Hough Transforms

Question 1

How do we convert the equation

y = mx +c

into a straight line equation in

Hough Parameter Space?

Answer 1

c = -xm +y

This gives us a straight line equation for the parameters c and m.

Question 2

How do we find the line that goes through the most number of points?

Answer 2

Figure out the hough line for each point.

Select the parameters at the point where the most lines cross.

Question 3

How are hough transforms done programmatically?

Answer 3

Create a large 2d table for the m and c values.

For each line, increment the entry in the table if the line passes through that point.

Threshold on the entries, to figure out what counts as a line

Question 4

Why is it problematic to use Cartesian co-ordinates with hough lines?

Answer 4

When our line is vertical. m will be infinity.

Instead we use polar co-ordinates

Question 5

Given a point (X,Y),

how would we get the lines that go through this point in polar co-ordinates?

Answer 5

r = Xcos(theta) + Ysin(theta)

where r and theta are the parameters we vary to get the different lines