Geometric Modeling and Calibration of Planar Multi-Projector Displays Using Rational Bezier Patches

In order to achieve seamless imagery in a planar multi-projector display, geometric distortions and misalignment of images within and across projectors have to be removed. Camera-based calibration methods are popular for achieving this in an automated fashion. Previous methods for geometric calibration fall into two categories: (a) methods that model the geometric function relating the projectors to cameras using simple linear models, like homography, to calibrate the display. These models assume perfect linear devices and cannot address projector nonlinearities, like lens distortions, which are common in most commodity projectors, (b) methods that use piecewise linear approximations to model the relationship between projectors and cameras. These require a dense sampling of the function space to achieve good calibration. In this paper, we present a new closed-form model that relates projectors to cameras in planar multi-projector displays, using rational Bezier patches. This model overcomes the shortcomings of the previous methods by allowing for projectors with significant lens distortion. It can be further used to develop an efficient and accurate geometric calibration method with a sparse sampling of the function.