A Survey of Catadioptric Omnidirectional Camera Calibration
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paper_title: Geometric properties of central catadioptric line images and their application in calibration

paper_content:

In central catadioptric systems lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough to determine the image of the absolute conic encoding the camera's intrinsic parameters. The sensitivity to errors is evaluated and the approach is used to calibrate a real camera.
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paper_title: Image-based homing

paper_content:

A system that allows a robot to acquire a model of its environment and to use this model to navigate is described. The system maps the environment as a set of snapshots of the world taken at target locations. The robot uses an image-based local homing algorithm to navigate between neighboring target locations. Features of the approach include an imaging system that acquires a compact, 360 degrees representation of the environment and an image-based, qualitative homing algorithm that allows the robot to navigate without explicitly inferring three-dimensional structure from the image. The results of an experiment in a typical indoor environment are described, and its argued that image-based navigation is a feasible alternative to approaches using three-dimensional models. >
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paper_title: A calibration method for paracatadioptric camera from sphere images

paper_content:

For paracatadioptric camera, the estimation of intrinsic parameters from sphere images is still an open and challenging problem. In this paper, we propose a calibration method for paracatadioptric camera based on sphere images, which only requires that the projected contour of parabolic mirror is visible on the image plane in one view. We have found that, under central catadioptric camera, a sphere is projected to two conics on the image plane, which are defined as a pair of antipodal sphere images. The conic that is visible on the image plane is called the sphere image, while the other invisible conic is called the antipodal sphere image. In the other aspect, according to the image formation of central catadioptric camera, these two conics can also be considered as the projections of two parallel circles on the viewing sphere by a virtue camera. That is to say, if three pairs of antipodal sphere images are known, central catadioptric camera can be directly calibrated by the calibration method based on two parallel circles. Therefore, the problem of calibrating central catadioptric camera is transferred to the estimations of sphere images and their antipodal sphere images. Based on this idea, we first initialize the intrinsic parameters of the camera by the projected contour of parabolic mirror, and use them to initialize the antipodal sphere images. Next, we study properties of several pairs of antipodal sphere images under paracatadioptric camera. Then, these properties are used to optimize sphere images and their antipodal sphere images, so as to calibrate the paracatadioptric camera. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.
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paper_title: Camera calibration from the quasi-affine invariance of two parallel circles

paper_content:

In this paper, a new camera calibration algorithm is proposed, which is from the quasi-affine invariance of two parallel circles. Two parallel circles here mean two circles in one plane, or in two parallel planes. They are quite common in our life.
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paper_title: Calibration of Central Catadioptric Cameras Using a DLT-Like Approach

paper_content:

In this study, we present a calibration technique that is valid for all single-viewpoint catadioptric cameras. We are able to represent the projection of 3D points on a catadioptric image linearly with a 6×10 projection matrix, which uses lifted coordinates for image and 3D points. This projection matrix can be computed from 3D–2D correspondences (minimum 20 points distributed in three different planes). We show how to decompose it to obtain intrinsic and extrinsic parameters. Moreover, we use this parameter estimation followed by a non-linear optimization to calibrate various types of cameras. Our results are based on the sphere camera model which considers that every central catadioptric system can be modeled using two projections, one from 3D points to a unitary sphere and then a perspective projection from the sphere to the image plane. We test our method both with simulations and real images, and we analyze the results performing a 3D reconstruction from two omnidirectional images.
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paper_title: Plane-based calibration of central catadioptric cameras

paper_content:

We present a novel calibration technique for all central catadioptric cameras using images of planar grids. We adopted the well-known sphere camera model to describe the catadioptric projection. We show that, using the so-called lifted coordinates, a linear relation mapping the grid points to the corresponding points on the image plane can be written as a 6×6 matrix H cata , which acts like the classical 3×3 homography for perspective cameras. We show how to compute the image of the absolute conic (IAC) from at least 3 homographies and how to recover from it the intrinsic parameters of the catadioptric camera. In the case of paracatadioptric cameras one such homography is enough to estimate the IAC, thus allowing the calibration from a single image.
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paper_title: A calibration method for paracatadioptric camera from sphere images

paper_content:

For paracatadioptric camera, the estimation of intrinsic parameters from sphere images is still an open and challenging problem. In this paper, we propose a calibration method for paracatadioptric camera based on sphere images, which only requires that the projected contour of parabolic mirror is visible on the image plane in one view. We have found that, under central catadioptric camera, a sphere is projected to two conics on the image plane, which are defined as a pair of antipodal sphere images. The conic that is visible on the image plane is called the sphere image, while the other invisible conic is called the antipodal sphere image. In the other aspect, according to the image formation of central catadioptric camera, these two conics can also be considered as the projections of two parallel circles on the viewing sphere by a virtue camera. That is to say, if three pairs of antipodal sphere images are known, central catadioptric camera can be directly calibrated by the calibration method based on two parallel circles. Therefore, the problem of calibrating central catadioptric camera is transferred to the estimations of sphere images and their antipodal sphere images. Based on this idea, we first initialize the intrinsic parameters of the camera by the projected contour of parabolic mirror, and use them to initialize the antipodal sphere images. Next, we study properties of several pairs of antipodal sphere images under paracatadioptric camera. Then, these properties are used to optimize sphere images and their antipodal sphere images, so as to calibrate the paracatadioptric camera. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.
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paper_title: A new linear algorithm for calibrating central catadioptric cameras

paper_content:

In this paper, a novel linear calibration algorithm based on lines is presented for central catadioptric cameras. We firstly derive the relationship between the projection on the viewing sphere of a space point and its catadioptric image. And then by the relationship we establish a group of linear constraints on the catadioptric parameters from the catadioptric projections of spatial lines. By using these linear constraints, any central catadioptric camera can be fully calibrated from a single view of three or more lines without prior knowledge on the camera. Extensive experiments show this algorithm can improve the calibration's robustness.
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Title: A Survey of Catadioptric Omnidirectional Camera Calibration

Section 1: Introduction
Description 1: Introduce the significance and challenges of camera calibration, especially for catadioptric omnidirectional cameras.

Section 2: The Construction Process of Catadioptric Omnidirectional System
Description 2: Describe the historical development and construction of catadioptric omnidirectional systems, including different types of mirrors and their respective systems.

Section 3: The Calibration of Catadioptric Omnidirectional Camera
Description 3: Explain the complexities of calibrating catadioptric cameras and outline the different calibration methods.

Section 4: Catadioptric image formation process
Description 4: Discuss the process of image formation in catadioptric systems, including relevant models and geometric constraints.

Section 5: The methods classification of catadioptric camera calibration
Description 5: Classify the various methods of catadioptric camera calibration, including methods based on different calibration objects, self-calibration, and mixed object calibration.

Section 5.1: The method based on three-dimensional control points
Description 5.1: Explain how calibration using three-dimensional control points works, listing some key techniques and their advantages.

Section 5.2: The method based on straight line
Description 5.2: Describe the method of using straight lines for calibration and its respective process and advantages.

Section 5.3: The method based on sphere
Description 5.3: Discuss the calibration method based on spheres, including its accuracy and geometric constraints.

Section 5.4: The method based on one-dimensional calibration object
Description 5.4: Elaborate on the use of one-dimensional calibration objects for camera calibration, and the flexibility and applications of this method.

Section 5.5: Self-calibration method
Description 5.5: Detail the self-calibration technique and discuss its development, advantages, and theoretical basis.

Section 5.6: The method based on mixed object
Description 5.6: Explain the mixed object calibration method which uses multiple types of calibration objects, and its unified approach using geometric algebra.

Section 6: Conclusion
Description 6: Summarize the key points of catadioptric camera calibration, including the methods discussed and their respective advantages and limitations.