CS 549 -Computer Vision-HW #2 Solved

Description

 

 

1. You have been asked to develop a medical imaging system to process a time series of 3-dimensional images of the heart, yielding a 4-dimensional image array with indices x, y, z, t. Give two distinct connectivity relations that could be used. What are a pixel’s neighbors under each connectivity relation?

 

2. In homogeneous coordinates, a rotation followed by a translation is represented by

𝑹𝑹   ⋮   𝑇𝑇⃗

⋯          ⋯

0    ⋮     1

 

𝑹𝑹−𝟏𝟏 What is the inverse operation? Hint: It is not  ⋯ 0

⋮   ⋮

−𝑇𝑇⃗ ⋯ . 1

 

3. An image has object and background pixels whose brightness values are distributed according to the Rayleigh distribution with parameters σ_o and σ_b with 0 < σ_b < σ_o. The probability of a pixel having brightness k is given by

 

−𝑘𝑘²                                             

𝑃𝑃_𝑜𝑜(𝑘𝑘) ⁼ _𝜎𝜎𝑘𝑘2 𝑒𝑒^2𝜎𝜎𝑜𝑜2 and 𝑃𝑃_𝑏𝑏(𝑘𝑘) = 𝑘𝑘2 𝑒𝑒2𝜎𝜎𝑏𝑏

𝑜𝑜                                                𝜎𝜎𝑏𝑏

 

Ima Robot wants to segment the image into object and background.

1. Assuming that background and object pixels are equally likely, find the decision rule that maximizes the probability of a correct decision, that is, pick the greater of P_o and P_b.
2. How does your answer to a. change if background and object pixels are not equally likely? Suppose that there are N_o object pixels and N_b background pixels, so that the total number of pixels is N=N_o+N_b. What is the new threshold T?

 

4. Not for extra credit: Binarize your selfie from HW0 in 2 ways:

 

1. Threshold the image such that ~50% of the pixels are black and ~50% are white.
2. Some other method of your choosing. Explain your method.