Robust Pose Estimation and Calibration of Catadioptric Cameras With Spherical Mirrors

Catadioptric cameras broaden the field of view and reveal otherwise occluded object parts. They differ geometrically from central-perspective cameras because of light reflection from the mirror surface. To handle these effects, we present new pose-estimation and reconstruction models for imaging through spherical mirrors. We derive a closed-form equivalent to the collinearity principle via which three methods are established to estimate the system parameters: a resection-based one, a trilateration-based one that introduces novel constraints that enhance accuracy, and a direct and linear transform-based one. The estimated system parameters exhibit improved accuracy compared to the state of the art, and analysis shows intrinsic robustness to the presence of a high fraction of outliers. We then show that 3D point reconstruction can be performed at accurate levels. Thus, we provide an in-depth look into the geometrical modeling of spherical catadioptric systems and practical enhancements of accuracies and requirements to reach them.

POSE ESTIMATION AND MAPPING USING CATADIOPTRIC CAMERAS WITH SPHERICAL MIRRORS

Catadioptric cameras have the advantage of broadening the field of view and revealing otherwise occluded object parts. However, they differ geometrically from standard central perspective cameras because of light reflection from the mirror surface which alters the collinearity relation and introduces severe non-linear distortions of the imaged scene. Accommodating for these features, we present in this paper a novel modeling for pose estimation and reconstruction while imaging through spherical mirrors. We derive a closed-form equivalent to the collinearity principle via which we estimate the system’s parameters. Our model yields a resection-like solution which can be developed into a linear one. We show that accurate estimates can be derived with only a small set of control points. Analysis shows that control configuration in the orientation scheme is rather flexible and that high levels of accuracy can be reached in both pose estimation and mapping. Clearly, the ability to model objects which fall outside of the immediate camera field-of-view offers an appealing means to supplement 3-D reconstruction and modeling.

POSE ESTIMATION AND MAPPING USING CATADIOPTRIC CAMERAS WITH SPHERICAL MIRRORS

Catadioptric cameras have the advantage of broadening the field of view and revealing otherwise occluded object parts. However, they differ geometrically from standard central perspective cameras because of light reflection from the mirror surface which alters the collinearity relation and introduces severe non-linear distortions of the imaged scene. Accommodating for these features, we present in this paper a novel modeling for pose estimation and reconstruction while imaging through spherical mirrors. We derive a closed-form equivalent to the collinearity principle via which we estimate the system’s parameters. Our model yields a resection-like solution which can be developed into a linear one. We show that accurate estimates can be derived with only a small set of control points. Analysis shows that control configuration in the orientation scheme is rather flexible and that high levels of accuracy can be reached in both pose estimation and mapping. Clearly, the ability to model objects which fall outside of the immediate camera field-of-view offers an appealing means to supplement 3-D reconstruction and modeling.

Forward projection model of non-central catadioptric cameras with spherical mirrors

SUMMARYNon-central catadioptric vision is widely used in robotics and vision but suffers from the lack of an explicit closed-form forward projection model (FPM) that relates a 3D point with its 2D image. The search for the reflection point where the scene ray is projected is extremely slow and unpractical for real-time applications. Almost all methods thus rely on the assumption of a central projection model, even at the cost of an exact projection.Two recent methods are able to solve this FPM, presenting a quasi-closed form FPM. However, in the special case of spherical mirrors, further enhancements can be made. We compare these two methods for the computation of the FPM and discuss both approaches in terms of practicality and performance. We also derive new expressions for the FPM on spherical mirrors (extremely useful to robotics and graphics) which speed up its computation.