Lecture 7/8 2D transformation and projection

Question 1

What transformations can be represented by p_prime
= M x p

Answer 1

Question 2

Visualise a 2D transform to scale an image

Answer 2

Question 3

Visualise a 2D transform to stretch an image

Answer 3

Question 4

Visualise a 2D transform to Flip an image horizontally

Answer 4

Question 5

Visualise a 2D transform to Shear / Skew an image

Answer 5

Question 6

Visualise a 2D transform to rotate an image ANTI-CLOCKWISE

Answer 6

Question 7

Visualise a 2D transform to rotate an image CLOCKWISE

Answer 7

Question 8

Answer 8

Question 9

How do you go from a set of homogeneous points to a set of un-homogeneous points?

Answer 9

Divide by 3rd point

Question 10

Visualise a 2D transform to translate an image

Answer 10

Question 11

Visualise a rotation followed translation by matrix

Answer 11

p0 = ( T R ) p

Question 12

Visualise a translation followed by rotation matrix ANTI-CLOCKWISE

Answer 12

p0 = ( R T ) p

Question 13

What are the steps to rotate about an arbitrary point

Answer 13

Question 14

How do I perform compound transformations using row vectors?

Answer 14

Question 15

How many points are needed to align images with an affine transform?

Answer 15

Question 16

How many points are needed to align images with a homography transform?

Answer 16

Question 17

How do we warp images given a known linear transform?

Answer 17

Question 18

Describe Bilinear interpolation

Answer 18

Question 19

Describe Nearest-neighbour
interpolation

Answer 19

Take a point from an image
[x, y] = [132.45, 80.26]

Round the x-coordinate
[132.45, 80.26] à [132, 80.26]

Round the y-coordinate
[132, 80.26] à [132, 80]

Considers only the nearest pixel

Question 20

What equations are used for bi-linear interpolation?

Answer 20