Direct self-calibration of central catadioptric omnidirectional cameras. (Une approche directe pour l'auto-calibration des caméras catadioptriques omnidirectionnelles centrales)

Calibrating a camera means determining the geometric properties of the imaging process, i.e., the transformation that maps a three-dimensional point, expressed with respect to a reference frame, onto its two-dimensional image whose coordinates are expressed in pixel units. This process is required when recovering 3D information. More precisely, we have to know the translation and rotation of the visual sensor with respect to the rest of the frame system (extrinsic parameters), and the different parameters of the lens, such as focal length, magnitude factors, optical center retinal location (intrinsic parameters). Although the camera calibration problem is well understood, no method allowing the robust on-line self-calibration for any central omnidirectional camera is known. Existing self-calibration techniques attempt to calibrate from point correspondences, lines, circles or a specific camera motion. Even though interesting results can be achieved, self-calibration still suffers from some limitations such as small number of feature points, difficult detection of lines, undesirable camera motion and taking into account a specific mirror. Consequently, the aim of this thesis is to propose a new algorithm that overcomes these limitations and can be adopted by any robotic application or by any other practical implementation in which the calibration process is not straightforward; this algorithm works directly with the image intensity, makes the minimum of assumptions about the particular structure of the scene being viewed, stays valid for all central catadioptric systems and needs no prior knowledge about extrinsic and intrinsic parameters. Also, part of this thesis is dedicated to formalize the uniqueness of the solution for the calibration problem of central catadioptric omnidirectional cameras. For the greatest part of the work on omnidirectional camera calibration it has been observed that, in the case of a non-planar mirror, two images acquired from different points of view suffice to calibrate an omnidirectional camera. However, to our knowledge, no theoretical proof of the uniqueness of the solution has been provided yet. In this thesis the calibration problem is formalized by using a unified model that is valid for all central catadioptric omnidirectional cameras. It can be adopted to traditional cameras when a planar mirror is considered. It is also shown that the uniqueness of the problem can be derived from the solution of non-linear equations. However, due to the complexity of the non-linear equations to be solved for the general case, this thesis devises the uniqueness of the solution for the case a parabolic mirror.