Morphological Image Processing
- 1. MORPHOLOGICAL IMAGE PROCESSING D.SHUNMUGAKUMARI ASSITANT PROFESSOR DEPARTMENT OF INFORMATION TECHNOLOGY
- 2. INTRODUCTION Morphology About the form and structure of animals and plants Mathematical morphology Using set theory Extract image component Representation and description of region shape
- 3. INTRODUCTION Sets in mathematical morphology represent objects in an image Example ◦ Binary image: the elements of a set is the coordinate (x,y) of the pixels, in Z2 ◦ Gray-level image: the element of a set is the triple, (x, y, gray-value), in Z3
- 4. OUTLINE Preliminaries – set theory Dilation and erosion Opening and closing
- 5. PRELIMINARIES – SET THEORY A be a set in Z2. a = (a1, a2) is an element of A. a is not an element of A Null (empty) set: Aa Aa
- 6. SET OPERATIONS A is a subset of B: every element of A is an element of another set B Union Intersection Mutually exclusive BA BAC BAC BA
- 8. GRAPHICAL EXAMPLES (CONT.) AwwAc BwAwwBA ,
- 9. LOGIC OPERATIONS ON BINARY IMAGES Functionally complete operations AND, OR, NOT
- 10. BA BA AB
- 11. OUTLINE Preliminaries Dilation and erosion Opening and closing
- 12. DILATION )ˆ( ABzBA z B:structuring element
- 13. DILATION Dilation is one of the basic operation in mathematical morphology. Dilation adds the pixels to the Boundaries of an object in an image. Dilation process in which binary image is expanded from its original image. W B
- 14. DILATION FORMULA, f(x) h(s)=max{f(x)+h(s-x)} f(x) original Image EXOR operation s Structuring pattern matching.
- 16. DILATION EXAMPLE Original Image expanded Dilation
- 17. EROSION ABzBA z )( z: displacement B:structuring element
- 18. EROSION (CONT.)
- 19. EROSION •Erosion is the Reverse process of the Dilation. •Erosion Remove the pixel on object boundaries. • B W
- 20. EROSION FORMULA f(x) h(s)=min{f(s+x)+h(x)} f(x) original Image EXNOR operation s Structuring pattern matching.
- 22. EROSION EXAMPLE Original Image EXNOR Erosion
- 23. STRUCTURING ELEMENT The number of pixel added or removed from the object in an image depends on the size and shape structuring element. •It’s s matrix 1’s and 0’s. The center pixel of the structuring element, called the origin.
- 26. DILATION AND EROSION ARE DUALS c z c ABzBA )()( cc z ABz )( )( c z ABz )ˆ( ABzBA z BAc ˆ
- 27. APPLICATION: BOUNDARY EXTRACTION Extract boundary of a set A: First erode A (make A smaller) A – erode(A) )( BAA=
- 28. APPLICATION: BOUNDARY EXTRACTION Using 5x5 structuring elementoriginal image
- 29. OUTLINE Preliminaries Dilation and erosion Opening and closing
- 30. OPENING Dilation: expands image w.r.t structuring elements Erosion: shrink image erosion+dilation = original image Opening= erosion + dilation BBABA )(
- 31. OPENING (CONT.)
- 32. OPENING (CONT.) Smooth the contour of an image, breaks narrow isthmuses, eliminates thin protrusions Find contour Fill in contour
- 33. CLOSING Closing = dilation + erosion BBABA )(
- 34. CLOSING (CONT.) Find contour Fill in contour Smooth the object contour, fuse narrow breaks and long thin gulfs, eliminate small holes, and fill in gaps