CS549- Computer Vision HW #3 Solved

Description

 

 

 

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.

 

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

 

 

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

 

 

2. Show that convolution is associative, that is

𝑓(𝑥⃗) ∗ ’𝑔(𝑥⃗) ∗ ℎ(𝑥⃗)* = (𝑓(𝑥⃗) ∗ 𝑔(𝑥⃗)) ∗ ℎ(𝑥⃗)

 

3. 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].

 

 

4. Use OpenCV or Matlab to smooth an image using the following operations:
   1. Box Filter with 𝑊 = 5 in both directions,
   2. Gaussian with σ=3, and
   3. 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?