Resetting the Affine Transformation matrix

In summary, the Affine Transformation Matrix is created by using a learned projection matrix and then resetting it using singular value decomposition. The SVD of the matrix T is shown and an IEEE paper states that the right orthogonal matrix does not affect the similarity measure based on Euclidean distance. The reason for this is unclear.
  • #1
Avinash Raj
4
0
Affine Transformation Matrix is said to be formed by initializing it using a learned projection matrix from a conventional algorithm like Eigenfaces or Fisherfaces; then it is reset by using the singular value decomposition T=UAV', where T is the transformation matrix.

Could somebody explain how the decomposition is obtained and what it is?
 
Physics news on Phys.org
  • #2
I didnt go into details of initialising the tranformation matrix as well as the "resetting". I presumed that those in the forum are learned enough to know the basics of affine transformation. Do let me know if somebody wants more data from me to be able to explain the concept to me.
 
  • #3
It is obvious that SVD of the matrix T is shown.

An IEEE paper (Face Verification With Balanced Thresholds) that I read few days back says "the right orthogonal matrix of SVD of a transformation matrix does not affect the similarity measure if based on Euclidean distance." I drew blanks in my attempts to understand how it is so and wikipedia wasnt a help at all. Could you tell me why the measure is invariant to the right orthogonal matrix?

Note - The right unitary matrix becomes orthogonal as only real matrices are considered in the problem.
 

Related to Resetting the Affine Transformation matrix

1. What is an Affine Transformation matrix?

An Affine Transformation matrix is a mathematical tool used in computer graphics and image processing to represent and manipulate 2D or 3D objects. It is a 2x3 or 3x3 matrix that includes translation, rotation, scaling, and shearing operations to transform an object's position, orientation, and size.

2. Why would I need to reset the Affine Transformation matrix?

Resetting the Affine Transformation matrix is necessary when you want to undo any previous transformations applied to an object. This is important when working with multiple objects or when you want to start with a clean slate to perform new transformations without any interference from previous ones.

3. How do I reset the Affine Transformation matrix?

To reset the Affine Transformation matrix, you need to set all the transformation values to their default values. This means setting the translation values to 0, rotation values to 0 or 1, and scaling values to 1. This will remove any previous transformations and restore the object to its original position, orientation, and size.

4. Can I reset individual transformations within the Affine Transformation matrix?

Yes, you can reset individual transformations within the Affine Transformation matrix. For example, if you only want to reset the rotation values, you can set them to 0 or 1, while leaving the translation and scaling values unchanged. This will only undo the rotation transformation and keep the other transformations intact.

5. Are there any consequences of resetting the Affine Transformation matrix?

Resetting the Affine Transformation matrix will remove any previous transformations applied to an object. This means that any changes made to the object's position, orientation, or size will be lost. It is important to use this tool carefully and only when necessary to avoid losing any important transformations that have been applied.

Similar threads

  • Linear and Abstract Algebra
Replies
5
Views
1K
Replies
27
Views
1K
  • Linear and Abstract Algebra
Replies
1
Views
982
  • Linear and Abstract Algebra
Replies
1
Views
1K
  • Linear and Abstract Algebra
Replies
6
Views
1K
  • Linear and Abstract Algebra
Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
2K
  • Linear and Abstract Algebra
Replies
17
Views
4K
Back
Top