Abstract
To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | S I A M Journal on Imaging Sciences |
| Vol/bind | 6 |
| Udgave nummer | 1 |
| Sider (fra-til) | 341-367 |
| Antal sider | 27 |
| ISSN | 1936-4954 |
| DOI | |
| Status | Udgivet - 12 feb. 2013 |
Emneord
- large deformation diffeomorphic metric mapping
- diffeomorphic registration
- reproducing kernel Hilbert space
- kernels
- momentum
- computational anatomy