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Sensors 2018, 18(2), 408; https://doi.org/10.3390/s18020408

An Omnidirectional Vision Sensor Based on a Spherical Mirror Catadioptric System

1
Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56122 Pisa, Italy
2
Dipartimento di Meccanica, Politecnico di Milano, Via Giuseppe La Masa, 1, 20156 Milano, Italy
*
Author to whom correspondence should be addressed.
Received: 21 December 2017 / Revised: 25 January 2018 / Accepted: 26 January 2018 / Published: 31 January 2018
(This article belongs to the Section Physical Sensors)
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Abstract

The combination of mirrors and lenses, which defines a catadioptric sensor, is widely used in the computer vision field. The definition of a catadioptric sensors is based on three main features: hardware setup, projection modelling and calibration process. In this paper, a complete description of these aspects is given for an omnidirectional sensor based on a spherical mirror. The projection model of a catadioptric system can be described by the forward projection task (FP, from 3D scene point to 2D pixel coordinates) and backward projection task (BP, from 2D coordinates to 3D direction of the incident light). The forward projection of non-central catadioptric vision systems, typically obtained by using curved mirrors, is usually modelled by using a central approximation and/or by adopting iterative approaches. In this paper, an analytical closed-form solution to compute both forward and backward projection for a non-central catadioptric system with a spherical mirror is presented. In particular, the forward projection is reduced to a 4th order polynomial by determining the reflection point on the mirror surface through the intersection between a sphere and an ellipse. A matrix format of the implemented models, suitable for fast point clouds handling, is also described. A robust calibration procedure is also proposed and applied to calibrate a catadioptric sensor by determining the mirror radius and center with respect to the camera. View Full-Text
Keywords: catadioptric sensor; forward projection model; backward projection model; spherical mirror; computer vision catadioptric sensor; forward projection model; backward projection model; spherical mirror; computer vision
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Barone, S.; Carulli, M.; Neri, P.; Paoli, A.; Razionale, A.V. An Omnidirectional Vision Sensor Based on a Spherical Mirror Catadioptric System. Sensors 2018, 18, 408.

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