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Fast eigenspace decomposition of correlated images.
C Y Chang1, A A Maciejewski, V Balakrishnan
1Semicond.. Technol. and Instrum. Inc., Plano, TX 75074, USA.
Summary
This study introduces an efficient algorithm for image eigenspace decomposition using circulant matrix theory. The method accurately approximates eigendecompositions for rotated, translated, and scaled images, enabling efficient subspace computation.
Area of Science:
- Computer Vision
- Image Processing
- Linear Algebra
Background:
- Eigenspace decomposition is crucial for image analysis.
- Existing methods can be computationally intensive.
- Circulant matrix theory offers analytical solutions for specific image transformations.
Purpose of the Study:
- To develop a computationally efficient algorithm for eigenspace decomposition of correlated images.
- To leverage circulant matrix theory for approximating eigendecompositions.
- To enable automatic determination of subspace dimensions with guaranteed accuracy.
Main Methods:
- Utilizing analytical expressions from circulant matrix theory for 2-D image planar rotations.
- Applying these expressions as approximations for 3-D object rotations and image translations/scaling.
- Developing a method to automatically determine subspace dimensions and compute bases.
Main Results:
- The algorithm provides good approximations for eigendecompositions of transformed images.
- It accurately determines the required subspace dimension for user-specified accuracy.
- Efficient computation of the subspace basis is achieved.
Conclusions:
- The proposed algorithm offers a computationally efficient solution for eigenspace decomposition.
- It demonstrates strong performance across various image types, including 3-D object rotations and video sequences.
- This approach facilitates accurate and fast image representation.
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