CAP 6416 Midterm Examination

(Computers and Vision)

Fall 1994

Each question is equally weighted.

Examination Questions

1. Suppose you are presented with an epipolar stereo camera system satisfying the following parameters:
   • The distance B between lens centers is 40mm.
   • The focal length l is 15mm.
   and that a point of correspondence is found in the left image at (3,-2) and in the right image at (2,-2).

   Draw a diagram representing this situation, and find the world coordinates of the corresponding material point.

2. Explain the statement "The Weber ratio is not a number," and tell what experiments calculating Weber ratios demonstrate about gray-level discrimination in the human vision system under varying illumination levels.

3. Describe how Fourier descriptors may be used to represent boundaries and explain why Gabor Szekely was careful to point out in his talk that in his use of Fourier descriptors he normalized his data by choosing a distinguished boundary point.

4. Give a clear definition of Blum's Medial Axis Transformation as originally formulated.

5. Describe how the opening operations of mathematical morphology might help you in counting the number of teeth in a binary image of a cog assuming:
   • Only one cog appears in each image and it is perfectly imaged.
   • The size of teeth on the cogs is known.
   Draw a picture to help illustrate your answer.

6. The text states that N log N additions and (N log N)/2 multiplications are required to compute the FFT of an N point sample. Described how the separability property of the Fourier transform is used to generate an algorithm for computing the FFT of an N by N image, and show how many additions and multiplications are required to compute the 2-D FFT of such an image.

7. The Fourier Transform displays what is referred to as conjugate symmetry because it is formed from the sum of real cos terms and imaginary sin terms, where cos and sin are (respectively) even and odd functions. The Hartley transform avoids the use of imaginary sin terms, instead just adding the cos and sin terms as real quantities.

   Knowing what you know of symmetry, even and odd functions, and the Fourier transform,

   • Express the Hartley transform (as described above).

   • Given the Hartley transform F(u) of a function f(x), show how to find the magnitude and phase of F(u).

8. Define the following image algebra concepts:
   • image

   • neighborhood

   • template

   Define the linear image template product operation and discuss its relation to correlation.