BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

M. Jacob, T. Blu, M. Unser

IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 633-642, June 2001.

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients are precomputed exactly as the solution of a two-scale relation. To demonstrate the performance improvement of the new method, we compare it with existing methods such as pixel-based approaches and approximation of the region by a polygon. We also propose an alternate scheme when the scaling function is sinc(x). 

@ARTICLE(http://bigwww.epfl.ch/publications/jacob0102.html,
AUTHOR="Jacob, M. and Blu, T. and Unser, M.",
TITLE="An Exact Method for Computing the Area Moments of Wavelet and
	Spline Curves",
JOURNAL="{IEEE} Transactions on Pattern Analysis and Machine
	Intelligence",
YEAR="2001",
volume="23",
number="6",
pages="633--642",
month="June",
note="")

© 2001 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.