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

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

D. Schmitter, M. Unser

IEEE Transactions on Image Processing, vol. 27, no. 1, pp. 365-378, January 2018.

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose elements are subspaces that contain all affine transformations of the training samples. The alignment relies on orthogonal projection operators that have a closed form. We then present algorithms to learn shape dictionaries according to the structure of the data that needs to be encoded: 1) projection-based functional principal-component analysis for homogeneous data and 2) continuous-domain sparse shape encoding to learn dictionaries that contain imbalanced data, outliers, or different types of shape structures. Through parametric spline curves, we provide a detailed and exact implementation of our method. We demonstrate that it requires fewer parameters than purely discrete methods and that it is computationally more efficient and accurate. We illustrate the use of our framework for dictionary learning of structures in biomedical images as well as for shape analysis in bioimaging. 

@ARTICLE(http://bigwww.epfl.ch/publications/schmitter1801.html,
AUTHOR="Schmitter, D. and Unser, M.",
TITLE="Landmark-Based Shape Encoding and Sparse-Dictionary Learning in
	the Continuous Domain",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2018",
volume="27",
number="1",
pages="365--378",
month="January",
note="")

© 2018 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.