數(shù)字圖像處理mathematicalmorphology(編輯修改稿)
2025-06-20 05:47 本頁面
【文章內(nèi)容簡介】 e properties. Example ?Image analysis consists of obtaining measurements characteristic to images under consideration. ?Geometric measurements (., object location, orientation, area, length of perimeter) Grayscale Images Binary Images Morphological Shape Operators – Objects are opaque and shape information is not additive !! – Shapes are usually bined by means of – Set Union (overlapping objects)： – Set Intersection (occluded objects): X X1 2?X1 X2X X X Xc2 1 1 2\ ? ?X2X1Morphological Shape Operators – Shape operators should distribute over setunions and setintersections (a type of ―linearity‖) ! ? ? ?? ? ?( ) = ( ) ( )X X X X1 2 1 2? ?Morphological Dilation ? ? ?? ? ?( ) = ( ) ( )X X X X1 2 1 2? ?Morphological Erosion Morphological Operators – Erosions and dilations are the most elementary operators of mathematical morphology. – More plicated morphological operators can be designed by means of bining erosions and dilations. Question What is Mathematical Morphology ? A (precise) Mathematical Answer Algebra Complete Lattices Operators ErosionsDilations Mathematical Morphology Topology HitorMiss Geometry Convexity Connectivity Distance Applications Image Processing and Analysis A mathematical tool that studies operators on plete lattices Mathematical Lattice theory for objects or operators in continuous or discrete spaces Topology and stochastic models Translation Invariant Operators ? ?( ) = [ ( )]X Xh hXXhhMorphological Erosion ? ? ?? ? ?( ) = ( ) ( )X X X X1 2 1 2? ?“ LINEARITY” ? ?? ?( ) = [ ( )]X Xh hTRANSLATION INVARIANCE }|{)( XBhBXX h ????? ?Morphological Erosion BhXBX?}|{)( XBhBXX h ????? ?Morphological Erosion Pablo Picasso, Pass with the Cape, 1960 Structuring Element Morphological
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