Int J Comput Vis (2012) 96:162–174 DOI 10.1007/s11263-011-0457-8 Planar Motion Estimation and Linear Ground Plane Rectification using an Uncalibrated Generic Camera Pierluigi Taddei · Ferran Espuny · Vincenzo Caglioti Received: 28 May 2009 / Accepted: 3 May 2011 / Published online: 19 May 2011 © Springer Science+Business Media, LLC 2011 Abstract We address and solve the self-calibration of a generic camera that performs planar motion while viewing (part of) a ground plane. Concretely, assuming initial sets of correspondences between several images of the ground plane as known, we are interested in determining both the camera motion and the geometry of the ground plane. The latter is obtained through the rectification of the image of the ground plane, which gives a bijective correspondence between pixels and points on the ground plane. We initially propose a method to determine the camera motion by using the motion flow between pairs of images. We perform this step with no need of camera calibration. Our solution requires the fixed ground point of the camera motion to be visible on both images. Once the camera motion is known, either by using our method or by other alternative means (e.g. GPS-based), we show that the rectification of the ground plane can be deter- mined linearly from at least three images up to a scale factor. Experimental results on real images are presented at the end of the paper to validate the proposed methods. This paper was written during an internship at Politecnico di Milano of Ferran Espuny, who received the financial support of the Spanish project MTM2006-14234-C02-01. P. Taddei ( ) Joint Research Centre of the European Commission, Ispra, Italy e-mail: pierluigi.taddei@polimi.it F. Espuny Dept. d’Àlgebra i Geometria, Universitat de Barcelona, Barcelona, Spain e-mail: fespuny@ub.edu V. Caglioti Politecnico di Milano, Milano, Italy e-mail: vincenzo.caglioti@polimi.it Keywords Self-calibration · Plane rectification · Visual odometry · Generic camera · Motion flow · Planar motion 1 Introduction Robot localization is a fundamental process in mobile robotics applications. One way to determine the displace- ments and measure the movement of a mobile robot is us- ing dead reckoning systems (such as monitoring the wheels revolutions or integrating accelerometers output). However these systems are not reliable since they provide noisy mea- surements and tend to diverge after few steps (Borenstein and Feng 1996). Visual odometry, i.e. methods based on visual estimation of the motion through images captured by one or more cam- eras, is exploited to obtain more reliable estimates. Many approaches to visual odometry are based on perspective cameras. Due to the narrow viewing cone of this camera model, the persistence of features during an image sequence is short, increasing the error cumulation. On the other hand, visual odometry systems based on panoramic cameras re- quire accurate calibration. These solutions are summarized in Sect. 2. Our purpose is to work with uncalibrated general cam- eras, not necessarily central, so as to benefit from the pos- sibility of panoramic viewing, leading to long feature per- sistence, and the simplicity of set-up, avoiding the need for calibration. The generic camera model, which associates one projection ray to each individual pixel, represents the most general mathematical model to describe a projection system (Grossberg and Nayar 2001; Sturm and Ramalingam 2004). Under this model, the relation among points on the ground plane and the image plane is not parametric and thus stan- dard visual odometry techniques cannot be applied.