We present the asymptotic expansion of the solution to a diffusion equation with a finite number of absorbing inclusions of small volume. We use the first few terms in this expansion measured at the domain boundary to reconstruct the absorption parameters of the inclusions and certain geometrical characteristics. We demonstrate theoretically and numerically that the number of inclusions, their ...

Electrocardiographic Imaging (ECGI) is a new imaging technique that noninvasively images cardiac electrical activity on the heart surface. In ECGI, a multielectrode vest is used to record the body surface potential maps (BSPMs). Then, using geometrical information from CT-scans and a mathematical algorithm we construct the electrical potentials on the heart surface. The reconstruction of cardia...

It is possible to recouer the three-dimensional structure of a scene using images taken with ancalibrated cameras and pixel correspondences between these images. But such reconstruction can only be performed up to a projective transformation of the SD space. Therefore constraints have t o be put on the reconstructed data in order t o gel the reconstruction in the euclidean space. Such constrain...

Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method call...

This paper investigates critical configurations for projective reconstruction from multiple images taken by a camera moving in a straight line. Projective reconstruction refers to a determination of the 3D geometrical configuration of a set of 3D points and cameras, given only correspondences between points in the images. A configuration of points and cameras is critical if it can not be determ...

We describe a reconstruction method of multiple motion scenes, which are the scenes containing multiple moving objects, from uncalibrated views. Assuming that the objects are moving with constant velocities, the method recovers the scene structure, the trajectories of the moving objects, the camera motion and the camera intrinsic parameters (except skews) simultaneously. The number of the movin...

We present a formulation of Einstein--Maxwell vacuum fields due to plane fronted electromagnetic waves sharing their wave fronts with gravitational waves. This is based on recent geometrical reconstruction by the authors which clearly identifies cases in collide or do not collide. In former case our construction suggests an explicit example searchlight beam, accompanied radiation, sweeps across...

A new method is presented for tomographic reconstruction of objects with homogeneous attenuation. The method is based on parametric representation with Non-Uniform Rational B-Splines (NURBS) and statistical inversion with a Markov Chain Monte Carlo (MCMC) algorithm. The method recovers the approximate boundary curve shape and the attenuation value of two-dimensional homogeneous objects. The bou...

Surface reconstruction methods allow advanced analysis of brain data beyond what can be achieved using volumetric images alone. For instance, signals from distinct functional areas within the cortical sheet can be aligned, averaged and compared across subjects, while correctly modeling the folded geometry of the cortex. Even so, automated generation of cortical surface meshes from MRI data ofte...

The method of moving frames provides powerful geometrical tools for the analysis of smoothly varying frame fields. However, in the face of missing measurements, a reconstruction problem arises, one that is largely unexplored for 3D frame fields. Here we consider the particular example of reconstructing impaired cardiac diffusion magnetic resonance imaging (dMRI) data. We combine moving frame an...