EPFL | Biomedical Imaging Group

Shape Projectors for Landmark-Based Spline Curves

D. Schmitter, M. Unser

IEEE Signal Processing Letters, vol. 24, no. 10, pp. 1517-1521, October 2017.

We present a generic method to construct orthogonal projectors for two-dimensional landmark-based parametric spline curves. We construct vector spaces that define a geometric transformation (e.g., affine, similarity, and scaling) that is applied to a reference curve. These vector spaces contain all parametric curves up to the chosen transformation. We define the vector spaces implicitly through an orthogonal projection operator and present a theorem that characterizes the projector for landmark-based spline curves, which are popular for the user-interactive analysis of biomedical images. Finally, we show how shape priors are constructed with the spline projector and provide an example of application for the segmentation of microscopy images in biology.

@ARTICLE(http://bigwww.epfl.ch/publications/schmitter1703.html,
AUTHOR="Schmitter, D. and Unser, M.",
TITLE="Shape Projectors for Landmark-Based Spline Curves",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2017",
volume="24",
number="10",
pages="1517--1521",
month="October",
note="")

© 2017 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.