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Digital Image Processing – Homework 5 solution

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EE420 – Digital Image Processing – Homework 5
Deliverables & Questions
1. The MATLAB code is attached to this PDF in a ‘/code’ folder.
2. The expressions for a ,b listed in Eq.(2) have different sign for ρ (cosθ ) and ρ (sin θ) because the
positive angle theta is growing in the negative direction of y. Meaning that ye is growing in the
negative y position. xe, on the other hand, is growing with x, and there for has a positive sign
(according to figure 2):
3. My estimate radius of the colored chips was 24. I used the function ‘imfindcircles()’ of the
image to find the radii of all the circles in the image.

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EE420 – Digital Image Processing – Homework 5
Deliverables & Questions
1. The MATLAB code is attached to this PDF in a ‘/code’ folder.
2. The expressions for a ,b listed in Eq.(2) have different sign for ρ (cosθ ) and ρ (sin θ) because the
positive angle theta is growing in the negative direction of y. Meaning that ye is growing in the
negative y position. xe, on the other hand, is growing with x, and there for has a positive sign
(according to figure 2):
3. My estimate radius of the colored chips was 24. I used the function ‘imfindcircles()’ of the
image to find the radii of all the circles in the image.
My parameters for the Canny edge detector were [0.05 0.15], and I found there using trial and
error – changed the values until I found the best ones.
4. I was able to detect all 28 circles in the image.
5. When I pick a large value for the threshold in houghpeaks, I could detect less circles.
For example, for threshold = 200, I could only detect 5 circles:
6. When I pick a small value for the threshold in houghpeaks, I could detect all of the circles.
For example, for threshold = 0.0000001:
I think that with such a small threshold, with a different image, the function would recognize
other non-circle shapes as circles (in this image there are not a lot of other shapes besides the
coins).
7. The yellow coins detected by the code:
8. Screenshots of the original image, output of Canny edge detector, the Hough Space diagram
with the peaks overlaid:
Original image:
Output of Canny edge detector:
Hough Space diagram with the peaks overlaid: