Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivities of different head tissues. The conductivity of tissues is subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing a lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of support points in the conductivity space. Our approach accelerates the computation time, while controlling the approximation error. Our method is tested on simulated and measured EEG data for brain and skull conductivity estimation. This test demonstrates that the approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.

Finite Element methods (FEM) usually require a mesh to describe the geometric domain on which the computations are occuring. These meshes must have several properties: 1) they must approximate the geometrical domain accurately, 2) they must have good numerical properties, and 3) they must be small enough so that the computations take a reasonable amount of time. These goals are somewhat contradictory and in many cases such as biomedical images - and particularly in the case of the head -, even though the geometric domains can effectively be extracted, eg from Magnetic Resonance Images (MRI), the generation of such meshes is quite difficult. This paper describes a technique that bypasses this mesh generation step going directly from a description by levelsets of the interfaces separating the various domains to the matrix associated to the FEM method. Using the levelsets description is quite convenient as it is already used by many segmentation tools. The technique is illustrated on spherical and realistic geometries for the Electroencephalography (EEG) direct problem.

This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If /spl omega/ denotes the 3 /spl times/ 3 symmetric matrix representing the image of that conic under the action of a camera with projection matrix P, it is shown that /spl omega/ /spl ap/ P/sup ~//spl Omega//sub /spl I.bar//P/sup ~T/ where V is the 3 /spl times/ 6 line projection matrix associated with P and /spl Omega//sub /spl I.bar// is a 6 /spl times/ 6 symmetric matrix of rank 3 representing the absolute quadratic complex. This simple relation between a camera's intrinsic parameters, its projection matrix expressed in a projective coordinate frame, and the metric upgrade separating this frame from a metric one - as respectively captured by the matrices /spl omega/, P/sup ~/ and /spl Omega//sub /spl I.bar// - provides a new framework for autocalibration, particularly well suited to typical digital cameras with rectangular or square pixels since the skew and aspect ratio are decoupled from the other intrinsic parameters in /spl omega/.

The forward electroencephalography (EEG) problem involves finding a potential V from the Poisson equation inverted Delta x (sigma inverted Delta V) f, in which f represents electrical sources in the brain, and sigma the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the boundary element method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this paper we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single- and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.

This paper focuses on the problem of calibration from a single view and a map of a scene. This situation arises quite often when modelling urban scenes, e.g. for augmented reality purposes. We show how some scenes constraints can be used to achieve a calibration like procedure. An example excerpted from a sequence of pictures for which self-calibration-like techniques consistently fail illustrates some of the benefits of the approach.

This article deals with the problem of recovering the three trifocal tensors between three views from a set of point correspondences. We give a new way of deriving the trifocal tensor based on Grassmann-Cayley algebra that sheds some new light on its structure and leads to a complete characterization of its geometric and algebraic properties which is fairly institute, i.e. geometric. We give a set of algebraic constraints satisfied by the 27 coefficients of the trifocal tensor which allow to parameterize it minimally with 18 coefficients. We then describe a robust method for estimating the trifocal tensor from point and line correspondences that uses this minimal parameterization. Experimental results show that this method as superior to the linear methods which had been previously published.

This paper intends to show that the second order spatio-temporal derivatives of de-forming image curves can be computed quite accurately from image sequences. These quantities, related to the second order optical flow parameters, are useful in the computation of the motion and the structure of a 3-D rigid curve from monocular image sequences. We show that they can be estimated directly from the points of the spatio-temporal surface generated by the image curve using polynomial approximation, and that the accuracy is at least comparable and often much better than that obtained using the other standard techniques. We consider particularly the special case of curvature because the estimation of that quantity has been studied before and show the results obtained using different methods. We then propose a "pseudo scale-space" method that should improve further the accuracy of the results.