International audience

Advanced shape analysis studies such as regression and classification need to be performed on curved manifolds, where often, there is a lack of standard statistical formulations. To overcome these limitations, we introduce a novel machine-learning method on the shape space of curves that avoids direct inference on infinite-dimensional spaces and instead performs Bayesian inference with spherical Gaussian processes decomposition. As an application, we study the shape of the cochlear spiral-shaped cavity within the petrous part of the temporal bone. This problem is particularly challenging due to the relationship between shape and gender, especially in children. Experimental results for both synthetic and real data show improved performance compared to state-of-the-art methods.

One of the challenging classification problems consists of learning relevant and meaningful relationships between high dimensional representations across a relatively few observed individuals. Since this problem could have drastic effects on the classification performance, we propose a Bayesian alternative in the case of logistic regression. The proposed method has the additional benefit to learn both the adaptive embedding, as a Gaussian process, and the dimensionality reduction, jointly within the same Bayesian framework. We illustrate the efficiency and the accuracy of our framework for classifying images of manufacturing defects.

We present a novel framework to analyze hand force signals and to capture their key spatio-temporal patterns in order to characterize Rheumatoid Arthritis. We introduce a new continuous representation of hand force and derive optimal intra-class alignments using the notion of Karcher means on the quotient space under the action of the warping group. We apply this idea to temporally register hand force signal data using non-linear time warping. As a result, the original signals are separated into their phase and amplitude components. To capture the amplitude and phase variabilities in force functions we compute the dominant eigenfunctions of the covariance operator using functional principal component analysis. Finally, we use support vector machine classifiers to learn priors from current state-of-the-art features and additional features derived from our functional data analysis framework. The experimental results demonstrate that the proposed framework generates clinically relevant features leading to state-of-the-art classification performance.

Learning and recognizing activity in videos is an especially important task in computer vision. However, it is hard to perform. In this paper, we propose a new method by combining local and global context information to extract a bag-of-words-like representation of a single space-time point. Each spacetime point is described by a bag of visual words that encodes its relationships with the remaining space-time points in the video, defining the space-time context. Experiments on the KTH benchmark of action recognition, show that our approach performs accurately compared to the state-of-the-art.

We present a new framework to fit a path to a given finite set of data points on a Riemannian manifold. The path takes the form of a continuously-differentiable concatenation of Riemannian Bezier segments. The selection of the control points that define the Bezier segments is partly guided by the differentiability requirement and by a minimal mean squared acceleration objective. We illustrate our approach on specific manifolds: the Euclidean plane (for sanity check), the sphere (as a first nonlinear illustration), the special orthogonal group (with rigid body motion applications), and the shape manifold (with 2D shape morphing applications).

International audience

We study the problem of joint registration and deformation analysis of endometrial tissue using 3D magnetic resonance imaging (MRI) and 2D trans-vaginal ultrasound (TVUS) measurements. In addition to the different imaging techniques involved in the two modalities, this problem is complicated due to: 1) different patient pose during MRI and TVUS observations, 2) the 3D nature of MRI and 2D nature of TVUS measurements, 3) the unknown intersecting plane for TVUS in MRI volume, and 4) the potential deformation of endometrial tissue during TVUS measurement process. Focusing on the shape of the tissue, we use expert manual segmentation of its boundaries in the two modalities and apply, with modification, recent developments in shape analysis of parametric surfaces to this problem. First, we extend the 2D TVUS curves to generalized cylindrical surfaces through replication, and then we compare them with MRI surfaces using elastic shape analysis. This shape analysis provides a simultaneous registration (optimal reparameterization) and deformation (geodesic) between any two parametrized surfaces. Specifically, it provides optimal curves on MRI surfaces that match with the original TVUS curves. This framework results in an accurate quantification and localization of the deformable endometrial cells for radiologists, and growth characterization for gynecologists and obstetricians. We present experimental results using semi-synthetic data and real data from patients to illustrate these ideas.

We propose a pattern theoretic approach for studying variability in shapes of facial surfaces. Our idea is to impose a specific, yet natural, coordinate system, called a curvilinear coordinate system, on facial surfaces. In this system, one coordinate xi1measures the distance of a point from the tip of the nose and its level curves are called the facial curves. The other coordinate xi2measures distances along these curves; level curves of this coordinate are orthogonal to the facial curves. To compare two facial surfaces we use elastic deformations that use stretching, shrinking, and bending to optimally register points across two surfaces. We will demonstrate this idea on Florida State University (FSU) 3D face database.

Recognition of human beings using shapes of their full facial surfaces is a difficult problem. Our approach is to approximate a facial surface using a collection of (closed) facial curves, and to compare surfaces by comparing their corresponding curves. The differences between shapes of curves are quantified using lengths of geodesic paths between them on a pre-defined curve shape space. The metric for comparing facial surfaces is a composition of the metric involving individual facial curves. These ideas are demonstrated in the context of face recognition using the nearest-neighbor classifier

We study shapes of facial surfaces for the purpose of face recognition. The main idea is to 1) represent surfaces by unions of level curves, called facial curves, of the depth function and 2) compare shapes of surfaces implicitly using shapes of facial curves. The latter is performed using a differential geometric approach that computes geodesic lengths between closed curves on a shape manifold. These ideas are demonstrated using a nearest-neighbor classifier on two 3D face databases: Florida State University and Notre Dame, highlighting a good recognition performance.

In this paper, we use the three-dimensional topological shape information for human face identification. We propose a new method to represent 3D faces as a topological graph. Fine registration of surfaces is done by first automatically finding topological connected components, and then constructing its topological graph representing the important topological changes on the face. The similarity calculation between 3D faces is processed using coarse-to-fine strategy while preserving the consistency of the graph structures, which result in establishing a correspondence between the parts of faces. The experiments made with a 144 3D faces dataset show the efficiency of our approach