Description
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1. The following binary image B = |
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is operated on by structuring elements S1 and S2
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S1=
S2=
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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( ⃗)
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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].
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Use OpenCV or Matlab to smooth an image using the following operations:
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Box Filter with= 5 in both directions,
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Gaussian with σ=3, and
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Median Filter using a 5×5 window (see Szieliski p. 108)
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Show the original image – your choice! – and the 3 smoothed images.
Answer the following: What happens if you change the window size?
