本次CS代写主要内容是Computer vision相关的理论问题

Spring 2021, TuTh 9:30AM-10:50AM

Homework #3

Due Date: 3/25/21, 11:59PM

Instructions

Spring 2021, TuTh 9:30AM-10:50AM

Homework #3

Due Date: 3/25/21, 11:59PM

• Answer the questions below, and provide as much of your work as necessary.

• Export or scan your homework and store it as a PDF version before submitting online to

UBLearns.

1 Interpolation (40 points)

Interpolation allows us to compute the value of a pixel that may fall off the normal discrete 2D Grid. Giventhefourpixelsbelow(i,j),(i+1,j),(i,j+1),and(i+1,j+1):

- Write out the formula for the interpolated value at f(x,y) at location (x,y) using bilinear interpolation.
- Assuming that a = 0.6 and b = 0.4, and the pixel values in red, compute the interpolated value f(x,y).

i) Using Average Interpolation

ii) Using Nearest Neighbor Interpolation.iii) Using Bilinear Interpolation.

2 Texture Synthesis (40 points)

An image that is generated with texture synthesis has a distribution of local patterns. Given this image below, where color of the pixel under the red box with the X is unknown:

• • • •

a) How many pixels (other than X) have a 3×3 neighborhood that matches the neighborhood of the 3×3 neighborhood of X?

b) What is the probability of X being Dark given its neighborhood in question 2a? Briefly justify how you computed this result.

c) For question 2a, how many pixels match if the neighborhood consists only of the four pixels above, below, left and right of X?

d) What is the probability of X being Light given its neighborhood in question 2c? Briefly justify how you computed this result.

Local Binary Patterns (20 points)

3

Local binary patterns are a feature that can be used to describe textures. They are efficient to compute and can be formed to describe many common texton-like features. Given the process for computing LBPs in a local neighborhood consisting of the 8 pixels around a pixel, consider the assumptions and the questions below.

• Assume that dark pixels have a lower value then light pixels, and X is dark in the previous figure. We want to compute the LBP feature for X. Assume the pixel directly to the right of X is the least significant bit and proceed counter clockwise.

i) What is the numeric value of the LBP feature of X according to these assumptions?

ii) What is the numeric value of the LBP feature if X was light?