2. Morphology Structural processing of images

3. Image Processing and Computer Vision: 33 Morphological Transformations Set theoretic methods of extracting quantitative descriptions of image components Boundaries Skeletons Convex hull Mainly binary, sometimes greylevel Two fundamental operations Erode, dilate

4. Image Processing and Computer Vision: 34 Thresholding Morphological operations usually applied to bilevel images (black and white) Generated by thresholding Greyscale Colour

5. Image Processing and Computer Vision: 35 Thresholding Greyscale Images Previous lecture If g(x,y) >  then g(x,y) = 1 else g(x,y) = 0

6. Image Processing and Computer Vision: 36 Thresholding Colour Images Partition colour cube: ifc r (x,y) >  r AND c g (x,y) >  g AND c b (x,y) >  b then c(x,y) = 1 else c(x,y) = 0

7. Image Processing and Computer Vision: 37 Thresholding Colour Images Colour matching

8. Image Processing and Computer Vision: 38 Preliminary Notation Translation of a region by x Reflection of a region

9. Image Processing and Computer Vision: 39 Formally Informally place the structuring element on a pixel of the object remove that pixel if the structuring element overlaps a non-object pixel Binary Erode

10. Image Processing and Computer Vision: 310 Binary Dilate Formally Informally All pixels covered by structuring element placed at all locations on region

11. Image Processing and Computer Vision: 311 Binary Open and Close Erosion shrinks an object Dilation expands it Can combine operators Open = erosion then dilation Close = dilation then erosion

12. Image Processing and Computer Vision: 312 Binary Open Opening smoothes regions Removes spurs Breaks narrow lines

13. Image Processing and Computer Vision: 313 Example Binary image DilateErode

14. Image Processing and Computer Vision: 314 Binary Close Closing fills gaps Holes in region Narrow gaps

15. Image Processing and Computer Vision: 315 Processing grey scale images Same methods can be applied to greyscale images Slight redefinition

16. Image Processing and Computer Vision: 316 Greyscale Erode Set operation replaced by min operation Output at a point is minimum of image pixel and structuring element pixel

17. Image Processing and Computer Vision: 317 Greyscale Dilate Set operation replaced by max operation Output is maximum of image and structuring element

18. Image Processing and Computer Vision: 318 Examples ErodeDilate

19. Image Processing and Computer Vision: 319 Distance Applies to binary images For each pixel in a region distance = minimum path to outside 00000 01110 01110 01110 00000 00000 01110 01210 01110 00000

20. Image Processing and Computer Vision: 320 Computation Use erosion Label removed pixel with iteration number Use relationship operator f(i,j) are neighbours of f(x,y)

21. Image Processing and Computer Vision: 321 Skeleton Reduces regions of a binary image to lines one pixel thick Preserves Shape Continuity How? Uses?

22. Image Processing and Computer Vision: 322 Algorithms Thinning Repeatedly thin image Retain end points and connections Distance Transform Skeleton lies along discontinuities Sort of local maxima or ridges

23. Image Processing and Computer Vision: 323 Applications Shape representation, maintaining topology Character recognition

24. Image Processing and Computer Vision: 324 Convex Hull Convex hull follows outline of object, except for concavities. Number and shape of regions between convex hull and object are characteristic of object shape.

25. Image Processing and Computer Vision: 325 Summary Binary morphology Erode, dilate, open, close Greyscale morphology Erode, dilate Distance Skeleton Convex Hull

26. Image Processing and Computer Vision: 326 Computers in the future may weigh no more than 1 ½ tons Popular Mechanics, 1949