Session 2 – Hough Transformation Ashay Tejwani. Video Processing In the last session we saw that an image can be represented by an array of RGB values.

Image Processing Workshop

Session 2 – Hough TransformationAshay Tejwani

Video ProcessingIn the last session we saw that an image can

be represented by an array of RGB values.

In video processing we:Break down the video into separate framesExtract each image as an arraySimply apply the relevant image processing

techniques.

Hough Transform

Why do we need it?Consider assessing this image:

So what does it do?Useful for detecting Parametric curves (such

as lines, circles, conics).Relatively unaffected by:

GapsNoise

How does it Work?The theory behind Hough Transform

An ExampleUsing Edge Detection Algorithm

1 2

4

5

3

An ExampleLet us consider a coordinate system

1 2

4

5

3

X

Y

Represent all lines in terms of R and Theta

Convention

4

5

X

Y1 2

3

ProcedureSelect one point at

a time, and consider all the combinations of R and Theta for which the line would pass through the given point.

4

5

X

Y1 2

3

LimitsBefore we start off, we

need to set a limit to the max and min values of R and Theta.

Min R=0,Max R= image diagonal

Min Theta=-90Max Theta=+904

5

X

Y1 2

3

(142,142)

(0,100)

An ExampleR=Xcos(Θ) + Y

sin(Θ)

For point 1, all lines will have R=0

4

5

X

Y1 2

3

(142,142)

(0,100)

An ExampleFor Point 2,

R=100, Theta=0R=70.7, Theta=45

For Point 3,R=100, Theta=90R=70.7, Theta=45

Plotting these in the 2-D array:

4

5

X

Y1 2

3

(142,142)

(0,100)

Plotting acceptable R- Θ pairs

R

The t a

Rmax

ThetamaxThetamin

Rmin

ResultThe points of intersection of these plots give

us a value of R and Θ. These R and Θ represent the lines passing

through the two points.

How to Code this?Open CV style

The logic- Voting!We create a 2-D matrix of all possible R and

Θ values.For each edge point you detect, consider all

the valid values of R and Θ.Increment the element of the array by 1 each

time it is valid for a point – Each point ‘votes’ for a valid line.

Which is equivalent to converting this into a matrix

R

The t a

Rmax

ThetamaxThetamin

Rmin

This matrix represents Hough SpaceTheta

R

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 1 1

0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 1 0 0 0 0

2 1 1 1 2 1 1 1 1 2

0 1 0 1 0 0 0 0 1 0

0 0 2 0 0 0 0 1 0 0

1 1 0 1 0 0 1 0 0 0

0 0 0 0 1 1 0 0 0 0

ResultFrom this array, we find all local Maxima.These correspond to the pair of R- Θ of lines

which pass through the given group of points.

AlgorithmFor all X{

For all Y{ if(edge point at (x,y)){ for all theta{

R= x*cos(theta) + y*sin(theta);increment one to the cell in the matrix

corresponding to R, theta.End all loops

Practical usage

Thank you