High accuracy and visibility-consistent dense multiview stereo.

Since the initial comparison of Seitz et al., the accuracy of dense multiview stereovision methods has been increasing steadily. A number of limitations, however, make most of these methods not suitable to outdoor scenes taken under uncontrolled imaging conditions. The present work consists of a complete dense multiview stereo pipeline which circumvents these limitations, being able to handle large-scale scenes without sacrificing accuracy. Highly detailed reconstructions are produced within very reasonable time thanks to two key stages in our pipeline: a minimum s-t cut optimization over an adaptive domain that robustly and efficiently filters a quasidense point cloud from outliers and reconstructs an initial surface by integrating visibility constraints, followed by a mesh-based variational refinement that captures small details, smartly handling photo-consistency, regularization, and adaptive resolution. The pipeline has been tested over a wide range of scenes: from classic compact objects taken in a laboratory setting, to outdoor architectural scenes, landscapes, and cultural heritage sites. The accuracy of its reconstructions has also been measured on the dense multiview benchmark proposed by Strecha et al., showing the results to compare more than favorably with the current state-of-the-art methods.

Variational, geometric, and statistical methods for modeling brain anatomy and function.

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.