Homework-7
Question 1
You are given a picture with 5 point at the following (x, y) coordinates:
(1,3), (2,1), (2,5), (3,3), (3,5)
Apply the Hough Transform algorithm to search for circles in the parametric representation
(x − x0)
2 + (y − y0)
2 = r
2
.
Quantize r
2
into three values: 2, 3, 4.
Quantize x0 into four values: −1, 1, 3, 5.
Quantize y0 into four values: −1, 1, 3, 5.
Follow these steps:
Initialization: Prepare and initialize to 0 the three dimensional accumulator space. You can visualize it
(and write it in your notebook) as 3 two dimensional arrays. The first for r
2 = 2, the second for r
2 = 3,
and the third for r
2 = 4.
Voting: for each point (x, y) of the five picture points
for each possible value of x0
for each possible value of y0
{
compute r
2
from the equation r
2 = (x − x0)
2 + (y − y0)
2
If r
2
is in the range 2–4 vote by incrementing the corresponding cell
}
(Notice that this requires calculating r
2 80 times.)
Choose a winner determine the cell with max number of votes.
a. What are the values of the accumulator space after the voting phase?
b. What is the most likely circle?
