Typical Uses of Erosion

Transcription

1 Erosion: Erosion is used for shrinking of element A by using element B One of the simplest uses of erosion is for eliminating irrelevant details from a binary image. Erosion:

2 Erosion

3 Typical Uses of Erosion 1. Removes isolated noisy pixels. 2. Smoothes object boundary(removes spiky edges). 3. Removes the outer layer of object pixels: - Object becomes slightly smaller. - Sets contour pixels of object to background value

4 Erosion Example

5 Erosion explained pixel by pixel A A B B

6 Structuring Element in Erosion Example Image Structuring Element Result

7 How It Works? During erosion, a pixel is turned on at the image pixel under the structuring element origin only when the pixels of the structuring element match the pixels in the image Both ON and OFF pixels should match. This example erodes regions horizontally from the right.

8 Structuring Element in Erosion Example Image Structuring Element Result

9 Structuring Element in Erosion Example Image Structuring Element Result

10 Structuring Element in Erosion Example Image Structuring Element Result

11 Structuring Element in Erosion Example Image Structuring Element Result

12 Structuring Element in Erosion Example Image Structuring Element Result

13 Structuring Element in Erosion Example Image Structuring Element Result

14 Mathematical Definition of Erosion 1. Erosion is the morphological dual to dilation. 2. It combines two sets using the vector subtraction of set elements. 3. Let A B denotes the erosion of A by B A B { x for every b B, exist an a A, x a b} { x x x b A for every b B)

15 Erosion explained pixel by pixel A B A B (1,1) (0,0)= (1,1) (1,2) (0,0)= (1,2) (1,3) (0,0)= (1,3) (1,4) (0,0)= (1,4) (0,4) (0,0)= (0,4) (2,4) (0,0)= (2,4) (3,4) (0,0)= (3,4) (4,4) (0,0)= (4,4) (1,1) (1,0)= (0,1) (1,2) (1,0)= (0,2) (1,3) (1,0)= (0,3) (1,4) (1,0)= (0,4) (0,4) (1,0)= (-1,4) (2,4) (1,0)= (1,4) (3,4) (1,0)= (2,4) (4,4) (1,0)= (3,4)

16 Erosion

17 In MATLAB Codes strel:this function creates amorphological structuring element. SE=strel( shape,parameters) shape parameters disk R line Len,deg square w rectangle [m n] Erosion image: imerode: This function erosion the image. I2=imerode( image,se)

18 Codes A = imread( Image.tif'); figure,imshow(a); se = strel('disk',3); A2 = imerode(a, se); figure,imshow(a2); se = strel('disk',5); A3 = imerode(a, se); figure,imshow(a3); se = strel('disk',10); A4 = imerode(a, se); figure,imshow(a4);

19 Example of Erosions with various sizes of structuring elements Structuring Element Pablo Picasso, Pass with the Cape, 1960

20 Erosion and Dilation summary

21 Boundary Extraction

22 Boundary Extraction First, erode A by B, then make set difference between A and the erosion The thickness of the contour depends on the size of constructing object B

23 Boundary Extraction

24 Edge detection original Dilate Dilate - original

25 Opening & Closing Opening and Closing are two important operators from mathematical morphology They are both derived from the fundamental operations of erosion and dilation They are normally applied to binary images

26 OPENING Opening of A by B, is simply erosion of A by B, followed by dilation of the result by B. A B ( A B) B We use opening for: o Smoothes object boundaries o Eliminates noise (isolated pixels) o Maintains object size

27 OPENING Opening is defined as an erosion followed by a dilation using the same structuring element The basic effect of an opening is similar to erosion but Less destructive than erosion Does not significantly change an object s size

28 Opening Example What combination of erosion and dilation gives: o cleaned binary image o object is the same size as in original Original

29 Opening Example Cont Erode original image. Dilate eroded image. Smoothes object boundaries, eliminates noise (isolated pixels) and maintains object size. Original Erode Dilate

30 CLOSING Closing of A by B, is dilation followed by erosion (opposite to opening). A B ( A B) B We use Closing for: osmoothes object boundaries oeliminates noise (small holes), fills gaps in contours and close up cracks in objects. o Maintains object size.

31 Close Dilation followed by erosion Serves to close up cracks in objects and holes due to pepper noise Does not significantly change object size

32 More examples of Closing What combination of erosion and dilation gives: o cleaned binary image o object is the same size as in original Original

33 More examples of Closing cont Dilate original image. Erode dilated image. Smoothes object boundaries, eliminates noise (holes) and maintains object size. Original Dilate Erode

34 Close = Dilate next Erode Open = Erode next Dilate Original image dilated Open and Close eroded eroded dilated Close Open

35 Spatial Filtering Closing o Opening & Opening o Closing

36 Use of opening and closing for morphological filtering

37 Open and Close Original image; opening; opening followed by closing

38 Codes f = imread('noisy-fingerprint.tif'); figure,imshow(f); se = strel('square', 3); fo = imopen(f,se); figure,imshow(fo); foc = imclose(fo,se); figure,imshow(foc);

39 Possible problems with Morphological Operators Erosion and dilation clean image but leave objects either smaller or larger than their original size. Opening and closing perform same functions as erosion and dilation but object size remains the same.