Lecture 8
4-2: Global transform and Image stitching, alignment
old what we did
Global operations
global transform
changing shape of operation
p=(x,y) → p=(x', y')
Computer Vision 59
, transformation T is a coordinate-changing machine: p′ = T (p)
a global T means that T is same for any point p. For linear transformation, we can represent T
as a matrix:
common transformation
scaling:
scaling a coordinate = multiplying each of its components by a scalar
uniform scaling = this scalar is same for all components (x2 everything x2)
non-uniform scaling = different scalars per component
2-D rotation
Computer Vision 60
, homogeneous coordinates
normally we have the following for translation x′ = x + tx ,y′ = y + ty
now representing this as a 3x3 matrix
first representing coordinates in 2D with 3 vector
using the rightmost column
Computer Vision 61
, shear =
affine translations
combinations of linear transformations, and translations. all the 6 you can change
properties:
origin does not necessarily map to origin
.... (not needed for exam)
transformation composition = chain of different operations together
Computer Vision 62
4-2: Global transform and Image stitching, alignment
old what we did
Global operations
global transform
changing shape of operation
p=(x,y) → p=(x', y')
Computer Vision 59
, transformation T is a coordinate-changing machine: p′ = T (p)
a global T means that T is same for any point p. For linear transformation, we can represent T
as a matrix:
common transformation
scaling:
scaling a coordinate = multiplying each of its components by a scalar
uniform scaling = this scalar is same for all components (x2 everything x2)
non-uniform scaling = different scalars per component
2-D rotation
Computer Vision 60
, homogeneous coordinates
normally we have the following for translation x′ = x + tx ,y′ = y + ty
now representing this as a 3x3 matrix
first representing coordinates in 2D with 3 vector
using the rightmost column
Computer Vision 61
, shear =
affine translations
combinations of linear transformations, and translations. all the 6 you can change
properties:
origin does not necessarily map to origin
.... (not needed for exam)
transformation composition = chain of different operations together
Computer Vision 62
