Straight lines have to be straight

Most algorithms in 3D computer vision rely on the pinhole camera model because of its simplicity, whereas video optics, especially low-cost wide-angle or fish-eye lenses, generate a lot of non-linear distortion which can be critical. To find the distortion parameters of a camera, we use the following fundamental property: a camera follows the pinhole model if and only if the projection of every line in space onto the camera is a line. Consequently, if we find the transformation on the video image so that every line in space is viewed in the transformed image as a line, then we know how to remove the distortion from the image. The algorithm consists of first doing edge extraction on a possibly distorted video sequence, then doing polygonal approximation with a large tolerance on these edges to extract possible lines from the sequence, and then finding the parameters of our distortion model that best transform these edges to segments. Results are presented on real video images, compared with distortion calibration obtained by a full camera calibration method which uses a calibration grid. Received: 27 December 1999 / Accepted: 8 November 2000     

Generalized Gradients: Priors on Minimization Flows

This paper tackles an important aspect of the variational problem underlying active contours: optimization by gradient flows. Classically, the definition of a gradient depends directly on the choice of an inner product structure. This consideration is largely absent from the active contours literature. Most authors, explicitely or implicitely, assume that the space of admissible deformations is ruled by the canonical L ² inner product. The classical gradient flows reported in the literature are relative to this particular choice. Here, we investigate the relevance of using (i) other inner products, yielding other gradient descents, and (ii) other minimizing flows not deriving from any inner product. In particular, we show how to induce different degrees of spatial consistency into the minimizing flow, in order to decrease the probability of getting trapped into irrelevant local minima. We report numerical experiments indicating that the sensitivity of the active contours method to initial conditions, which seriously limits its applicability and efficiency, is alleviated by our application-specific spatially coherent minimizing flows. We show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors. Electronic supplementary material  Electronic supplementary material is available for this article at     

Modal effects in optical fibre connections: theory and experimentation

Simple expressions of modal self and cross transfer coefficients have been established in the case of an optical fibre connection with small defects. A complete theoretical study leads to exhibit special azimuthal properties for the LP_1,n modes family which had not been noticed up to date. Experimental applications of these properties in techniques of modal metrology are used in order to evaluate the quality of multimode or monomode connectors by the precise determination of the transverse offset between two fibres.     

The Vector Distance Functions

We present a novel method for representing and evolving objects of arbitrary dimension. The method, called the Vector Distance Function (VDF) method, uses the vector that connects any point in space to its closest point on the object. It can deal with smooth manifolds with and without boundaries and with shapes of different dimensions. It can be used to evolve such objects according to a variety of motions, including mean curvature. If discontinuous velocity fields are allowed the dimension of the objects can change. The evolution method that we propose guarantees that we stay in the class of VDF's and therefore that the intrinsic properties of the underlying shapes such as their dimension, curvatures can be read off easily from the VDF and its spatial derivatives at each time instant. The main disadvantage of the method is its redundancy: the size of the representation is always that of the ambient space even though the object we are representing may be of a much lower dimension. This disadvantage is also one of its strengths since it buys us flexibility.     

Editorial

International Journal of Computer Vision -     

Estimation of displacements from two 3D frames obtained from stereo

A method for estimating 3D displacements from two stereo frames is presented. It is based on the hypothesize-and-verify paradigm used to match 3D line segments between the two frames. In order to reduce the complexity of the method, an assumption is made that objects are rigid. The formulate a set of complete rigidity constraints for 3D line segments and integrate the uncertainty of measurements in this formation. The hypothesize-and-verify stages of the method use an extended Kalman filter to produce estimates of the displacements and of their uncertainty. The algorithm is shown to work on indoor and natural scenes. It is also shown to be easily extended to the case in which several mobile objects are present. The method is quite robust, fast, and has been thoroughly tested on hundreds of real stereo frames     

Building Three-Dimensional Object Models from Image Sequences

We present the results from a working system designed to reconstruct a complete CAD/CAM surface model for objects that have both smooth and sharp surface boundaries. The input is a sequence of images of the object; the output is a 3-D surface mesh that can be manipulated and rendered with standard CAD/CAM tools. It is now well known that complete surface information (second-order differential surface properties) can be recovered at edges generated by the extremal boundary of a 3-D surface, In this paper we present new results in applying this theoretical framework to many views of a real object to build a complete 3-D model. Our experiments place these multiple frames in a common coordinate system using known motion, if available, or by otherwise automatically computing object motion based on our classification of edges in the reconstruction process. Experimental results are shown for bath real and synthetic data.     

Editorial

International Journal of Computer Vision -