Towards 3D facial morphometry | EPFL Graph Search

In anesthesiology, the detection and anticipation of difficult tracheal intubation is crucial for patient safety. When undergoing general anesthesia, a patient who is unexpectedly difficult to intubate risks potential life-threatening complications with poor clinical outcomes, ranging from severe harm to brain damage or death. Conversely, in cases of suspected difficulty, specific equipment and personnel will be called upon to increase safety and the chances of successful intubation. Research in anesthesiology has associated a certain number of morphological features of the face and neck with higher risk of difficult intubation. Detecting and analyzing these and other potential features, thus allowing the prediction of difficulty of tracheal intubation in a robust, objective, and automatic way, may therefore improve the patients' safety. In this thesis, we first present a method to automatically classify images of the mouth cavity according to the visibility of certain oropharyngeal structures. This method is then integrated into a novel and completely automatic method, based on frontal and profile images of the patient's face, to predict the difficulty of intubation. We also provide a new database of three dimensional (3D) facial scans and present the initial steps towards a complete 3D model of the face suitable for facial morphometry applications, which include difficult tracheal intubation prediction. In order to develop and test our proposed method, we collected a large database of multimodal recordings of over 2700 patients undergoing general anesthesia. In the first part of this thesis, using two dimensional (2D) facial image analysis methods, we automatically extract morphological and appearance-based features from these images. These are used to train a classifier, which learns to discriminate between patients as being easy or difficult to intubate. We validate our approach on two different scenarios, one of them being close to a real-world clinical scenario, using 966 patients, and demonstrate that the proposed method achieves performance comparable to medical diagnosis-based predictions by experienced anesthesiologists. In the second part of this thesis, we focus on the development of a new 3D statistical model of the face to overcome some of the limitations of 2D methods. We first present EPFL3DFace, a new database of 3D facial expression scans, containing 120 subjects, performing 35 different facial expressions. Then, we develop a nonrigid alignment method to register the scans and allow for statistical analysis. Our proposed method is based on spectral geometry processing and makes use of an implicit representation of the scans in order to be robust to noise or holes in the surfaces. It presents the significant advantage of reducing the number of free parameters to optimize for in the alignment process by two orders of magnitude. We apply our proposed method on the data collected and discuss qualitative results. At its current level of performance, our fully automatic method to predict difficult intubation already has the potential to reduce the cost, and increase the availability of such predictions, by not relying on qualified anesthesiologists with years of medical training. Further data collection, in order to increase the number of patients who are difficult to intubate, as well as extracting morphological features from a 3D representation of the face are key elements to further improve the performance.

Statistical limits of high-dimensional inference problems

Clément Dominique Luneau

This thesis focuses on two kinds of statistical inference problems in signal processing and data science. The first problem is the estimation of a structured informative tensor from the observation of a noisy tensor in which it is buried. The structure comes from the possibility to decompose the informative tensor as the sum of a small number of rank-one tensors (small compared to its size). Such structure has applications in data science where data, organized into arrays, can often be explained by the interaction between a few features characteristic of the problem. The second problem is the estimation of a signal input to a feedforward neural network whose output is observed. It is relevant for many applications (phase retrieval, quantized signals) where the relation between the measurements and the quantities of interest is not linear. We look at these two statistical models in different high-dimensional limits corresponding to situations where the amount of observations and size of the signal become infinitely large. These asymptotic regimes are motivated by the ever-increasing computational power and storage capacity that make possible the processing and handling of large data sets. We take an information-theoretic approach in order to establish fundamental statistical limits of estimation in high-dimensional regimes. In particular, the main contributions of this thesis are the proofs of exact formulas for the asymptotic normalized mutual information associated with these inference problems. These are low-dimensional variational formulas that can nonetheless capture the behavior of a large system where each component interacts with all the others. Owing to the relationship between mutual information and Bayesian inference, we use the solutions to these variational problems to rigorously predict the asymptotic minimum mean-square error (MMSE), the error achieved by the (Bayes) optimal estimator. We can thus compare algorithmic performances to the statistical limit given by the MMSE. Variational formulas for the mutual information are referred to as replica symmetric (RS) ansätze due to the predictions of the heuristic replica method from statistical physics. In the past decade proofs of the validity of these predictions started to emerge. The general strategy is to show that the RS ansatz is both an upper and lower bound on the asymptotic normalized mutual information. The present work leverages on the adaptive interpolation method that proposes a unified way to prove the two bounds. We extend the adaptive interpolation to situations where the order parameter of the problem is not a scalar but a matrix, and to high-dimensional regimes that differ from the one for which the RS formula is usually conjectured. Our proofs also demonstrate the modularity of the method. Indeed, using statistical models previously studied in the literature as building blocks of more complex ones (e.g., estimated signal with a model of structure), we derive RS formulas for the normalized mutual information associated with estimation problems that are relevant to modern applications.

EPFL2021

Statistical limits of high-dimensional inference problems

Clément Dominique Luneau

EPFL2021