Marta Wilczkowiak

Camera calibration and 3D reconstruction from single images using parallelepipeds

In this paper parallelepipeds and their use in camera calibration and 3D reconstruction processes are studied. Parallelepipeds naturally characterize rigidity constraints present in a scene, such as parallelism and orthogonality. A subclass of parallelepipeds-the cuboids-has been frequently used over the past to partially calibrate cameras. However, the full potential of parallelepipeds, in camera calibration as well as in scene reconstruction, has never been clearly established. We propose a new framework for the use of parallelepipeds which is based on an extensive study of this potential. In particular, we exhibit the complete duality that exists between the intrinsic metric characteristics of a parallelepiped and the intrinsic parameters of a camera. Our framework allows to fully exploit parallelepipeds and thus overcomes several limitations of calibration approaches based on cuboids. To illustrate this framework, we present an original and very efficient interactive method for 3D reconstruction from single images. This method allows to quickly build a scene model from a single uncalibrated image.

Using geometric constraints through parallelepipeds for calibration and 3D modeling

This paper concerns the incorporation of geometric information in camera calibration and 3D modeling. Using geometric constraints enables more stable results and allows us to perform tasks with fewer images. Our approach is motivated and developed within a framework of semi-automatic 3D modeling, where the user defines geometric primitives and constraints between them. In this paper, first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described. Then, a factorization-based algorithm exploiting this relation is developed. Using images of parallelepipeds, it allows us to simultaneously calibrate cameras, recover shapes of parallelepipeds, and estimate the relative pose of all entities. Besides geometric constraints expressed via parallelepipeds, our approach simultaneously takes into account the usual self-calibration constraints on cameras. The proposed algorithm is completed by a study of the singular cases of the calibration method. A complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described. The proposed methods are validated by various experiments with real and simulated data, for single-view as well as multiview cases.

The Analysis of Ambiguous Solutions in Linear Systems and its Application to Computer Vision

The success of practical systems based on computer vision algorithms may critically depend on the correct treatment of degenerate configurations and missing data. However, even if theoretical basis exist, it appears that few efforts have been made to solve these problems in practice. In this paper, we address estimation problems based on linear constraints and for which degenerate cases are in principle easy to detect. Many algorithms, in particular in computer vision, either do not detect them or simply stop and produce no output. In many cases however, degenerate situations nevertheless allow a reliable estimation of a subset of the unknowns. We present a practical approach for splitting the variable set of a degenerate linear system into underconstrained and well defined variables. It means that even if the system as a whole is underconstrained, we can still extract useful information and give the correct solution for a subset of the unknowns. Our method is based on singular value decompositions (SVD). Using a very simple analysis of the matrix nullspace, it becomes easy and fast to split the variables into uniquely defined and ambiguous ones. To illustrate our approach, we present its applications to a novel iterative 3D reconstruction algorithm as well as to plane-based camera calibration.

VISIRE: photorealistic 3D reconstruction from video sequences

Traditionally, building 3D reconstructions of large scenarios such as a museum or historical site has been costly, time consuming and required the contribution of expert personnel. Usually the results showed an artificial look and had little interactivity. However, newly developed technologies in the areas of video analysis, camera calibration and texture fusion allow us to think in a much more satisfying scenario where the user with the only aid of a domestic video camera is able to acquire all the information it is required to construct the 3D model of the desired environment in an easy and comfortable manner. In this paper, the results obtained in the EC funded project VISIRE are presented. VISIRE attempts to construct photorealistic 3D models of large scenarios using as input multiple freehand video sequences. Once acquired, the computer vision software processes the video information off-line in order to obtain the 3D mesh together with the textures required to obtain a 3D model highly resembling the original.