Complexity ends here!

2. The Hough transform is a feature extraction
technique used in image analysis, computer
vision, and digital image processing. The
purpose of the technique is to find imperfect
instances of objects within a certain class of
shapes by a voting procedure.

3. More accurately,

4. Simple Visual Instance Of Hough Transform

5. Hough-transform is best known as a method "to find
Straight Lines" in an image. Unfortunately, people who
encounter the concept for the first time.

6. Hough-transform Visualize Instance of Edges

7. Hough-transform
Visualize Instance
of Face Indeed

8. It was initially invented for machine analysis of
bubble chamber photographs (Hough, 1959).
The Hough transform was patented as “U.S.
Patent 3,069,654” in 1962 and assigned to the
U.S. Atomic Energy Commission with the name
"Method and Means for Recognizing Complex
Patterns". This patent uses a slope-intercept
parameterization for straight lines, which
awkwardly leads to an unbounded transform
space since the slope can go to infinity.

9. And at first used to find lines in images a
decade later by Duda in 1972.

10. o The goal is to find the location of lines in
images.
o This problem could be solved by e.g.
Morphology and a linear structuring element,
or by correlation.
o We would need to handle rotation, zoom,
distortions etc.
o Hough transform can detect lines, circles and
other structures if their parametric equation is
known.
o It can give robust detection under noise and
partial occlusion.

11.  As a simple example, consider the common
problem of fitting a set of line segments to a set of
discrete image points (e.g. pixel locations output
from an edge detector).
Following Figure shows some possible solutions to
this problem. Here the lack of a priori knowledge
about the number of desired line segments (and the
ambiguity about what constitutes a line segment)
render this problem under-constrained.

12. Figure:
a) Coordinate points. b)
and c) Possible straight line
fittings.

13. We can analytically describe a line segment in a
number of forms. However, a convenient
equation for describing a set of lines uses
parametric or normal notion:

14. Where “r” is the length of a normal from the
origin to this line and “θ” is the orientation of
with respect to the X-axis. (See Figure 2.) For
any point “(x,y)” on this line, “r” and “θ” are
constant.

15. Figure 2: Parametric description of a straight
line.

16. o The input image must be a thresholded edge
image.
o The magnitude results computed by the Sobel
o Operator can be thresholded and used as input.

17. Thresh Holed Edges

18. Prior to applying Hough transform:
Compute edge magnitude from input image.
As always with edge detection, simple lowpass
filtering can be applied first.
Threshold the gradient magnitude image.

19. Prior to applying Hough transform:

20. Quantize the parameter space (a,b), that is, divide
it into cells.
This quantized space is often referred to as the
accumulator cells.
In the figure in the next slide a(min) is the
minimal value of a cell.
Count the number of times a line intersects a
given cell.
– For each point (x,y) with value 1 in the binary
image, find the values of (a,b) in the range
[a(min),a(max)],[b(min),b(max)] defining the line
corresponding to this point.

21. – Increase the value of the accumulator for
these (a',b') point.
– Then proceed with the next point in the
image.
Cells receiving a minimum number of “votes”
are assumed to correspond to lines in (x,y)
space.
– Lines can be found as peaks in this
accumulator space.

23. Here I want to Finish my
Presentation about Hough
Transform.
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