Problem Set 1: Edges and Lines

1. Edge image

a0) Input image - a1) Edge image

2. Hough Transform for Lines

a) Hough space - b) Highlighted Peaks - c) Highlighted lines

3. Hough Transform for Lines on Noisy Image

a0) Noisy input Image - a1) Filtered image - b1) Edge image of noisy image - b2) Edge image of filtered image

c1) Hough space of edge image - c2) Noisy input image with highlighted lines

4. Hough Transform for Lines on a more Complex Image

a0) Input image - a1) Filtered input image - b1) Edge image

c1) Hough space - c2) Original input image with highlighted lines

5. Hough Transform for Circles

a0) Input image - a1) Smoothed image - a2) Edge image

a3) Detected circles for r=20px - b1) Detected circles for r in [20,50] px

6. Hough Transform for Lines on Cluttered Image

a0) Input image - a1) Highlighted detected lines - c1) Detected Lines under constraints

c) The boundaries of the pens were extracted by selecting the lines that complied with two constraints. In particular, the selection algorithm only kept the lines that had at least one approximate parallel line (delta_theta < delta_theta_max) and in a distance smaller than rho_max.

7. Hough Transform for Circles on Cluttered Image

a0) Input image - a1) Highlighted circles

8. Hough Transform for Lines and Circles on Distorted Cluttered Image

a0) Input image - a1) Highlighted lines and circles

b) The circles in the distorted input image are actually ellipses and thus cannot be accurately detected by a Hough transform for circles. This could probably be solved by using a Hough transform for ellipses or by applying a homography transform to partially fix the distortion and turn the ellipses back to circles.