Edge linking in image processing

This manuscript addresses the edge linking operation and basic of Hough transform.

1. Image Segmentation-2
Subject: Image Procesing & Computer Vision
Dr. Varun Kumar
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 1 / 10

2. Outlines
1
Linking of edge points
Local processing
Global processing (Hough transform)
2
References
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 2 / 10

3. Previous discussion
Edge in an image
It is a region, where the image intensity changes drastically.
Methods for edge points detection:
1
Local processing
2
Global processing
Note:Ideally discontinuity detection techniques should identify pixels
lying on the boundary between regions.
)In practice there may be breaks in boundary and spurious intensity
discontinuities.
1
2
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 3 / 10

4. Local processing:
Take an edge detected image.
Analyze each pixel in small neighborhood of every point (x,y).
All points that are similar in nature are linked.
This forms a boundary of pixels that are similar in nature.
Similarity
Strength of the response of the gradient operator
Direction of gradient
Edge pixels (x
0
;y
0
) and (x;y) are similar, if
jrf(x;y) rf(x
0
;y
0
)j T
and
jrf(x;y)rf(x
0
;y
0
)j<A(x
0
;y
0
)2Nxy
Here,T!Non-negative threshold andA!Angle threshold
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 4 / 10

5. Global processing (Hough transform)
Note:
If intercept and slope remain constant then innite number of points
can exist in the given liney=mx+c.
In Fig.2, (x;y) is supposed to be constant andc and mare variable.
For xed point (x;y), there may exist innite number of lines for
dierentcandm.
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 5 / 10

6. Hugh transform
Let (xk;yk) is a image point that is mapped into amcplane
c=mxk+yk
Heremvaries frommmintommax.
mp)cqand A(p;q)!A(p;q) + 1
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 6 / 10

7. Continued{
Let=xcos+ysin!Normal form
=90
o
=
p
M
2
+N
2
whereMN!Image size
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 7 / 10

8. Continued{
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 8 / 10

9. Important observation (Hough transform)
when c and m are variable
1
Our image location (x,y) remain constant, we changecandm.
2
By changingcandm,we get innite number of lines.
3
We put some thresholding criteria, that gives us the more suitable
line. These lines can be treated as the edge line.
whenandare variables
1
Similarly in normal form, if x and y remain constant, and by changing
and, innite numbers of line can be drawn.
2
By applying the thresholding criteria, we can get the more suitable
line that will be our edge line..
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 9 / 10

10. References
M. Sonka, V. Hlavac, and R. Boyle,Image processing, analysis, and machine vision.
Cengage Learning, 2014.
D. A. Forsyth and J. Ponce, \A modern approach,"Computer vision: a modern
approach, vol. 17, pp. 21{48, 2003.
L. Shapiro and G. Stockman, \Computer vision prentice hall,"Inc., New Jersey,
2001.
R. C. Gonzalez, R. E. Woods, and S. L. Eddins,Digital image processing using
MATLAB. Pearson Education India, 2004.
Subject: Image Procesing & Computer VisionDr. Varun Kumar(IIIT Surat)Lecture 27 10 / 10