Camera Self-Calibration Using the Kruppa Equations and the SVD of the Fundamental Matrix: The Case of Varying Intrinsic Parameters

Estimation of the camera intrinsic calibration parameters is a prerequisite to a wide variety of vision tasks related to motion and stereo analysis. A major breakthrough related to the intrinsic calibration problem was the introduction in the early nineties of the autocalibration paradigm, according to which calibration is achieved not with the aid of a calibration pattern but by observing a number of image features in a set of successive images. Until recently, however, most research efforts have been focused on applying the autocalibration paradigm to estimating constant intrinsic calibration parameters. Therefore, such approaches are inapplicable to cases where the intrinsic parameters undergo continuous changes due to focusing and/or zooming. In this paper, our previous work for autocalibration in the case of constant camera intrinsic parameters is extended and a novel autocalibration method capable of handling variable intrinsic parameters is proposed. The method relies upon the Singular Value Decomposition of the fundamental matrix, which leads to a particularly simple form of the Kruppa equations. In contrast to the classical formulation that yields an over-determined system of constraints, a purely algebraic derivation is proposed here which provides a straightforward answer to the problem of determining which constraints to employ among the set of available ones. Additionally, the new formulation does not employ the epipoles, which are known to be difficult to estimate accurately. The intrinsic calibration parameters are recovered from the developed constraints through a nonlinear minimization scheme that explicitly takes into consideration the uncertainty associated with the estimates of the employed fundamental matrices. Detailed experimental results using both simulated and real image sequences demonstrate the feasibility of the approach

Camera self-calibration and analysis of singular cases

Master'sMASTER OF ENGINEERIN

Advances in 3D reconstruction

La tesi affronta il problema della ricostruzione di scene tridimensionali a partire da insiemi non strutturati di fotografie delle stesse. Lo stato dell'arte viene avanzato su diversi fronti: il primo contributo consiste in una formulazione robusta del problema di struttura e moto basata su di un approccio gerarchico, contrariamente a quello sequenziale prevalente in letteratura. Questa metodologia abbatte di un ordine di grandezza il costo computazionale complessivo, risulta inerentemente parallelizzabile, minimizza il progressivo accumulo degli errori e elimina la cruciale dipendenza dalla scelta della coppia di viste iniziale comune a tutte le formulazioni concorrenti. Un secondo contributo consiste nello sviluppo di una nuova procedura di autocalibrazione, particolarmente robusta e adatta al contesto del problema di moto e struttura. La soluzione proposta consiste in una procedura in forma chiusa per il recupero del piano all'infinito data una stima dei parametri intrinseci di almeno due camere. Questo metodo viene utilizzato per la ricerca esaustiva dei parametri interni, il cui spazio di ricerca Š strutturalmente limitato dalla finitezza dei dispositivi di acquisizione. Si Š indagato infine come visualizzare in maniera efficiente e gradevole i risultati di ricostruzione ottenuti: a tale scopo sono stati sviluppati algoritmi per il calcolo della disparit… stereo e procedure per la visualizzazione delle ricostruzione come insiemi di piani tessiturati automaticamente estratti, ottenendo una rappresentazione fedele, compatta e semanticamente significativa. Ogni risultato Š stato corredato da una validazione sperimentale rigorosa, con verifiche sia qualitative che quantitative.The thesis tackles the problem of 3D reconstruction of scenes from unstructured picture datasets. State of the art is advanced on several aspects: the first contribute consists in a robust formulation of the structure and motion problem based on a hierarchical approach, as opposed to the sequential one prevalent in literature. This methodology reduces the total computational complexity by one order of magnitude, is inherently parallelizable, minimizes the error accumulation causing drift and eliminates the crucial dependency from the choice of the initial couple of views which is common to all competing approaches. A second contribute consists in the discovery of a novel slef-calibration procedure, very robust and tailored to the structure and motion task. The proposed solution is a closed-form procedure for the recovery of the plane at infinity given a rough estimate of focal parameters of at least two cameras. This method is employed for the exaustive search of internal parameters, whise space is inherently bounded from the finiteness of acquisition devices. Finally, we inevstigated how to visualize in a efficient and compelling way the obtained reconstruction results: to this effect several algorithms for the computation of stereo disparity are presented. Along with procedures for the automatic extraction of support planes, they have been employed to obtain a faithful, compact and semantically significant representation of the scene as a collection of textured planes, eventually augmented by depth information encoded in relief maps. Every result has been verified by a rigorous experimental validation, comprising both qualitative and quantitative comparisons

Self-calibrated, multi-spectral photometric stereo for 3D face capture

This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data