Refine
Year of publication
Document Type
- In Proceedings (165) (remove)
Language
- English (165)
Has Fulltext
- no (165)
Institute
- Visual and Data-centric Computing (152)
- Visual Data Analysis (151)
- Visual Data Analysis in Science and Engineering (89)
- Therapy Planning (52)
- Image Analysis in Biology and Materials Science (26)
- Numerical Mathematics (14)
- Vergleichende Visualisierung (5)
- Computational Medicine (3)
- Geometric Data Analysis and Processing (3)
- Computational Systems Biology (1)
In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely Bézier splines in the manifold.
To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric.
Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems.
We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression.