Sparse Adaptive Parameterization of Variability in Image Ensembles

International audienceThis paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles. Dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a Hamiltonian flow of self-interacting particles. The proposed approach estimates a template image representative of a given image set, an optimal set of control points that focuses on the most variable parts of the image, and template-to-image registrations that quantify the variability within the image set. The method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain. The optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent. The selection of the control points is done by adding a L 1 prior to the objective function, which is optimized using the FISTA algorithm

APPLICATION OF NEURAL NETWORKS TO EMULATION OF RADIATION PARAMETERIZATIONS IN GENERAL CIRCULATION MODELS

A novel approach based on using neural network (NN) techniques for approximation of physical components of complex environmental systems has been applied and further developed in this dissertation. A new type of a numerical model, a complex hybrid environmental model, based on a combination of deterministic and statistical learning model components, has been explored. Conceptual and practical aspects of developing hybrid models have been formalized as a methodology for applications to climate modeling and numerical weather prediction. The approach uses NN as a machine or statistical learning technique to develop highly accurate and fast emulations for model physics components/parameterizations. The NN emulations of the most time consuming model physics components, short and long wave radiation (LWR and SWR) parameterizations have been combined with the remaining deterministic components of a general circulation model (GCM) to constitute a hybrid GCM (HGCM). The parallel GCM and HGCM simulations produce very similar results but HGCM is significantly faster. The high accuracy, which is of a paramount importance for the approach, and a speed-up of model calculations when using NN emulations, open the opportunity for model improvement. It includes using extended NN ensembles and/or more frequent calculations of full model radiation resulting in an improvement of radiation-cloud interaction, a better consistency with model dynamics and other model physics components. First, the approach was successfully applied to a moderate resolution (T42L26) uncoupled NCAR Community Atmospheric Model driven by climatological SST for a decadal climate simulation mode. Then it has been further developed and subsequently implemented into a coupled GCM, the NCEP Climate Forecast System with significantly higher resolution (T126L64) and time dependent CO2 and tested for decadal climate simulations, seasonal prediction, and short- to medium term forecasts. The developed highly accurate NN emulations of radiation parameterizations are on average one to two orders of magnitude faster than the original radiation parameterizations. The NN approach was extended by introduction of NN ensembles and a compound parameterization with quality control of larger errors. Applicability of other statistical learning techniques, such as approximate nearest neighbor approximation and random trees, to emulation of model physics has also been explore

Entropy-based particle correspondence for shape populations

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies

Geodesic image regression with a sparse parameterization of diffeomorphisms

pre-printImage regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L1 penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality

Geodesic shape regression in the framework of currents

pre-printShape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low di- mensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes