The focus of this work is calibration of the land-use module of an integrated land-use and transportation model (ILUTM). The calibration task involves estimating key parameters that dictate the output of the land-use module. Hence, an algorithm based on maximum-likelihood estimation (MLE) is developed for calibration. Furthermore, the observed values of the outputs from the land-use module are assumed to admit a Gaussian error. The ILUTM methodology used here is TRANUS which is used to model the city of Grenoble in France. The aforementioned algorithm is then applied to calibrate the land-use module of the Grenoble model. The covariance of the Gaussian error term is assumed to be unknown. It is represented as a function of the land-use module inputs and "hyperparameters.â' The resulting MLE optimization problem has 111 parameters to be estimated, 90 of which are land use parameters and 21 are hyperparameters of the Gaussian covariance kernel. The performance of the proposed calibration methodology is then compared to the traditional calibration techniques used for land use and transportation models, when applied to the Grenoble land-use model. It is observed that the proposed method outperforms the traditional technique when compared based upon a given quantity of interest.

In this paper, we address the problem of segmenting data defined on a manifold into a set of regions with uniform properties. In particular, we propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex energy and then enjoys significant favorable properties: it is robust to initialization and avoid the problem of the existence of local minima present in many variational models. The contributions of this paper are threefold: firstly we adapt the convex image labeling model to manifolds; in particular the total variation formulation. Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction. We demonstrate the efficiency of our method by testing it on various data.

We introduce an original approach for the cerebral white matter connectivity mapping from diffusion tensor imaging (DTI). Our method relies on a global modeling of the acquired magnetic resonance imaging volume as a Riemannian manifold whose metric directly derives from the diffusion tensor. These tensors will be used to measure physical three-dimensional distances between different locations of a brain diffusion tensor image. The key concept is the notion of geodesic distance that will allow us to find optimal paths in the white matter. We claim that such optimal paths are reasonable approximations of neural fiber bundles. The geodesic distance function can be seen as the solution of two theoretically equivalent but, in practice, significantly different problems in the partial differential equation framework: an initial value problem which is intrinsically dynamic, and a boundary value problem which is, on the contrary, intrinsically stationary. The two approaches have very different properties which make them more or less adequate for our problem and more or less computationally efficient. The dynamic formulation is quite easy to implement but has several practical drawbacks. On the contrary, the stationary formulation is much more tedious to implement; we will show, however, that it has many virtues which make it more suitable for our connectivity mapping problem. Finally, we will present different possible measures of connectivity, reflecting the degree of connectivity between different regions of the brain. We will illustrate these notions on synthetic and real DTI datasets.

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This paper addresses the problem of image-based surface reconstruction. The main contribution is the computation of the exact derivative of the reprojection error functional. This allows its rigorous minimization via gradient descent surface evolution. The main difficulty has been to correctly take into account the visibility changes that occur when the surface moves. A geometric and analytical study of these changes is presented and used for the computation of derivative. Our analysis shows the strong influence that the movement of the contour generators has on the reprojection error. As a consequence, during the proper minimization of the reprojection error, the contour generators of the surface are automatically moved to their correct location in the images. Therefore, current methods adding additional silhouettes or apparent contour constraints to ensure this alignment can now be understood and justified by a single criterion: the reprojection error.

This paper presents a shape representation and a variational framework for the construction of diffeomorphisms that establish "meaningful"correspondences between images, in that they preserve the local geometry of singularities such as region boundaries. At the same time, the shape representation allows enforcing shape information locally in determining such region boundaries. Our representation is based on a kernel descriptor that characterizes local shape. This shape descriptor is robust to noise and forms a scale-space in which an appropriate scale can be chosen depending on the size of features of interest in the scene. In order to preserve local shape during the matching procedure, we introduce a novel constraint to traditional energybased approaches to estimate diffeomorphic deformations, and enforce it in a variational framework.

We propose a novel, fast and robust technique for the computation of anatomical connectivity in the brain. Our approach exploits the information provided by Diffusion Tensor Magnetic Resonance Imaging (or DTI) and models the white matter by using Riemannian geometry and control theory. We show that it is possible, from a region of interest, to compute the geodesic distance to any other point and the associated optimal vector field. The latter can be used to trace shortest paths coinciding with neural fiber bundles. We also demonstrate that no explicit computation of those 3D curves is necessary to assess the degree of connectivity of the region of interest with the rest of the brain. We finally introduce a general local connectivity measure whose statistics along the optimal paths may be used to evaluate the degree of connectivity of any pair of voxels. All those quantities can be computed simultaneously in a Fast Marching framework, directly yielding the connectivity maps. Apart from being extremely fast, this method has other advantages such as the strict respect of the convoluted geometry of white matter, the fact that it is parameter-free, and its robustness to noise. We illustrate our technique by showing results on real and synthetic datasets. OurGCM(Geodesic Connectivity Mapping) algorithm is implemented in C++ and will be soon available on the web.

Shape from shading is known to be an ill-posed problem. We show in this paper that if we model the problem in a different way than it is usually done, more precisely by taking into account the 1/r/sup 2/ attenuation term of the illumination, shape from shading becomes completely well-posed. Thus the shading allows to recover (almost) any surface from only one image (of this surface) without any additional data (in particular, without the knowledge of the heights of the solution at the local intensity "minima", contrary to [P. Dupuis et al. (1994), E. Prados et al. (2004), B. Horn (1986), E. Rouy et al. (1992), R. Kimmel et al. (2001)]) and without regularity assumptions (contrary to [J. Oliensis et al. (1993), R. Kimmel et al. (1995)], for example). More precisely, we formulate the problem as that of solving a new partial differential equation (PDE), we develop a complete mathematical study of this equation and we design a new provably convergent numerical method. Finally, we present results of our new shape from shading method on various synthetic and real images.

This article proposes a solution of the Lambertian shape from shading (SFS) problem in the case of a pinhole camera model (performing a perspective projection). Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach allows us to naturally deal with nonsmooth solutions and provides a mathematical framework for proving correctness of our algorithms. Our work extends previous work in the area in three aspects. First, it models the camera as a pinhole whereas most authors assume an orthographic projection, thereby extending the applicability of shape from shading methods to more realistic images. In particular it extends the work of E. Prados et al. (2002) and E. Rouy et al. (1992). Second, by adapting the brightness equation to the perspective problem, we obtain a new partial differential equation (PDE). Results about the existence and uniqueness of its solution are also obtained. Third, it allows us to come up with a new approximation scheme and a new algorithm for computing numerical approximations of the "continuous" solution as well as a proof of their convergence toward that solution.