Gaussian Process Morphable Models (GPMMs) unify a variety of non-rigid deformation models for surface and image registration. Deformation models, such as B-splines, radial basis functions, and PCA models are defined as a probability distribution using a Gaussian process. The method depends heavily on the low-rank approximation of the Gaussian process, which is mandatory to obtain a parametric representation of the model. In this article, we propose the use of the pivoted Cholesky decomposition for this task, which has the following advantages: (1) Compared to the current state of the art used in GPMMs, it provides a fully controllable approximation error. The algorithm greedily computes new basis functions until the user-defined approximation accuracy is reached. (2) Unlike the currently used approach, this method can be used in a black-box-like scenario, whereas the method automatically chooses the amount of basis functions for a given model and accuracy. (3) We propose the Newton basis as an alternative basis for GPMMs. The proposed basis does not need an SVD computation and can be iteratively refined. We show that the proposed basis functions achieve competitive registration results while providing the mentioned advantages for its computation.

It is well known that deep learning approaches to face recognition suffer from various biases in the available training data. In this work, we demonstrate the large potential of synthetic data for analyzing and reducing the negative effects of dataset bias on deep face recognition systems. In particular we explore two complementary application areas for synthetic face images: 1) Using fully annotated synthetic face images we can study the face recognition rate as a function of interpretable parameters such as face pose. This enables us to systematically analyze the effect of different types of dataset biases on the generalization ability of neural network architectures. Our analysis reveals that deeper neural network architectures can generalize better to unseen face poses. Furthermore, our study shows that current neural network architectures cannot disentangle face pose and facial identity, which limits their generalization ability. 2) We pre-train neural networks with large-scale synthetic data that is highly variable in face pose and the number of facial identities. After a subsequent fine-tuning with real-world data, we observe that the damage of dataset bias in the real-world data is largely reduced. Furthermore, we demonstrate that the size of real-world datasets can be reduced by 75% while maintaining competitive face recognition performance. The data and software used in this work are publicly available.

Active Shape Models (ASMs) are a classical and widely used approach for fitting shape models to images. In this paper, we propose a fully probabilistic interpretation of ASM fitting as Bayesian inference. To infer the posterior, we use the Metropolis-Hastings algorithm. We then use the maximum a posteriori sample as the segmentation result. Our approach has several advantages compared to classical ASM fitting: (1) We are left with fewer parameters that we need to choose. (2) It is less prone to get trapped in local minima. (3) It becomes straightforward to extend the approach to include additional information, such as expert annotations. (4) It is even simpler to implement than the classical ASM fitting method. We apply our algorithm to the SLIVER dataset and show that it achieves a higher segmentation accuracy than the standard ASM approach. We further demonstrate the flexibility and expressivity of the framework by integrating experts annotations along parts of the outline to further increase the accuracy. The code used for fitting is based on open-source software and made available to the community.

It is well known that deep learning approaches to face recognition and facial landmark detection suffer from biases in modern training datasets. In this work, we propose to use synthetic face images to reduce the negative effects of dataset biases on these tasks. Using a 3D morphable face model, we generate large amounts of synthetic face images with full control over facial shape and color, pose, illumination, and background. With a series of experiments, we extensively test the effects of priming deep nets by pre-training them with synthetic faces. We observe the following positive effects for face recognition and facial landmark detection tasks: 1) Priming with synthetic face images improves the performance consistently across all benchmarks because it reduces the negative effects of biases in the training data. 2) Traditional approaches for reducing the damage of dataset bias, such as data augmentation and transfer learning, are less effective than training with synthetic faces. 3) Using synthetic data, we can reduce the size of real-world datasets by 75 recognition and by 50 performance. Thus, offering a means to focus the data collection process on less but higher quality data.

Today's most successful facial image analysis systems are based on deep neural networks. However, a major limitation of such deep learning approaches is that their performance depends strongly on the availability of large annotated datasets. In this work, we prime deep neural networks by pre-training them with synthetic face images for specific facial analysis tasks. We demonstrate that this approach enhances both the generalization performance as well as the dataset efficiency of deep neural networks. Using a 3D morphable face model, we generate arbitrary amounts of annotated data with full control over image characteristics such as facial shape and color, pose, illumination, and background. With a series of experiments, we extensively test the effect of priming deep neural networks with synthetic face examples for two popular facial image analysis tasks: face recognition and facial landmark detection. We observed the following positive effects for both tasks: 1) Priming with synthetic face images improves the generalization performance consistently across all benchmark datasets. 2) The amount of real-world data needed to achieve competitive performance is reduced by 75% for face recognition and by 50% for facial landmark detection. 3) Priming with synthetic faces is consistently superior at enhancing the performance of deep neural networks than data augmentation and transfer learning techniques. Furthermore, our experiments provide evidence that priming with synthetic faces is able to enhance performance because it reduces the negative effects of biases present in real-world training data. The proposed synthetic face image generator, as well as the software used for our experiments, have been made publicly available.

Knowledge about the thickness of the cortical bone is of high interest for fracture risk assessment. Most finite element model solutions overlook this information because of the coarse resolution of the CT images. To circumvent this limitation, a three-steps approach is proposed. 1) Two initial surface meshes approximating the outer and inner cortical surfaces are generated via a shape regression based on morphometric features and statistical shape model parameters. 2) The meshes are then corrected locally using a supervised learning model build from image features extracted from pairs of QCT (0.3-1 mm resolution) and HRpQCT images (82 pm resolution). As the resulting meshes better follow the cortical surfaces, the cortical thickness can be estimated at sub-voxel precision. 3) The meshes are finally regularized by a Gaussian process model featuring a two-kernel model, which seamlessly enables smoothness and shape-awareness priors during regularization. The resulting meshes yield high-quality mesh element properties, suitable for construction of tetrahedral meshes and finite element simulations. This pipeline was applied to 36 pairs of proximal femurs (17 males, 19 females, 76112 years) scanned under QCT and HRpQCT modalities. On a set of leave-one-out experiments, we quantified accuracy (root mean square error = 0.36 +/- 0.29 mm) and robustness (Hausdorff distance = 3.90 +/- 1.57 mm) of the outer surface meshes. The error in the estimated cortical thickness (0.05 +/- 0.40 mm), and the tetrahedral mesh quality (aspect ratio = 1.4 +/- 0.02)are also reported. The proposed pipeline produces finite element meshes with patient specific bone shape and sub-voxel cortical thickness directly from CT scans. It also ensures that the nodes and elements numbering remains consistent and independent of the morphology, which is a distinct advantage in population studies. (C) 2018 Elsevier B.V. All rights reserved.

It is unknown what kind of biases modern in the wild face datasets have because of their lack of annotation. A direct consequence of this is that total recognition rates alone only provide limited insight about the generalization ability of a Deep Convolutional Neural Networks (DCNNs). We propose to empirically study the effect of different types of dataset biases on the generalization ability of DCNNs. Using synthetically generated face images, we study the face recognition rate as a function of interpretable parameters such as face pose and light. The proposed method allows valuable details about the generalization performance of different DCNN architectures to be observed and compared. In our experiments, we find that: 1) Indeed, dataset bias has a significant influence on the generalization performance of DCNNs. 2) DCNNs can generalize surprisingly well to unseen illumination conditions and large sampling gaps in the pose variation. 3) Using the presented methodology we reveal that the VGG-16 architecture outperforms the AlexNet architecture at face recognition tasks because it can much better generalize to unseen face poses, although it has significantly more parameters. 4) We uncover a main limitation of current DCNN architectures, which is the difficulty to generalize when different identities to not share the same pose variation. 5) We demonstrate that our findings on synthetic data also apply when learning from real-world data. Our face image generator is publicly available to enable the community to benchmark other DCNN architectures.

Recent advances in deep learning have significantly increased the performance of face recognition systems. The performance and reliability of these models depend heavily on the amount and quality of the training data. However, the collection of annotated large datasets does not scale well and the control over the quality of the data decreases with the size of the dataset. In this work, we explore how synthetically generated data can be used to decrease the number of real-world images needed for training deep face recognition systems. In particular, we make use of a 3D morphable face model for the generation of images with arbitrary amounts of facial identities and with full control over image variations, such as pose, illumination, and background. In our experiments with an off-the-shelf face recognition software we observe the following phenomena: 1) The amount of real training data needed to train competitive deep face recognition systems can be reduced significantly. 2) Combining large-scale real-world data with synthetic data leads to an increased performance. 3) Models trained only on synthetic data with strong variations in pose, illumination, and background perform very well across different datasets even without dataset adaptation. 4) The real-to-virtual performance gap can be closed when using synthetic data for pre-training, followed by fine-tuning with real-world images. 5) There are no observable negative effects of pre-training with synthetic data. Thus, any face recognition system in our experiments benefits from using synthetic face images. The synthetic data generator, as well as all experiments, are publicly available.

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 and 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.

Gaussian Process Morphable Models (GPMMs) are a unifying approach to non-rigid surface and image registration, where a deformation prior is defined using a Gaussian process. By a simple exchange of the covariance function we can formulate a wide variety of different deformation priors, such as spline-based models, free-form deformations or statistical shape and deformation models. How well the method works in practical applications depends crucially on how well a low-rank approximation of the Gaussian process can be computed. In this article we propose the use of the pivoted Cholesky decomposition for this task. This method makes it possible to efficiently compute a low-rank approximation for very large point sets, such as given by 3D meshes or 3D image grids, with a rigorously controlled approximation error. Compared to the current state of the art, which is based on the Nystro m method, the approximation error is controllable and can be specified by a user-defined threshold. Further we propose a computationally more efficient and greedy alternative to currently used Karhunen-Loeve expansion. This makes it possible to compute more accurate model approximations at the same computational costs. Detailed experiments from the registration of high quality human face scans and medical CT images containing the forearm with Ulna and Radius demonstrate the efficiency of the method and the computational advantages over the Nystrom method.

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.

In this paper we propose a new approach for spatially-varying registration using Gaussian process priors. The method is based on the idea of spectral tempering, i.e. the spectrum of the Gaussian process is modified depending on a user defined tempering function. The result is a non-stationary Gaussian process, which induces different amount of smoothness in different areas. In contrast to most other schemes for spatially-varying registration, our approach does not require any change in the registration algorithm itself, but only affects the prior model. Thus we can obtain spatially-varying versions of any registration method whose deformation prior can be formulated in terms of a Gaussian process. This includes for example most spline-based models, but also statistical shape or deformation models. We present results for the problem of atlas based skull-registration of cone beam CT images. These datasets are difficult to register as they contain a large amount of noise around the teeth. We show that with our method we can become robust against noise, but still obtain accurate correspondence where the data is clean.

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness.