3D Reconstruction with Uncalibrated Cameras Using the Six-Line Conic Variety

We present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras with square pixels but otherwise arbitrarily varying intrinsic and extrinsic parameters. Our results, based on a novel geometric approach, include a closed-form solution for the case of three cameras and two known vanishing points and an efficient one-dimensional search algorithm for the case of four cameras and one known vanishing point. In addition, an algorithm for a reliable automatic detection of vanishing points on the images is presented. These techniques fit in a 3D reconstruction scheme oriented to urban scenes reconstruction. The satisfactory performance of the techniques is demonstrated with tests on synthetic and real data

QUBIC: The QU Bolometric Interferometer for Cosmology

One of the major challenges of modern cosmology is the detection of B-mode polarization anisotropies in the CMB. These originate from tensor fluctuations of the metric produced during the inflationary phase. Their detection would therefore constitute a major step towards understanding the primordial Universe. The expected level of these anisotropies is however so small that it requires a new generation of instruments with high sensitivity and extremely good control of systematic effects. We propose the QUBIC instrument based on the novel concept of bolometric interferometry, bringing together the sensitivity advantages of bolometric detectors with the systematics effects advantages of interferometry. Methods: The instrument will directly observe the sky through an array of entry horns whose signals will be combined together using an optical combiner. The whole set-up is located inside a cryostat. Polarization modulation will be achieved using a rotating half-wave plate and interference fringes will be imaged on two focal planes (separated by a polarizing grid) tiled with bolometers. We show that QUBIC can be considered as a synthetic imager, exactly similar to a usual imager but with a synthesized beam formed by the array of entry horns. Scanning the sky provides an additional modulation of the signal and improve the sky coverage shape. The usual techniques of map-making and power spectrum estimation can then be applied. We show that the sensitivity of such an instrument is comparable with that of an imager with the same number of horns. We anticipate a low level of beam-related systematics thanks to the fact that the synthesized beam is determined by the location of the primary horns. Other systematics should be under good control thanks to an autocalibration technique, specific to our concept, that will permit the accurate determination of most of the systematics parameters.Comment: 12 pages, 10 figures, submitted to Astronomy and Astrophysic

Method for 3D modelling based on structure from motion processing of sparse 2D images

A method based on Structure from Motion for processing a plurality of sparse images acquired by one or more acquisition devices to generate a sparse 3D points cloud and of a plurality of internal and external parameters of the acquisition devices includes the steps of collecting the images; extracting keypoints therefrom and generating keypoint descriptors; organizing the images in a proximity graph; pairwise image matching and generating keypoints connecting tracks according maximum proximity between keypoints; performing an autocalibration between image clusters to extract internal and external parameters of the acquisition devices, wherein calibration groups are defined that contain a plurality of image clusters and wherein a clustering algorithm iteratively merges the clusters in a model expressed in a common local reference system starting from clusters belonging to the same calibration group; and performing a Euclidean reconstruction of the object as a sparse 3D point cloud based on the extracted parameters

Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning

Boosting techniques and neural networks are particularly effective machine learning methods for insurance pricing. Often in practice, there are nevertheless endless debates about the choice of the right loss function to be used to train the machine learning model, as well as about the appropriate metric to assess the performances of competing models. Also, the sum of fitted values can depart from the observed totals to a large extent and this often confuses actuarial analysts. The lack of balance inherent to training models by minimizing deviance outside the familiar GLM with canonical link setting has been empirically documented in W\"uthrich (2019, 2020) who attributes it to the early stopping rule in gradient descent methods for model fitting. The present paper aims to further study this phenomenon when learning proceeds by minimizing Tweedie deviance. It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. Autocalibration is then proposed as a remedy. This new method to correct for bias adds an extra local GLM step to the analysis. Theoretically, it is shown that it implements the autocalibration concept in pure premium calculation and ensures that balance also holds on a local scale, not only at portfolio level as with existing bias-correction techniques. The convex order appears to be the natural tool to compare competing models, putting a new light on the diagnostic graphs and associated metrics proposed by Denuit et al. (2019)

Simultaneous Parameter Calibration, Localization, and Mapping

The calibration parameters of a mobile robot play a substantial role in navigation tasks. Often these parameters are subject to variations that depend either on changes in the environment or on the load of the robot. In this paper, we propose an approach to simultaneously estimate a map of the environment, the position of the on-board sensors of the robot, and its kinematic parameters. Our method requires no prior knowledge about the environment and relies only on a rough initial guess of the parameters of the platform. The proposed approach estimates the parameters online and it is able to adapt to non-stationary changes of the configuration. We tested our approach in simulated environments and on a wide range of real-world data using different types of robotic platforms. (C) 2012 Taylor & Francis and The Robotics Society of Japa

Estimating hyperparameters and instrument parameters in regularized inversion. Illustration for SPIRE/Herschel map making

We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post density for all unknown quantities, given the observations. This density is explored by a Markov Chain Monte-Carlo sampling technique based on a Gibbs loop and including a Metropolis-Hastings step. The numerical evaluation relies on the SPIRE instrument of the Herschel observatory. Using simulated and real observations, we show that the hyperparameters and instrument parameters are correctly estimated, which opens up many perspectives for imaging in astrophysics

Applications of image-based, multi-view stereo reconstruction methods = (Aplicaciones de los métodos de reconstrucción estéreo multivista)

These slides present several 3-D reconstruction methods to obtain the geometric structure of a scene that is viewed by multiple cameras. We focus on the combination of the geometric modeling in the image formation process with the use of standard optimization tools to estimate the characteristic parameters that describe the geometry of the 3-D scene. In particular, linear, non-linear and robust methods to estimate the monocular and epipolar geometry are introduced as cornerstones to generate 3-D reconstructions with multiple cameras. Some examples of systems that use this constructive strategy are Bundler, PhotoSynth, VideoSurfing, etc., which are able to obtain 3-D reconstructions with several hundreds or thousands of cameras. En esta presentación se tratan varios métodos de reconstrucción 3-D para la obtención de la estructura geométrica de una escena que es visualizada por varias cámaras. Se enfatiza la combinación de modelado geométrico del proceso de formación de la imagen con el uso de herramientas estándar de optimización para estimar los parámetros característicos que describen la geometría de la escena 3-D. En concreto, se presentan métodos de estimación lineales, no lineales y robustos de las geometrías monocular y epipolar como punto de partida para generar reconstrucciones con tres o más cámaras. Algunos ejemplos de sistemas que utilizan este enfoque constructivo son Bundler, PhotoSynth, VideoSurfing, etc., los cuales, en la práctica pueden llegar a reconstruir una escena con varios cientos o miles de cámaras