Eccentricity on an Image Caused by Projection of a Circle and a Sphere

Matsuoka, R.; Maruyama, S.

doi:10.5194/isprsannals-iii-5-19-2016

Cited by 6 publications

(7 citation statements)

References 3 publications

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“…However, due to the principle of perspective projection, the center of each circular pip did not coincide with the center of its projected ellipse, as illustrated in Figure 3. To find the corresponding points for radial distortion correction, the offset between the projected circle center and the ellipse center was computed using the circular projection model proposed by Matsuoka and Maruyama (2016). To be more specific, let ( )…”

Section: Radial Distortion Correctionmentioning

confidence: 99%

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A Straightforward Camera Calibration Method Based on a Single Low-cost Cubical Target

Cai,

Xia,

Chan

2024

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. Calibrating optical sensors with common targets facilitates the efficient and convenient acquisition of the sensor's internal parameters. In this paper, we present a new method of camera calibration utilizing a low-cost foamy cube, in a form of dice, which is based on the fact that arrangement of pip and cubical die surfaces is mutually orthogonal. Initially, each face and pips are identified through the color information on the die’s surfaces. Subsequently, the centers of pips are corrected using a circular projection model, and radial distortion coefficients are estimated based on centers’ one-to-one correspondences. After that, the tangent information between pairs of pips on orthogonal dice faces are utilized to compute vanishing points, leading to estimation of intrinsic parameters. Experimental results demonstrate that our method has similar effects compared to well-known checkerboard calibration method, reaching an average relative error of 2.43%, simplifying the calibration process in practical applications and showcasing good practicality and robustness.

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Section: Radial Distortion Correctionmentioning

confidence: 99%

“…x y z is unknown, it can be solved by simultaneously solving a system of equations constructed by Matsuoka and Maruyama (2016).…”

Section: Radial Distortion Correctionmentioning

confidence: 99%

A Straightforward Camera Calibration Method Based on a Single Low-cost Cubical Target

Cai,

Xia,

Chan

2024

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…4. This disparity in the image gives the eccentricity of the projection ε = e s − e 0 which has to be considered (Matsuoka and Maruyama 2016) when constructing the new method.…”

Section: Implicit Representationmentioning

confidence: 99%

A Minimal Solution for Image-Based Sphere Estimation

Toth

Hajder

2023

Int J Comput Vis

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We propose a novel minimal solver for sphere fitting via its 2D central projection, i.e., a special ellipse. The input of the presented algorithm consists of contour points detected in a camera image. General ellipse fitting problems require five contour points. However, taking advantage of the isotropic spherical target, three points are enough to define the tangent cone parameters of the sphere. This yields the sought ellipse parameters. Similarly, the sphere center can be estimated from the cone if the radius is known. These proposed geometric methods are rapid, numerically stable, and easy to implement. Experimental results—on synthetic, photorealistic, and real images—showcase the superiority of the proposed solutions to the state-of-the-art methods. A real-world LiDAR-camera calibration application justifies the utility of the sphere-based approach resulting in an error below a few centimeters.

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“…The same can be applied to determine the Y-coordinate of the centre. Let y centre = (y D + y E )/2, substituting with y D and y E from the equations x D and x E which yields to (22).…”

Section: B Centre Location Curvementioning

confidence: 99%

“…All these facts and effects could lead to an eccentric error of the projected centre of the target in the image [20], [21]. This eccentricity is defined by the disparity of the true target centre projection onto the image and the centre of the projection in the image [22], [23]. Figure 1 illustrates the three forms of distortions of a target in the image.…”

Section: Introductionmentioning

confidence: 99%

Perspective Distortion Modeling for Image Measurements

et al. 2020

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A perspective distortion modelling for monocular view that is based on the fundamentals of perspective projection is presented in this work. Perspective projection is considered to be the most ideal and realistic model among others, which depicts image formation in monocular vision. There are many approaches trying to model and estimate the perspective effects in images. Some approaches try to learn and model the distortion parameters from a set of training data that work only for a predefined structure. None of the existing methods provide deep understanding of the nature of perspective problems. Perspective distortions, in fact, can be described by three different perspective effects. These effects are pose, distance and foreshortening. They are the cause of the aberrant appearance of object shapes in images. Understanding these phenomena have long been an interesting topic for artists, designers and scientists. In many cases, this problem has to be necessarily taken into consideration when dealing with image diagnostics, high and accurate image measurement, as well as accurate pose estimation from images. In this work, a perspective distortion model for every effect is developed while elaborating the nature of perspective effects. A distortion factor for every effect is derived, then followed by proposed methods, which allows extracting the true target pose and distance, and correcting image measurements.

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Eccentricity on an Image Caused by Projection of a Circle and a Sphere

Cited by 6 publications

References 3 publications

A Straightforward Camera Calibration Method Based on a Single Low-cost Cubical Target

A Straightforward Camera Calibration Method Based on a Single Low-cost Cubical Target

A Minimal Solution for Image-Based Sphere Estimation

Perspective Distortion Modeling for Image Measurements

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