Homework 03 Solution

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1. The following binary image B = is operated on by structuring elements S1 and S2 S1= S2= ● ● Assume that any pixels outside the region shown are 0. This is equivalent to assuming that B is embedded in a (potentially infinitely) larger image that is all 0. a. What is obtained by dilating…

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1. The following binary image B =

is operated on by structuring elements S1 and S2

S1=

S2=

Assume that any pixels outside the region shown are 0. This is equivalent to assuming that B is embedded in a (potentially infinitely) larger image that is all 0.

a. What is obtained by dilating B by S1 and then eroding that result by S2?

b. What is obtained by dilating B by S2 and then eroding that result by S1?

2. Show that convolution is associative, that is

( ⃗) ∗ ‘ ( ⃗) ∗ ℎ( ⃗)* = ( ( ⃗) ∗ ( ⃗)) ∗ ℎ( ⃗)

  1. What is the Discrete Fourier Transform of the simple x-direction mask, assuming that the 1 value is at the origin?

Use the 1-D DFT formula on p. 118 of Szeliski. You should be able to express the result as [constants] × e[something] × sin[something].

  1. Use OpenCV or Matlab to smooth an image using the following operations:

    1. Box Filter with= 5 in both directions,

    1. Gaussian with σ=3, and

    1. Median Filter using a 5×5 window (see Szieliski p. 108)

Show the original image – your choice! – and the 3 smoothed images.

Answer the following: What happens if you change the window size?

Homework 03 Solution
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