EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Inner-Product Calculus


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

An Inner-Product Calculus for Periodic Functions and Curves

A. Badoual, D. Schmitter, M. Unser

IEEE Signal Processing Letters, vol. 23, no. 6, pp. 878-882, June 2016.



Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and L2 distances between such curves. In particular, we present formulas for the direct and exact evaluation of correlation matrices in the case of closed (i.e., periodic) parametric curves and periodic signals. We give simplifications for practical cases that involve B-splines. To illustrate this approach, we also propose a least-squares approximation scheme that is able to resample curves while minimizing aliasing artifacts. Another application is the exact calculation of the enclosed area.


@ARTICLE(http://bigwww.epfl.ch/publications/badoual1601.html,
AUTHOR="Badoual, A. and Schmitter, D. and Unser, M.",
TITLE="An Inner-Product Calculus for Periodic Functions and Curves",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2016",
volume="23",
number="6",
pages="878--882",
month="June",
note="")

© 2016 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.