Shih_Image_Processing_and_Mathematical_Morpholo.pdf

viii Contents
3.3 Grayscale Opening and Closing ....................................................... 33
References ................................................................................................... 35
4 Basic Morphological Algorithms .......................................................... 37
4.1 Boundary Extraction ........................................................................... 37
4.2 Region Filling ...................................................................................... 39
4.3 Extraction of Connected Components ............................................. 39
4.4 Convex Hull ......................................................................................... 41
4.5 Thinning .............................................................................................. 43
4.6 Thickening ........................................................................................... 45
4.7 Skeletonization .................................................................................... 45
4.8 Pruning ................................................................................................. 47
4.9 Morphological Edge Operator ........................................................... 48
4.9.1 Simple Morphological Edge Operators .................................. 48
4.9.2 Blur-Minimum Morphological
Edge Operators .......................................................................... 51
References ................................................................................................... 52
5 Basic Morphological Filters .................................................................... 55
5.1 Alternating Sequential Filters ........................................................... 56
5.1.1 Morphological Adjunction ....................................................... 57
5.1.2 Redundancy Removal in ASFs ................................................ 58
5.1.3 Defi nitions of the New Class of ASFs .................................... 59
5.1.4 Properties of the New Class of ASFs ...................................... 61
5.2 Recursive Morphological Filters ....................................................... 67
5.3 Soft Morphological Filters ................................................................. 72
5.3.1 Properties of Soft Morphological Operations ....................... 77
5.3.2 Idempotent Soft Morphological Filters .................................. 78
5.4 OSSM Filters ........................................................................................ 82
5.4.1 One-Dimensional Filtering Analysis ..................................... 84
5.4.2 Two-Dimensional Filtering Analysis ..................................... 85
5.4.3 Relationship between the OSSM
Dilation and Erosion ................................................................ 86
5.4.4 Properties of OSSM Filters and Relationship
to Other Nonlinear Filters ....................................................... 86
5.4.5 Experimental Results ............................................................... 90
5.4.6 Extensive Applications ............................................................. 92
5.5 RSM Filters (RSMFs) ........................................................................... 97
5.5.1 Properties of RSMFs ............................................................... 103
5.5.2 Idempotent RSMFs ................................................................. 105
5.5.3 Cascaded RSMFs ..................................................................... 106
5.6 ROSSM Filters .................................................................................... 107
5.7 Regulated Morphological Filters .................................................... 111
5.8 Fuzzy Morphological Filters ............................................................ 116
References ................................................................................................. 123