Klaus Baggesen Hilger

Energy Comes Together in Denmark: The Key to a Future Fossil-Free Danish Power System

The transition of the Danish energy system to a system based only on renewable energy in 2050 carries many challenges. For Denmark to become independent of fossil energy sources, wind power and biomass are expected to become the main sources of energy. Onshore and offshore wind farms are expected to provide the majority of electricity, and biomass and electricity are expected to become the major sources of heating. On the way toward the 100% renewable goal in 2050, the Danish government has proposed a 2035 midterm goal to cover the energy consumption for power and heat with renewables.

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized shapes and improves the capability of reconstruction of the training data. Furthermore, the method leads to an overall reduction in the total variance of the point distribution model. Thus, it finds correspondence between semi-landmarks that are highly correlated in the shape tangent space. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.

Growth modeling of human mandibles using non-Euclidean metrics

From a set of 31 three-dimensional computed tomography (CT) scans we model the temporal shape and size of the human mandible for analysis, simulation, and prediction purposes. Each anatomical structure is represented using 14851 semi-landmarks, and mapped into Procrustes tangent space. Exploratory subspace analyses are performed leading to linear models of mandible shape evolution in Procrustes space. The traditional variance analysis results in a one-dimensional growth model. However, working in a non-Euclidean metric results in a multimodal model with uncorrelated modes of biological variation related to independent component analysis. The applied non-Euclidean metric is governed by the correlation structure of the estimated noise in the data. The generative models are compared, and evaluated on the basis of a cross validation study. The new non-Euclidean analysis is completely data driven. It not only gives comparable results w.r.t. previous studies of the mean modeling error, but seems to better correlate to growth, and in addition provides the data analyst with alternative hypothesis of plausible shape evolution; hence aiding in the understanding of cranio-facial growth.

Markov random field restoration of point correspondences for active shape modeling

In this paper it is described how to build a statistical shape model using a training set with a sparse of landmarks. A well defined model mesh is selected and fitted to all shapes in the training set using thin plate spline warping. This is followed by a projection of the points of the warped model mesh to the target shapes. When this is done by a nearest neighbour projection it can result in folds and inhomogeneities in the correspondence vector field. The novelty in this paper is the use and extension of a Markov random field regularisation of the correspondence field. The correspondence field is regarded as a collection of random variables, and using the Hammersley-Clifford theorem it is proved that it can be treated as a Markov Random Field. The problem of finding the optimal correspondence field is cast into a Bayesian framework for Markov Random Field restoration, where the prior distribution is a smoothness term and the observation model is the curvature of the shapes. The Markov Random Field is optimised using a combination of Gibbs sampling and the Metropolis-Hasting algorithm. The parameters of the model are found using a leave-one-out approach. The method leads to a generative model that produces highly homogeneous polygonised shapes with improved reconstruction capabilities of the training data. Furthermore, the method leads to an overall reduction in the total variance of the resulting point distribution model. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.

Probabilistic generative modelling

The contribution of this paper is the adaption of data driven methods for decomposition of tangent shape variability proposed in a probabilistic framework. By Bayesian model selection we compare two generative model representations derived by principal components analysis and by maximum autocorrelation factors analysis.

Active Shape Analysis of Mandibular Growth

This work contains a clinical validation using biological landmarks of a Geometry Constrained Diffusion registration of mandibular surfaces. Canonical Correlations Analysis is extended to analyse 3D landmarks and the correlations are used as similarity measures for landmark clustering. A novel Active Shape Model is proposed targeting growth modelling by applying Partial Least Squares regression in decomposing the Procrustes tangent space. Shape centroid size is applied as dependent variable but the method generalizes to handle other, both uni- and multivariate, effects probing for high covariation wrt. shape variation.