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

Microscopy Image Segmentation via Point and Shape Regularized Data Synthesis

Current deep learning-based approaches for the segmentation of microscopy images heavily rely on large amount of training data with dense annotation, which is highly costly and laborious in practice. Compared to full annotation where the complete contour of objects is depicted, point annotations, specifically object centroids, are much easier to acquire and still provide crucial information about the objects for subsequent segmentation. In this paper, we assume access to point annotations only during training and develop a unified pipeline for microscopy image segmentation using synthetically generated training data. Our framework includes three stages: (1) it takes point annotations and samples a pseudo dense segmentation mask constrained with shape priors; (2) with an image generative model trained in an unpaired manner, it translates the mask to a realistic microscopy image regularized by object level consistency; (3) the pseudo masks along with the synthetic images then constitute a pairwise dataset for training an ad-hoc segmentation model. On the public MoNuSeg dataset, our synthesis pipeline produces more diverse and realistic images than baseline models while maintaining high coherence between input masks and generated images. When using the identical segmentation backbones, the models trained on our synthetic dataset significantly outperform those trained with pseudo-labels or baseline-generated images. Moreover, our framework achieves comparable results to models trained on authentic microscopy images with dense labels, demonstrating its potential as a reliable and highly efficient alternative to labor-intensive manual pixel-wise annotations in microscopy image segmentation. The code is available.Comment: Accepted by The 3rd MICCAI Workshop on Data Augmentation, Labeling, and Imperfection

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