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

Trigonometric Interpolation Kernel to Construct Deformable Shapes for User-Interactive Applications

D. Schmitter, R. Delgado-Gonzalo, M. Unser

IEEE Signal Processing Letters, vol. 22, no. 11, pp. 2097–2101, November 2015.

We present a new trigonometric basis function that is capable of perfectly reproducing circles, spheres and ellipsoids while at the same time being interpolatory. Such basis functions have the advantage that they allow to construct shapes through a sequence of control points that lie on their contour (2-D) or surface (3-D) which facilitates user-interaction, especially in 3-D. Our piecewise exponential basis function has finite support, which enables local control for shape modification. We derive and prove all the necessary properties of the kernel to represent shapes that can be smoothly deformed and show how idealized shapes such as ellipses and spheres can be constructed. 

@ARTICLE(http://bigwww.epfl.ch/publications/schmitter1502.html,
AUTHOR="Schmitter, D. and Delgado-Gonzalo, R. and Unser, M.",
TITLE="Trigonometric Interpolation Kernel to Construct Deformable Shapes
	for User-Interactive Applications",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2015",
volume="22",
number="11",
pages="2097--2101",
month="November",
note="")

© 2015 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.