Thèse : Davesh Adlakha : Exploiting partial camera motion and geométry knowledge in uncalibrated 3D vision

Davesh Adlakha is pleased to invite you to his thesis defense that will take place on Monday 
December 12 at 14h in the auditorium A301 of the Pole API Illkirch (300 Bd. Sébastien Brant, Illkirch). 
The defense will be in English and will be followed by a reception.

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

Team : RDH

Abstract

This thesis concerns 3D computer vision, where the fundamental problem is reconstructing a scene in 3D 
from multiple images captured from different viewpoints. Known as Structure-from-Motion (SfM), 
this problem has various applications, such as in cultural heritage and augmented reality. We investigate 
uncalibrated SfM, where a reconstruction only up to a projective transformation can be obtained from 
feature correspondences across images. The goal is to recover a metric representation of the scene from
the projective one. This involves locating the so-called Absolute Conic (AC) on the plane at infinity that 
acts as a virtual calibration object analogous to a physical calibration pattern used in calibrated SfM. 
The main contributions of this thesis are two-fold. The first contribution exploits a vague knowledge of 
the camera motion that the viewpoint is typically changed mildly between images to ensure sufficient over
lap 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. Based on this constraint, we show the existence 
of a new quasi-affine reconstruction of a scene with respect to the “Hodographs of the Horopter”, new 
geometric objects that we introduce in this thesis. We propose a semidefinite programming problem to 
recover such reconstruction from a projective one and present a constrained Levenberg-Marquardt optimization 
method to upgrade it to affine. The metric reconstruction is then recovered by solving linear equations. 
The second 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 and propose a method for an affine upgrade that relies on polynomial 
optimization using the so-called Lasserre’s hierarchy of convex relaxations. Experiments with synthetic data and real images 
validate our proposed methods.

Jury

Pascal Monasse: Professor, Ecole des Ponts ParisTech (Reviewer)

Andrea Fusiello: Associate Professor, University of Udine, Italy (Reviewer)

Pascal Vasseur: Professor, University of Picardie Jules Verne, Amiens (Examiner)

Peter Sturm: Research Director, INRIA Grenoble Rhone-Alpes (Examiner)

Michel de Mathelin: Professor, University of Strasbourg (Thesis director)

Adlane Habed: Associate Professor, University of Strasbourg (Advisor)

Fabio Morbidi: Associate Professor, University of Picardie Jules Verne, Amiens (Advisor)

Cédric Demonceaux: Professor, University of Burgundy - Franche-Comté (Advisor)