Lilian Calvet

Structure-from-Motion paradigms integrating circular points: application to camera tracking

Supervisor(s) and Committee member(s): Rapporteurs :
BARTOLI Adrien, Professor, Université d’Auvergne
HARTLEY Richard, Professor, Australian National University
Opponents :
STURM Peter, Director of Research, INRIA Rhône-Alpes
FOFI David, Professor, Université de Bourgogne
CHARVILLAT Vincent, Professor, ENSEEIHT (supervisor)
GURDJOS Pierre, CNRS research engineer, ENSEEIHT (supervisor)


The thesis deals with the problem of 3D reconstruction of a rigid scene from a collection of views acquired by a digital camera. The problem addressed, referred as the Structure-from-Motion (SfM) problem, consists in computing the camera motion (including its trajectory) and the 3D characteristics of the scene based on 2D trajectories of imaged features through the collection. We propose theoretical foundations to extend some SfM paradigms in order to integrate real as well as complex imaged features as input data, and more especially imaged circular points. Circular points of a projective plane consist in a complex conjugate point-pair which is fixed under plane similarity ; thus endowing the plane with an Euclidean structure. We introduce the notion of circular markers which are planar markers that allows to compute, without any ambiguity, imaged circular points of their supporting plane in all views. Aside from providing a very “rich” euclidean information, such features can be matched even if they are arbitrarily positioned on parallel planes thanks to their invariance under plane similarity ; thus increasing their visibility compared to natural features. We show how to benefit from this geometric property in solving the projective SfM problem via a rank-reduction technique, referred to as projective factorization, of the matrix whose entries are images of real, complex and/or circular features. One of the critical issues in such a SfM paradigm is the self-calibration problem, which consists in updating a projective reconstruction into an euclidean one. We explain how to use the euclidean information provided by imaged circular points in the self-calibration algorithm operating in the dual projective space and relying on linear equations. All these contributions are finally used in an automatic camera tracking application relying on markers made up of concentric circles (called CCTags). The problem consists in computing the 3D camera motion based on a video sequence. This kind of application is generally used in the cinema or TV industry to create special effects. The camera tracking proposed in this work in designed in order to provide the best compromise between flexibility of use and accuracy.

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