Binary Image Analysis

1. Binary Image Analysis

2. Binary Image B(r,c) 0 represents the background 1 represents the foreground 00010010001000 00011110001000 00010010001000

3. Binary Image Analysis • is used in a number of practical applications, e.g. • Part inspection • Shape analysis • Enhancement • Document processing

4. What kinds of operations? • Separate objects from background and from one another • Aggregate pixels for each object • Compute features for each object

5. Example: red blood cell image • Many blood cells are separate objects • Many touch – bad! • Salt and pepper noise from thresholding • How useable is this data?

6. Results of analysis • 63 separate objects detected • Single cells have area about 50 • Noise spots • Gobs of cells

7. Binary Image Operations • Thresholding a gray-tone image • Convolution • Morphology • Feature extractions (area, centroid) • Connected components analysis

8. 1. Thresholding • Convert gray level or color image into binary image • Use histogram • Definition: The Histogram of a gray-level image I is defined as • H(m) = { (r,c) : I(r,c) =m) } • Where m spans the gray values

9. Histogram-Directed Thresholding How can we use a histogram to separate an image into 2 (or several) different regions? Is there a single clear threshold? 2? 3?

10. Histogram • Background is black • Healthy cherry is bright • Bruise is medium dark • Histogram shows two cherry regions (black background has been removed) pixel counts 0 256 gray-tone values

11. Automatic Thresholding: Otsu’s Method Grp 1 Grp 2 Assumption: the histogram is bimodal t Method: find the threshold t that minimizes the weighted sum of within-group variances for the two groups that result from separating the gray tones at value t.

12. Thresholding Example original gray tone image binary thresholded image

13. 2. Convolution • Given a gray level image I(r,c) and a mask m(r,c) convolution is I(r,c)*m(r,c)= ΣΣ I(k,l) . m(r-k,m-l) Masks

14. SMOOTHING MASKS

15. Convolution of an İmage with a Mask

17. Image Enhancement WITH AVERAGING AND THRESHOLDING

18. 3. Mathematical Morphology • Morphology: Study of forms of animals and plants • Mathematical Morphology: Study of shapes • Similar to convolution • Arithmetic operations Set Operations

19. Need to define Image as a Set • Given a binary image I (r,c), assume 1 correspond to object 0 correspond to backround. • Define a set with elements to the coordinates of the object • X = { (r1,c1), (r2,c2),….}

20. 111000 111000 000000 000000 • X=

21. Set Operations

22. Set Operations on Images AND, OR

23. TRANSLATION REFLECTION

24. Set Operations

25. Morphologic Operations Binary mathematical morphology consists of two basic operations dilation and erosion and several composite relations closing and opening

26. Dilation: Dilation expands the connected sets of 1s of a binary image. It can be used for 1. growing regions 2. filling holes and gaps

27. Structuring Elements A structuring element is a shape mask used in the basic morphological operations. They can be any shape and size that is digitally representable, and each has an origin. box disk hexagon something box(length,width) disk(diameter)

28. Dilation with Structuring Element S: ={ Z: (Sz)∩ B≠ Φ} B  S The arguments to dilation and erosion are • a binary image B • a structuring element S dilate(B,S) takes binary image B, places the origin of structuring element S over each 1-pixel, and ORs the structuring element S into the output image at the corresponding position. 0 0 0 0 0 1 1 0 0 0 0 0 dilate 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 S B B  S origin

29. DILATION

30. DILATION

31. Erosion BΘS ={ Z: (Sz) B} Erosion shrinks the connected sets of 1s of a binary image. It can be used for 1. shrinking features 2. Removing bridges, branches and small protrusions

32. Erosion with Structuring Elements erode(B,S) takes a binary image B, places the origin of structuring element S over every pixel position, and ORs a binary 1 into that position of the output image only if every position of S (with a 1) covers a 1 in B. origin 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 erode S B B S

33. EROSİON:

34. IMAGE ENHANCEMENT WİTH MORPHOLOGY

35. Example to Try 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 S B 1 1 1 1 1 1 1 1 1 erode dilate with same structuring element

36. Opening and Closing • Closing is the compound operation of dilation followed • by erosion (with the same structuring element) • Opening is the compound operation of erosion followed • by dilation (with the same structuring element)

37. Use of Opening Original Opening Corners • What kind of structuring element was used in the opening? • How did we get the corners?

38. OPENİNG AND CLOSİNG

39. FINGERPRİNT RECOGNİTİON

40. HOW DO YOU REMOVE THE HOLES Hole: A closed backround region surrounded by object pixels

41. Erode with hole ring and dilate with hole mask

42. Morphological Analysis for Bone detection

43. OBJECT DETECTION

44. BOUNDARY EXTRACTİON Boundary: A set of one-pixel-wide connected pixels which has at least one neighbor outside the object

45. BOUNDARY EXTRACTİON

46. Skeleton Finding Skeleton: Set of one-pixel wide connected pixels which are at equal distance from at least two boundary pixels

47. Morphological Image Processing

49. Morphological Operations

50. Morphological Operations