Posterior shape models

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

Gaussian Process Morphable Models

Statistical shape models (SSMs) 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 SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the 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, an SSM 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 SSM. 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, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images

Empirically Analyzing the Effect of Dataset Biases on Deep Face Recognition Systems

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.Comment: Accepted to CVPR 2018 Workshop on Analysis and Modeling of Faces and Gestures (AMFG

Morphable Face Models - An Open Framework

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

An Efficient Maximum Likelihood Solution in Normal Model having Constant but Unknown Coefficients of Variation

A number of independent normal normal populations having constant but unknown coefficienls of variation are considered. The model is of more general form. There is no restriction on the number of groups and the sample size in each group may differ from one another. An efficient method of solutions based on the maximum likelihood procedure is developed. The maximum likelihood equations are reduced to a single equation. This results in a numerically exact solutions. Monte Carlo evaluations are studied. Examples from the literature are taken to illustrate the method. The estimators for the means are shown to be asymptotically more efficient than the ordinary means. The asymptotic relative efficiency increases as the relative sample size increases

Error-Controlled Model Approximation for Gaussian Process Morphable Models

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

Analyzing and Reducing the Damage of Dataset Bias to Face Recognition With Synthetic Data

It is well known that deep learning approaches to facerecognition suffer from various biases in the available train-ing data. In this work, we demonstrate the large potentialof synthetic data for analyzing and reducing the negativeeffects of dataset bias on deep face recognition systems. Inparticular we explore two complementary application areasfor synthetic face images: 1) Using fully annotated syntheticface images we can study the face recognition rate as afunction of interpretable parameters such as face pose. Thisenables us to systematically analyze the effect of differenttypes of dataset biases on the generalization ability of neu-ral network architectures. Our analysis reveals that deeperneural network architectures can generalize better to un-seen face poses. Furthermore, our study shows that currentneural network architectures cannot disentangle face poseand facial identity, which limits their generalization ability.2) We pre-train neural networks with large-scale syntheticdata that is highly variable in face pose and the number offacial identities. After a subsequent fine-tuning with real-world data, we observe that the damage of dataset bias inthe real-world data is largely reduced. Furthermore, wedemonstrate that the size of real-world datasets can be re-duced by 75% while maintaining competitive face recogni-tion performance. The data and software used in this workare publicly available

Efficient computation of low-rank Gaussian process models for surface and image registration

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-Loève 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 Nyström method