Model-based vision part 1 - Lecture 11 - Week 5

Question 1

What is dimensionality reduction?

Answer 1

Reducing the number of dimensions of data.

In 2D:
- Plot a line of best fit through the data
- Measure how close to the line of best fit each point it
- Use these measurements as your 1 dimension reading

Question 2

What is the Principle Component Analysis (PCA) algorithm for?

Answer 2

1. Assemble the data into a matrix
   (size: number of samples x number of variables)
2. Compute the covariance Matrix (see later)
3. Find the eigenvalues(lambda i) and Eigenvectors (vi) of C
   Each lambda i gives the variance in the direction vi
   Total Variance, T = sum from i to N of (lambda i)
4. Choose the K largest eigenvalues to account for p% of T (because we want to reduce the number of dimensions)
   For example, we might choose p = 0.95

Question 3

What is the covariance matrix of:
x y
1 1
3 0
-1 -1

Answer 3

8/3 2/3
2/3 2/3

Question 4

How are eigenvalues / eigenvectors found for a square matrix A?

Answer 4

solve |A - lambda * I| = 0
Where I is an identity matrix and ~~ is the determinant

https://www.mathsisfun.com/algebra/matrix-determinant.html to see how to calculate the determinant

Question 5

If a covariance matrix has eigenvalues 1.19 and 0.19 what is the total variance?

Answer 5

T = 1.19 + 0.19 = 1.38

The proportion of variance in the data for v1 is p = 1.19/1.38 = 0.86

Question 6

If the proportion of variance in the data for v1 is p = 1.19/1.38 = 0.86 what does that say about the data variation if we projected the data points onto v1?

Answer 6

We would retain 86% of the variation in the data if we performed that projection

Question 7

What does ASM stand for?

Answer 7

Active Shape Models

Question 8

What type of shape matching do ASMs allow for, and what does that mean

Answer 8

non-rigid

Shape matches where the shape can be scaled, rotated, translated, etc… They allow shapes to change so that parts of the shape can move (soft of) independently

Question 9

In the equation X = x + Vb (where x is the mean shape, what does V and b refer to and what happens when they are changed

Answer 9

V is the vector of all of the eigenvalues, b is the shape parameter vector (A vector of 40 values. The values in b are varied to create more shape models variations based on the mean shape

Question 10

What is the set of parameters for active shape models?

Answer 10

(s, theta, r, b) s for scale, r for translation, theta for rotation, b for the shape parameter vector