Theory Of Projection In Computer Vision

What are various types of linear 2D transformation?
Rigid : Translation + Rotation
Similarity : Translation + Rotation + Uniform Scale
Affine : Translation + Rotation + Scale + Shear

Projective : Cross-ratio preserving
(RSAP)

What is 2D translation?
Moves a point to a new location by adding translation amounts to the coordinates of the point.
P' = P + T

What are image pyramids?
An image pyramid is a collection of images - all arising from a single original image - that are successively downsampled until some desired stopping point is reached.

What are two common kinds of image pyramids?
1. Gaussian pyramid : Used to downsample image
2. Laplacian pyramid : Used to upsample an image lower in the pyramid.

What is 2D Scaling?
Changes the size of the object by multiplying the coordinates of the points by scaling factor Sx and Sy.

P' = SP

What is 2D rotation?
P' = RP

How do we homogenize coordinate?

Under certain assumptions, affine transformations can be used the effects of perspective projection

Position of the image center on the image
Focal Length
Scaling factors for row and column pixels
Lens distortion.

What is calibration?
Finding the function that maps 3D points to 2D image plane.

What is about finding the corners?
1. Corner Detector
2. Canny edge detector plus fitting lines to the detected edges.
3. Manual input

When do we call R a rotation ma

An image pyramid is a collection of images - all arising from a single original image - that are successively downsampled until