Biomedical Imaging GroupSTI
English only   BIG > Publications > Least-Squares Affine

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Affine Transformations of Images: A Least Squares Formulation

M. Unser, M.A. Neimark, C. Lee

Proceedings of the 1994 IEEE International Conference on Image Processing (ICIP'94), Austin TX, USA, November 13-16, 1994, vol. III, pp. 558-561.

We present a general framework for the design of discrete geometrical transformation operators, including rotations and scaling. The first step is to fit the discrete input image with a continuous model that provides an exact interpolation at the pixel locations. The corresponding image model is selected within a certain subspace V(φ)L2(RP) that is generated from the integer translates of a generating function φ; particular examples of this construction include polynomial spline and bandlimited signal representations. Next, the geometrical transformation is applied to the fitted model, and the result is re-projected onto the representation space. This procedure yields a solution that is optimal in the least squares sense. We show that this method can be implemented exactly using a combination of digital filters and a re-sampling step that uses a modified sampling kernel. We then derive explicit implementation formulas for the piecewise constant and cubic spline image models. Finally, we consider image processing examples and show that the present method compares very favorably with a standard interpolation that uses the same model.

AUTHOR="Unser, M. and Neimark, M.A. and Lee, C.",
TITLE="Affine Transformations of Images: {A} Least Squares
BOOKTITLE="Proceedings of the 1994 {IEEE} International Conference
        on Image Processing ({ICIP'94})",
address="Austin TX, USA",
month="November 13-16,",

© 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.