Linear solution for the pose estimation of noncentral catadioptric systems

We propose a novel calibration method for catadioptric systems made up of an axial symmetrical mirror and a pinhole camera with its optical center located at the mirror axis. The calibration estimates the relative camera/mirror position and the extrinsic rotation and translation w.r.t. the world frame. The procedure requires a single image of a (possibly planar) calibration object. We show how most of the calibration parameters can be estimated using linear methods (Direct-Linear-Transformation algorithm) and cross-ratio. Two remaining parameters are obtained by using non-linear optimization. We present experimental results on simulated and real images.

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“…We assume, however, that the pinhole camera is internally calibrated (a common assumption, e.g. [33,14,18,34]).…”

Section: Our Methods Is Capable Of Calibratingmentioning

confidence: 99%

“…Some calibration methods assume an independent calibration of the perspective camera [14,15,16], which can be robustly achieved using well-established techniques for conventional cameras. Many consider the mirror shape to be accurately known from the manufacturing process [17,18,19,20].…”

Section: Previous Work On Catadioptric Calibrationmentioning

confidence: 99%

Calibration of mirror position and extrinsic parameters in axial non-central catadioptric systems

Perdigoto

Araújo

2013

Computer Vision and Image Understanding

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“…where the discriminant is given by: ( 5) and the appropriate root must be chosen in the same way as stated for the Snell Law.…”

Section: Fermat Principlementioning

confidence: 99%

“…This mapping between the 3D points and the image 2D points is the projection model searched for. Goncalves and Araujo have also partially addressed this problem [5].…”

Section: Introductionmentioning

confidence: 98%

Projection through quadric mirrors made faster

Gonçalves

Nogueira

2009

2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops

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This paper presents a novel framework to project 3D points through curved mirrors to an image device. The problem solved is the search for the reflection point for an arbitrary vision system with a quadric shaped mirror. The main advantage claimed for the framework presented is its computer efficiency while providing better accuracy since the search for the reflection point is made in a parameterized curve that is function of a single unknown. The alternative solvers are the classical Snell Law and the Fermat Principle that, as proved in experiments, present a much slower convergence than the new method since they have a multidimensional search space rather than a unidimensional one. This new method can be used to speed up calibration of noncentral catadioptric systems based on reprojection error. It can also be used for rendering purposes since it enhances the performance of the projection of points through mirrors while enhancing its accuracy, whether the mirror is part of the vision system (catadioptric camera) or if it is only a specular surface in the scene that reflects light in arbitrary directions. Another application of this framework is for illumination purposes, providing a faster way to compute reflected light direction or for the computation of the direction of the light source. Experiments in performance evaluation show the usefulness of the method presented.

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“…Gebken [14] presented a novel perspective pose estimation for omnidirectional vision that involves a parabolic central catadioptric sensor by using small data sets, combining geometry and stochastics such that they obtain pose Sensors 2021, 21, 4008 2 of 13 from only three image points. Goncalvep [15] proved that any reflection point belongs to an analytical quadric that intersects the mirror quadric itself and presented a linear method to estimate the pose for the noncentral omnidirectional system. Ilizirov [16] proposed deriving the metric between internal reflections; a closed form similar to the principle of collinearity was obtained and then extended to a linear model.…”

Section: Introductionmentioning

confidence: 99%

Pose Estimation of Omnidirectional Camera with Improved EPnP Algorithm

Gong

Xiping

et al. 2021

Sensors

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The omnidirectional camera, having the advantage of broadening the field of view, realizes 360° imaging in the horizontal direction. Due to light reflection from the mirror surface, the collinearity relation is altered and the imaged scene has severe nonlinear distortions. This makes it more difficult to estimate the pose of the omnidirectional camera. To solve this problem, we derive the mapping from omnidirectional camera to traditional camera and propose an omnidirectional camera linear imaging model. Based on the linear imaging model, we improve the EPnP algorithm to calculate the omnidirectional camera pose. To validate the proposed solution, we conducted simulations and physical experiments. Results show that the algorithm has a good performance in resisting noise.

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Linear solution for the pose estimation of noncentral catadioptric systems

Cited by 3 publications

References 17 publications

Calibration of mirror position and extrinsic parameters in axial non-central catadioptric systems

Calibration of mirror position and extrinsic parameters in axial non-central catadioptric systems

Projection through quadric mirrors made faster

Pose Estimation of Omnidirectional Camera with Improved EPnP Algorithm

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