29-06-2012, 02:03 PM
Basic Geometric Transformations
[attachment=26112]
Objectives:
To understand some basic level image transformations, such as, rotation, scaling and translation.
To perform inverse transformation on an image.
Translation
It is often useful to concatenate several transformations to produce a composite result. Thus the use of square matrices simplifies the notational representation of this process. Therefore,
Rotation:
The transformations used for 3D rotation are inherently more complex than other transformations.
To rotate a point about another arbitrary point in space requires three transformations:
(i) Translate the arbitrary point to the origin
(ii) Perform the rotation
(iii) Translate the point back to its original position
Concatenation and Inverse Transformations:
Several transformations can be represented by a single 4 X 4 transformation matrix.
For eg., translation, scaling and rotation about the Z axis of a point ‘v’ is given by
Summary:
The basic gray level transformations such as, translation, scaling and rotation are studied.
The inverse operations are also learned.
[attachment=26112]
Objectives:
To understand some basic level image transformations, such as, rotation, scaling and translation.
To perform inverse transformation on an image.
Translation
It is often useful to concatenate several transformations to produce a composite result. Thus the use of square matrices simplifies the notational representation of this process. Therefore,
Rotation:
The transformations used for 3D rotation are inherently more complex than other transformations.
To rotate a point about another arbitrary point in space requires three transformations:
(i) Translate the arbitrary point to the origin
(ii) Perform the rotation
(iii) Translate the point back to its original position
Concatenation and Inverse Transformations:
Several transformations can be represented by a single 4 X 4 transformation matrix.
For eg., translation, scaling and rotation about the Z axis of a point ‘v’ is given by
Summary:
The basic gray level transformations such as, translation, scaling and rotation are studied.
The inverse operations are also learned.