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Canny Edge Detection Assignment, Assignments of Computer Science

University of California - San DiegoComputer Science

An assignment on implementing the canny edge detector, including filtering, nonmaximum suppression, and hysteresis thresholding and linking. It also provides instructions on how to apply the edge detector to test images with varying parameters.

Typology: Assignments

Pre 2010

Uploaded on 03/28/2010

koofers-user-ovw
koofers-user-ovw 🇺🇸

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Assignment 2
Due: May 1
Part I: Written Problems
1. Consider modeling a camera with a pinhole model. Let the image
plane be an array of 640 by 480 square pixels that is located 25mm
from the center of projection. Let the image plane be 20mm in the
horizontal direction.
a. In degrees, what is the horizontal and vertical field of view? Show
your work.
b. Consider imaging a plane that is known to be located precisely
1mfrom the optical center and parallel to the image plane, and you
are told that your edge detector has an accuracy of 0.3 pixel. For an
edge detected at the very center of the image, how accurately can you
locate the edge in 3D?
c. If the edge is detected (+200, +200) pixels from the center, how
accurately can you locate the edge in 3D? Is it the same as your answer
to part b?
2. Given two 1-D signals f(x) and g(x), show that
d
dx[f(x)∗g(x)] = df(x)
dx
∗g(x)
and that
d
dx[f(x)∗g(x)] = f(x)∗
dg(x)
dx
where ∗denotes convolution.
Part II: Canny Edge Detector
Your goal is to implement the Canny edge detector as described in the text
(Trucco and Veri) including the three main steps of filtering, nonmaximum
suppression, and hysteresis thresholding and linking. You will apply your
edge detector to a set of images found on the web page. You should be able
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Assignment 2

Due: May 1

Part I: Written Problems

  1. Consider modeling a camera with a pinhole model. Let the image plane be an array of 640 by 480 square pixels that is located 25mm from the center of projection. Let the image plane be 20mm in the horizontal direction. a. In degrees, what is the horizontal and vertical field of view? Show your work. b. Consider imaging a plane that is known to be located precisely 1 m from the optical center and parallel to the image plane, and you are told that your edge detector has an accuracy of 0.3 pixel. For an edge detected at the very center of the image, how accurately can you locate the edge in 3D? c. If the edge is detected (+200, +200) pixels from the center, how accurately can you locate the edge in 3D? Is it the same as your answer to part b?
  2. Given two 1-D signals f(x) and g(x), show that

d dx [f (x) ∗ g(x)] = df (x) dx ∗ g(x)

and that

d dx [f (x) ∗ g(x)] = f (x) ∗ dg(x) dx where ∗ denotes convolution.

Part II: Canny Edge Detector

Your goal is to implement the Canny edge detector as described in the text (Trucco and Veri) including the three main steps of filtering, nonmaximum suppression, and hysteresis thresholding and linking. You will apply your edge detector to a set of images found on the web page. You should be able

to specify three parameters: σ (the filter standard deviation), τl (the low threshold), τh (the high threshold). Some specific notes:

  • For convolution, your filter width should be 3σ where σ is measured in pixels.
  • You must implement the convolution operation yourself (e.g., you can’t use the built-in conv2 or gradient routines in matlab).
  • For simplicity, you can ignore the boundary in convolution, i.e if the image size is (H,W) and kernel size is 2m+1, then the result has size(H- 2m,W-2m).
  • To explore the role of changing each of three parameters, you will include the output of running the edge detector six times. In the first pair, choose reasonable values for τl and τh, and then vary σ to show the effect of varying filter width. In the second pair, fix σ and τl and vary τh. For the final pair. fix σ and τh and vary τl.

Hand in:

  1. Source code. Write separate functions for each step, i.e: filtering, nonmaximum suppression, and hysteresis thresholding and linking.
  2. Pick one image and one value of σ, show four images with:

(a) The component of the gradient with respect to x. (b) The component of the gradient with respect to y. (c) The magnitude of the gradient (edge strength). (d) The result of nonmaximum supression.

  1. For each of the test images, the result of applying the edge detector with the six choices of parameters as described above.
  2. Zip all files and email to TA at [email protected]. You may convert the images to other format (jpeg, gif etc) to make the file smaller.
  3. Also, print the the source code and images described above and hand in together with the written problems in class, May
    1. Clearly label your figures.