We present a novel method for co-registration of two independent statistical shape models. We solve the problem of aligning a face model to a skull model with stochastic optimization based on Markov Chain Monte Carlo (MCMC). We create a probabilistic joint face-skull model and show how to obtain a distribution of plausible face shapes given a skull shape. Due to environmental and genetic factors, there exists a distribution of possible face shapes arising from the same skull. We pose facial reconstruction as a conditional distribution of plausible face shapes given a skull shape. Because it is very difficult to obtain the distribution directly from MRI or CT data, we create a dataset of artificial face-skull pairs. To do this, we propose to combine three data sources of independent origin to model the joint face-skull distribution: a face shape model, a skull shape model and tissue depth marker information. For a given skull, we compute the posterior distribution of faces matching the tissue depth distribution with Metropolis-Hastings. We estimate the joint face-skull distribution from samples of the posterior. To find faces matching to an unknown skull, we estimate the probability of the face under the joint face-skull model. To our knowledge, we are the first to provide a whole distribution of plausible faces arising from a skull instead of only a single reconstruction. We show how the face-skull model can be used to rank a face dataset and on average successfully identify the correct match in top 30%. The face ranking even works when obtaining the face shapes from 2D images. We furthermore show how the face-skull model can be useful to estimate the skull position in an MR-image.

In this paper, we present a novel open-source pipeline for face registration based on Gaussian processes as well as an application to face image analysis. Non-rigid registration of faces is significant for many applications in computer vision, such as the construction of 3D Morphable face models (3DMMs). Gaussian Process Morphable Models (GPMMs) unify a variety of non-rigid deformation models with B-splines and PCA models as examples. GPMM separate problem specific requirements from the registration algorithm by incorporating domain-specific adaptions as a prior model. The novelties of this paper are the following: (i) We present a strategy and modeling technique for face registration that considers symmetry, multi-scale and spatially-varying details. The registration is applied to neutral faces and facial expressions. (ii) We release an open-source software framework for registration model-building demonstrated on the publicly available BU3D-FE database. The released pipeline also contains an implementation of an Analysis-by-Synthesis model adaption of 2D face images, tested on the Multi-PIE and LFW database. This enables the community to reproduce, evaluate and compare the individual steps of registration to model-building and 3D/2D model fitting. (iii) Along with the framework release, we publish a new version of the Basel Face Model (BFM-2017) with an improved age distribution and an additional facial expression model.

Models of shape variations have become a central component for the automated analysis of images. An important class of shape models are point distribution models (PDMs). These models represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of PDMs, which we refer to as Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loève expansion. To compute the expansion, we make use of an approximation scheme based on the Nyström method. The resulting model can be seen as a continuous analog of a standard PDM. However, while for PDMs the shape variation is restricted to the linear span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, a PDM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the PDM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes, including methods for multi-scale or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modeling from the fitting process, this is all achieved without changes to the fitting algorithm. To demonstrate the applicability and versatility of GPMMs, we perform a set of experiments in typical usage scenarios in medical image analysis and computer vision: The model-based segmentation of 3D forearm images and the building of a statistical model of the face. To complement the paper, we have made all our methods available as open source.

Non-rigid registration is central to many problems in computer vision and medical image analysis. We propose a registration algorithm which is regularized by prior knowledge in the form of a statistical deformation model. This model is obtained from previous registrations performed on a set of noise-free training examples given by images, or shapes represented by level set functions. Contrary to similar approaches, our method does not strictly constrain the result to lie in the span of the statistical model but rather uses the model for Tikhonov regularization. Therefore, our method can be used to reduce the influence of noise and artifacts even when the model contains only a few typical examples. This automatically gives rise to a bootstrapping strategy for building statistical models from noisy data sets requiring only a limited number of high quality examples. We demonstrate the effectiveness of the approach on synthetic and medical images.

As mobile ad hoc networks provide a wide range of possibly critical services, providing quality of service guarantees becomes an essential element. Yet there is a limited understanding of the performance characteristics of different resource allocation algorithms. In particular, there is little work that comparatively studies different algorithms in the same traffic environment. Therefore we study two algorithms, ad hoc-TARA and an algorithm based on the gradient projection method, for optimised bandwidth allocation in ad hoc networks under overload situations. The focus is on convergence properties and performance measured in terms of accumulated utility. The simulation results show that the gradient projection algorithm converges to an optimal solution even in large, dynamic networks, but that in such dynamic environments the convergence time can significantly influence the overall performance. In comparison, the near-optimal algorithm ad hoc-TARA, which quickly adapts to changes in the state of the network, can exhibit superior performance. Further we illustrate how different parameter settings influence the performance of the algorithms. We conclude that finding an optimal allocation comes at a high price in the rapidly changing environments of ad hoc networks and that near-optimal allocation can be an ample alternative.

We consider an optimization problem in probabilistic inference: Given n hypotheses Hj, m possible observations Ok, their conditional probabilities pkj, and a particular Ok, select a possibly small subset of hypotheses excluding the true target only with some error probability ε. After specifying the optimization goal we show that this problem can be solved through a linear program in mn variables that indicate the probabilities to discard a hypothesis given an observation. Moreover, we can compute optimal strategies where only O(m+n) of these variables get fractional values. The manageable size of the linear programs and the mostly deterministic shape of optimal strategies makes the method practicable. We interpret the dual variables as worst-case distributions of hypotheses, and we point out some counterintuitive nonmonotonic behaviour of the variables as a function of the error bound ε. One of the open problems is the existence of a purely combinatorial algorithm that is faster than generic linear programming.