1. COMP 9517 Computer Vision Binary Image Analysis 4/15/2018
COMP 9517 S2, 2009

2. Binary Image Analysis
How to do this? ?
4/15/2018
COMP 9517 S2, 2009

3. Binary Image Analysis
How to obtain binary images from scale-level images?
How to extract connected groups of pixels (components)?
How to process the separate components?
How to extract properties of components for use in high-level tasks?
4/15/2018
COMP 9517 S2, 2009

4. Binary Image
Definition: A binary image is a digital image with all pixel values 0 or 1
Foreground: a subset of image pixels that are of interest in an image analysis task
Background: the rest of the image
A binary image B can be obtained from a gray-scale image or colour image through a selection operator:
Thresholding: subset of gray tones or colour space
Classification, segmentation, etc
4/15/2018
COMP 9517 S2, 2009

5. Binary Image Example A gray-scale image contains the character “C”
Threshold t=200 to obtain a binary image
1s denote foreground pixels, 0s background pixels 1
4/15/2018
COMP 9517 S2, 2009

6. Binary Image Analysis
Thresholding: convert gray scale image to binary image
Labelling: connected component labelling
Counting: object counting
Thinning & Thickening: join and/or separate components
Component Properties: extract features for higher level processes
4/15/2018
COMP 9517 S2, 2009

7. Applications Document analysis Industrial machine vision
Counting, recognition, localisation and inspection tasks
4/15/2018
COMP 9517 S2, 2009

8. Thresholding
Binary image can be obtained from gray-scale images by thresholding
Choose foreground and background based on the distribution of gray tones
Types of thresholding:
threshold above: p ≥ the threshold t
threshold below: p < t
threshold inside: t1 ≤ p < t2
threshold outside: p < t1 or p ≥ t2
4/15/2018
COMP 9517 S2, 2009

9. How to choose the thresholds
The basis for choosing a threshold is the histogram of the gray-tone image
The histogram h of gray-tone image I is defined by
Where m spans the gray-level values.
4/15/2018
COMP 9517 S2, 2009

10. Compute A Histogram Compute the histogram H of gray-scale image I
Procedure histogram(I,H) {
//Initialise the bins of the histogram to zero.
for i=0 to MaxVal
H[i] = 0;
//Compute values by accumulation.
for r=0 to MaxRow
for c=0 to MaxCol {
grayval = I[r,c];
H[grayval] = H[grayval] + 1; }
4/15/2018
COMP 9517 S2, 2009

11. Threshold from Histogram
Bimodal:
one mode corresponding to dark pixels
the other one corresponding to light pixels
choose any value in the valley between two modes
Overlapped modes – more difficult t t
4/15/2018
COMP 9517 S2, 2009

12. Pixel and Neighbourhoods
Not only the value of a pixel but also its neighbours are used
4-neighbours and 8-neighbours
N4[r,c]: {[r-1,c],[r+1,c],[r,c-1], and [r,c+1]}
N8[r,c]: N4[r,c] + {[r-1,c-1], [r-1,c+1], [r+1, c-1], and [r+1,c-1]}
A pixel [r’,c’] neighbours a pixel [r,c] if [r’,c’] lies in the selected type of neighbourhood of [r,c] N W * E S NW N NE W * E SW S SE
4/15/2018
COMP 9517 S2, 2009

13. Masks
Mask: a set of pixel positions and corresponding values called weights
Origin of a mask: usually the centre of the mask 1 1 2 4 1
4/15/2018
COMP 9517 S2, 2009

14. Applying a Mask Convolution: apply a mask to an image
yields same size output image
for each pixel, place the mask on the image with the mask origin on that pixel
value of pixel under the mask multiplied by the corresponding mask weight
summed up to a single output value for the pixel
4/15/2018
COMP 9517 S2, 2009

15. Example of Applying a Mask40 80
640
800
1120
1280 40 50 70 80 1 2 4
the sum of the weights
4/15/2018
COMP 9517 S2, 2009

16. Example of Applying a Mask40 80 *1 *2 *4 40 80
640 40 80 40 80 *1 *2 *4
640
800 1 2 4
4/15/2018
COMP 9517 S2, 2009

17. Connected Component Labelling
Definition: a connected component labelling of a binary image B is a labelled image LB in which the value of each pixel is the label of its connected component. 1 1 2 3
4/15/2018
COMP 9517 S2, 2009

18. Recursive Labelling B is the original binary image;
LB will be the labelled connected component image.
Recursive_connected_components(B, LB) {
LB = negate(B);
label = 0;
Find_components(LB, label); }
Find_components(LB,label){
for (r=0 to MaxRow)
for (c=0 to MaxCol)
if (LB[r, c]==-1){
label = label + 1;
Search(LB, label, r, c);
Search(LB, label, r, c) {
LB[r, c] = label;
Nset = neighbours(r, c);
for ([r’, c’] in Nset)
if (LB[r’, c’]==-1) Search(LB, label, r, c);
4/15/2018
COMP 9517 S2, 2009

19. Recursive Labelling 4/15/2018 COMP 9517 S2, 2009 1 2 * 3 4 1 -1 1 -1 11 -1 1 -1 1 -1 1 2 -1 1 2 -1
4/15/2018
COMP 9517 S2, 2009

20. Binary Image Morphology
Morphology refers to form, structure and the shape of a region in computer vision
Mathematical morphology: set operations
Structuring element: a shape presented by a binary image, any size and arbitrary structure
Common structuring element: Box, Disk & Ring 1 1 1
4/15/2018
COMP 9517 S2, 2009

21. Basic Morphology Operations
Dilation: enlarges a region
Erosion: makes a region smaller
Closing: closes up internal holes and eliminate bays on boundaries
Opening: gets rid of juts
4/15/2018
COMP 9517 S2, 2009

22. Dilation
Definition: the dilation of a binary image B by structuring element S is denoted by and is defined by
S is swept over B
When the origin of S touches 1 in B, S is ORed to the output image
4/15/2018
COMP 9517 S2, 2009

23. Dilation 1 1 1 S 1 1 1 1 B 1 1 1
4/15/2018
COMP 9517 S2, 2009

24. Erosion
Definition: the erosion of a binary image B by structuring element S is denoted by B S and is defined by
B S
S is swept over B
When every element of S covers a 1-pixel in B, the pixel in B corresponding to the origin of S is ORed to the output image
4/15/2018
COMP 9517 S2, 2009

25. Erosion 1 1 S 1 1 1 1 B 1 1
4/15/2018
COMP 9517 S2, 2009

26. Closing
Definition: The closing of a binary image B by structuring element S is denote by and is defined by 1 S 1 1 1 B
4/15/2018
COMP 9517 S2, 2009

27. Opening
Definition: the opening of a binary image B by structuring element S is denoted by and is defined by 1 S 1 1 1 B
4/15/2018
COMP 9517 S2, 2009

28. Conditional Dilation
Remove noise by erosion, but want to keep entire components
Definition: give an original binary image B, a processed binary image C and a structuring element S, let and The conditional dilation of C by S with respect to B is defined by
where the index m is the smallest index satisfy
4/15/2018
COMP 9517 S2, 2009

29. Conditional Dilation
C is repeatedly dilated by S, and each result is reduce to only the pixels that were 1s in B 1 1 V S 1 1 1 1 B C
AND
4/15/2018
COMP 9517 S2, 2009

30. Other Morphological Algorithms
Boundary extraction
4/15/2018
COMP 9517 S2, 2009

31. Basic Morphological Algorithms
Region Filling
4/15/2018
COMP 9517 S2, 2009

32. Applications of Morphology
Opening & closing to separate components and remove holes
Thresholding
Opening + Closing
4/15/2018
COMP 9517 S2, 2009

33. Applications of Morphology
Industrial inspection – identify defects
hole_ring, hole_mask, gear_body, sampling_ring_spacer, sampling_ring_width, tip_spacing , defect_cue a b c d f g h e
4/15/2018
COMP 9517 S2, 2009

34. Applications of Morphology
Feature extraction
Extract shape corners
Original image B Resultant opening R Corner image C=B-R
4/15/2018
COMP 9517 S2, 2009

35. Region Properties
Properties of the regions as input to higher- level procedures for decision making
Area:
Centroid:
Perimeter
4/15/2018
COMP 9517 S2, 2009

36. Region Properties Perimeter length Circularity Mean radial distance
Standard deviation of radial distance
4/15/2018
COMP 9517 S2, 2009

37. Region Properties Bounding box and extremal points
Extremal axis length
4/15/2018
COMP 9517 S2, 2009

38. Region Properties Second-order row moment Second-order column moment
Second-order mixed moment
4/15/2018
COMP 9517 S2, 2009

39. Region Adjacency Graphs
Definition: a region adjacency graph(RAG) is a graph in which each node represents a region of the image, and an edge connects two nodes if the two regions are adjacent. 1 2 -1 3 -2 -3 1 -1 2 -3 3 -2
4/15/2018
COMP 9517 S2, 2009

40. References
Shaoo, P.K., and others A survey of thresholding techniques. Compu. Vision, Graphics, and Image Proc. V.41:
Rosefeld,A., and J.L. Pfaltz, Sequential operations in digital picture processing. Journal of the Association for Computing Machinery, Vol. 13:
Serra, J Image Analysis and Mathematical Morphology. Academic Press, New York.
4/15/2018
COMP 9517 S2, 2009

41. Acknowledgement
Some material, including images and tables, were drawn from the textbook and Digital Image Processing by Gonzalesz and Woods.
4/15/2018
COMP 9517 S2, 2009