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.
What is obtained by dilating B by S1 and then eroding that result by S2?
What is obtained by dilating B by S2 and then eroding that result by S1?
Show that convolution is associative, that is
𝑓(𝑥⃗) ∗ ’𝑔(𝑥⃗) ∗ ℎ(𝑥⃗)* = (𝑓(𝑥⃗) ∗ 𝑔(𝑥⃗)) ∗ ℎ(𝑥⃗)
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].
Use OpenCV or Matlab to smooth an image using the following operations:Box Filter with 𝑊 = 5 in both directions,
Gaussian with σ=3, and
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?
