Learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data
We introduce a hierarchical model which allows to estimate a group-average piecewise-geodesic trajectory in the Riemannian space of measurements and individual variability. This model falls into the well defined mixed-effect models. The subject-specific trajectories are defined through spatial and temporal transformations of the group-average piecewise-geodesic path, component by component. Thus we can apply our model to a wide variety of situations. Due to the non-linearity of the model, we use the Stochastic Approximation Expectation-Maximization algorithm to estimate the model parameters. Experiments on synthetic data validate this choice. The model is then applied to the metastatic renal cancer chemotherapy monitoring: we run estimations on RECIST scores of treated patients and estimate the time they escape from the treatment. Experiments highlight the role of the different parameters on the response to treatment.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Spatiotemporal Manifold Prediction Model for Anterior Vertebral Body Growth Modulation Surgery in Idiopathic Scoliosis
Anterior Vertebral Body Growth Modulation (AVBGM) is a minimally invasive surgical technique that gradually corrects spine deformities while preserving lumbar motion. However the selection of potential surgical patients …
4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data
We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces …
Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms
We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spa…
HippocampusLearning spatiotemporal trajectories from manifold-valued longitudinal data
We propose a Bayesian mixed-effects model to learn typical scenarios of changes from longitudinal manifold-valued data, namely repeated measurements of the same objects or individuals at several points in time. The model…
A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manif…
Dimensionality Reduction