QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge

International audienceWe present a new quasi-affine reconstruction of a scene and its application to camera self-calibration. We refer to this reconstruction as QUARCH (QUasi-Affine Reconstruction with respect to Camera centers and the Hodographs of horopters). A QUARCH can be obtained by solving a semidefinite programming problem when, (i) the images have been captured by a moving camera with constant intrinsic parameters, and (ii) a vague knowledge of the relative orientation (under or over 120°) between camera pairs is available. The resulting reconstruction comes close enough to an affine one allowing thus an easy upgrade of the QUARCH to its affine and metric counterparts. We also present a constrained Levenberg-Marquardt method for nonlinear optimization subject to Linear Matrix Inequality (LMI) constraints so as to ensure that the QUARCH LMIs are satisfied during optimization. Experiments with synthetic and real data show the benefits of QUARCH in reliably obtaining a metric reconstruction

QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge

International audienceWe present a new quasi-affine reconstruction of a scene and its application to camera self-calibration. We refer to this reconstruction as QUARCH (QUasi-Affine Reconstruction with respect to Camera centers and the Hodographs of horopters). A QUARCH can be obtained by solving a semidefinite programming problem when, (i) the images have been captured by a moving camera with constant intrinsic parameters, and (ii) a vague knowledge of the relative orientation (under or over 120°) between camera pairs is available. The resulting reconstruction comes close enough to an affine one allowing thus an easy upgrade of the QUARCH to its affine and metric counterparts. We also present a constrained Levenberg-Marquardt method for nonlinear optimization subject to Linear Matrix Inequality (LMI) constraints so as to ensure that the QUARCH LMIs are satisfied during optimization. Experiments with synthetic and real data show the benefits of QUARCH in reliably obtaining a metric reconstruction

Exploiting partial camera motion and geometry knowledge in uncalibrated 3D vision

Reconstruire la structure 3D de la scène à partir de plusieurs images est un problème fondamental de la vision par ordinateur, appelé Structure-from-Motion (SfM). Nous nous intéressons au problème de SfM non calibrée, où seule une structure à une ambiguïté projective peut être obtenue. Le but est de transformer la reconstruction projective en une reconstruction métrique, ce qui consiste à localiser la conique absolue sur le plan à l'infini. Cette thèse présente deux contributions principales. La première exploite une connaissance partielle de la géométrie de la caméra, en particulier que la caméra a des pixels carrés. La plupart des caméras modernes satisfont cette hypothèse. Nous formulons une nouvelle contrainte polynomiale sur le plan à l'infini sous cette hypothèse. La deuxième contribution exploite une vague connaissance du mouvement de la caméra, que le point de vue change légèrement lors de la capture d'images pour établir des correspondances entre les images. Nous prouvons que le plan à l'infini est confiné à un groupe convexe en exploitant les limites de l'angle de rotation relatif entre les paires de caméras. Nous proposons des méthodes dédiées à chaque contribution et présentons les résultats d'expérimentations conduites aussi bien sur des données synthétiques que sur des images réelles.Reconstructing a scene in 3D from multiple images is a fundamental problem in computer vision known as Structure-from-Motion (SfM). We investigate uncalibrated SfM, where a reconstruction only up to a projective transformation can be obtained. The goal is to recover a metric reconstruction from the projective one that involves locating the so-called Absolute Conic on the plane at infinity. The main contributions of this thesis are twofold. The first contribution exploits partial knowledge of the camera geometry, specifically that the camera has square pixels. This assumption is satisfied by most modern cameras. We formulate a new polynomial constraint on the plane at infinity under this assumption. The second contribution exploits a vague knowledge of the camera motion that the viewpoint is typically changed mildly between images to ensure sufficient overlap to match features. We show that bounds on the relative rotation angle between camera pairs can be used to constrain the plane at infinity to a convex set. We propose dedicated methods for each contribution and report the experimental evaluation conducted using synthetic and real data

Exploitation de connaissances partielles sur le mouvement et la géométrie des caméras en vision 3D non calibrée

Reconstructing a scene in 3D from multiple images is a fundamental problem in computer vision known as Structure-from-Motion (SfM). We investigate uncalibrated SfM, where a reconstruction only up to a projective transformation can be obtained. The goal is to recover a metric reconstruction from the projective one that involves locating the so-called Absolute Conic on the plane at infinity. The main contributions of this thesis are twofold. The first contribution exploits partial knowledge of the camera geometry, specifically that the camera has square pixels. This assumption is satisfied by most modern cameras. We formulate a new polynomial constraint on the plane at infinity under this assumption. The second contribution exploits a vague knowledge of the camera motion that the viewpoint is typically changed mildly between images to ensure sufficient overlap to match features. We show that bounds on the relative rotation angle between camera pairs can be used to constrain the plane at infinity to a convex set. We propose dedicated methods for each contribution and report the experimental evaluation conducted using synthetic and real data.Reconstruire la structure 3D de la scène à partir de plusieurs images est un problème fondamental de la vision par ordinateur, appelé Structure-from-Motion (SfM). Nous nous intéressons au problème de SfM non calibrée, où seule une structure à une ambiguïté projective peut être obtenue. Le but est de transformer la reconstruction projective en une reconstruction métrique, ce qui consiste à localiser la conique absolue sur le plan à l'infini. Cette thèse présente deux contributions principales. La première exploite une connaissance partielle de la géométrie de la caméra, en particulier que la caméra a des pixels carrés. La plupart des caméras modernes satisfont cette hypothèse. Nous formulons une nouvelle contrainte polynomiale sur le plan à l'infini sous cette hypothèse. La deuxième contribution exploite une vague connaissance du mouvement de la caméra, que le point de vue change légèrement lors de la capture d'images pour établir des correspondances entre les images. Nous prouvons que le plan à l'infini est confiné à un groupe convexe en exploitant les limites de l'angle de rotation relatif entre les paires de caméras. Nous proposons des méthodes dédiées à chaque contribution et présentons les résultats d'expérimentations conduites aussi bien sur des données synthétiques que sur des images réelles

Stratified Autocalibration of Cameras with Euclidean Image Plane

International audienceThis paper tackles the problem of stratified autocalibration of a moving camera with Euclidean image plane (i.e. zero skew and unit aspect ratio) and constant intrinsic parameters. We show that with these assumptions, in addition to the polynomial derived from the so-called modulus constraint, each image pair provides a new quartic polynomial in the unknown plane at infinity. For three or more images, the plane at infinity estimation is stated as a constrained polynomial optimization problem that can efficiently be solved using Lasserre's hierarchy of semidefinite relaxations. The calibration parameters and thus a metric reconstruction are subsequently obtained by solving a system of linear equations. Synthetic data and real image experiments show that the new polynomial in our proposed algorithm leads to a more reliable performance than existing methods