.2 Detection of Ridge Points ......................................... 223 8.2.2.3 Trivial Uphill Generation ......................................... 223 8.2.3 Basic Defi nitions ...................................................................... 224 8.2.3.1 Base Point .................................................................... 224 8.2.3.2 Apex Point ................................................................... 225 8.2.3.3 Directional-Uphill Generation ................................. 225 8.2.3.4 Directional-Downhill Generation ........................... 226 8.2.4 The Skeletonization Algorithm and Connectivity Properties ........................................................ 227 8.2.5 A Modifi ed Algorithm ........................................................... 230 8.3 Morphological Shape Description .................................................. 231 8.3.1 Introduction ............................................................................ 231 8.3.2 G-Spectrum ............................................................................. 233 8.3.3 The Properties of G-Spectrum ............................................. 234 References ................................................................................................. 242
Page 6: To my loving wife and children, to
Page 9: viii Contents 3.3 Grayscale Opening
Page 13 and 14: xii Contents 10.1.2.3 Additional Si
Page 16 and 17: Preface Image processing and mathem
Page 18 and 19: Preface xvii morphological fi lters
Page 20: Acknowledgments Portions of the boo
Page 23 and 24: xxii Author Dr. Shih has contribute
Page 26 and 27: 1 Introduction to Mathematical Morp
Page 28 and 29: Introduction to Mathematical Morpho
Page 34: Introduction to Mathematical Morpho
Page 37 and 38: 12 Image Processing and Mathematica
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4 Basic Morphological Algorithms In
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Basic Morphological Algorithms 39 N
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Basic Morphological Algorithms 41 0
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Basic Morphological Algorithms 45 i
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Basic Morphological Algorithms 49 F
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Basic Morphological Algorithms 51 s
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Basic Morphological Algorithms 53 S
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56 Image Processing and Mathematica
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100 Image Processing and Mathematic
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7 Feature Extraction Feature extrac
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Feature Extraction 185 morphology f
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Feature Extraction 187 If the cente
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Feature Extraction 189 FIGURE 7.4 A
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Feature Extraction 191 FIGURE 7.8 U
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Feature Extraction 193 FIGURE 7.11
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Feature Extraction 195 (a) (b) (c)
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Feature Extraction 197 The original
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Feature Extraction 205 4. The outpu
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Feature Extraction 207 A question a
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Feature Extraction 209 We present a
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Feature Extraction 211 In additiona
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8 Object Representation Prior to ob
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Object Representation 215 a single
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Object Representation 217 dimension
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Object Representation 219 FIGURE 8.
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Object Representation 221 convergen
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Object Representation 223 - - - - -
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Object Representation 225 than or e
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Object Representation 229 Proof of
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Object Representation 233 analysis,
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Object Representation 235 Propositi
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Object Representation 237 invarianc
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Object Representation 239 We then h
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Object Representation 241 From Equa
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Object Representation 243 Ghosh, P.
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9 Decomposition of Morphological St
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Decomposition of Morphological Stru
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400 Index Base point defi nitions,
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402 Index Decomposition (Continued)
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404 Index Erosion (Continued) sweep
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406 Index H Heijmans, Henk, 5 Hemie
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408 Index Mathematical morphology a
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410 Index O Object representation,
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412 Index Rotational erosion operat
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414 Index Sweep morphology (Continu
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