The common self-polar triangle of separate circles: Properties and applications to camera calibration

Huang, Hsin-Liang; Zhang, Hui; Cheung, Yiu-ming

doi:10.1109/icip.2016.7532542

Cited by 8 publications

(14 citation statements)

References 16 publications

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“…The calibration algorithms based on the images of the circular points and the orthogonal vanishing points are denoted as ICP and OVP, respectively. A previously reported algorithm [28] that uses the common self-polar triangle of separate circles is denoted as CST, while an algorithm [29] based on two similar circles is denoted as TSC. Finally, an algorithm [27] that uses circle-pairs with common tangents is denoted as CCT.…”

Section: Methodsmentioning

confidence: 99%

“…where I is an identity matrix. Equations (8) and (28) suggest that the generalised eigenvector, L, of C * 1 , C * 2 is the null space of circle family C * (β) consisting of the base circles, C * 1 and C * 2 . On substituting (28) into (9), we get :…”

Section: Appendixes Appendix Amentioning

confidence: 99%

“…Moreover, the vanishing line of the supporting plane can be determined using two vanishing points in the image plane. Huang et al [28] found that any two separating coplanar circles have a unique common self-polar triangle. Specifically, one vertex of the common self-polar triangle lies on the line at infinity.…”

Section: Introductionmentioning

confidence: 99%

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Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

2020

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In the domain of computer vision, camera calibration is a key step in recovering the twodimensional Euclidean structure. Circles are considered important image features similar to points, lines, and conics. In this paper, a novel linear calibration method is proposed using two separate same-radius (SSR) circles as the calibration pattern. We show that the distinct pair of dual circles encodes three lines, two of which are parallel to each other and perpendicular to the remaining line. When any two coplanar or parallel circles degenerate to SSR circles, a solution can be found to recover another pair of parallel lines based on the geometric properties of the SSR circles. Using the vanishing points obtained as the key helper for determining the imaged circular points and the orthogonal vanishing points, we deduce the constraints on the image of the absolute conic (IAC) and then employ it for complete camera calibration. Furthermore, a closed-form solution for the extrinsic parameters can be obtained based on the projective invariance of the conic dual to the circular points. Evaluations based on simulated and real data confirmed the effectiveness and feasibility of the proposed algorithms. INDEX TERMS Camera calibration, conic dual, image of circular points, parallel lines, SSR circles.

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Section: Methodsmentioning

confidence: 99%

Section: Appendixes Appendix Amentioning

confidence: 99%

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Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

2020

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“…As shown in Fig. 2, vanishing line l ∞ passes through v 1 and v 2 [29]: where λ l is a non-zero scale factor and × denotes the cross product. Because vanishing line l ∞ is the projection of the infinity line on π 1 , and circle C 1 can be considered as the intersecting line of cone Q 1 and world plane π 1 , vanishing line l ∞ intersects sphere image c 1 at the imaged circular points I and J.…”

Section: A Algebraic Properties Of a Pair Of Right Circular Conesmentioning

confidence: 99%

“…On the one hand, estimate I n and J n on c n1 from Eqs. (28) and (29). On the other hand, compute two pairs of orthogonal vanishing points v nj andṽ nj according to the relationship between the diameter and conjugate diameter of c n1 , i.e.…”

Section: Tmentioning

confidence: 99%

Camera Calibration Using Projective Invariants of Sphere Images

2020

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Two novel linear camera calibration algorithms were investigated in this study. In general, an occluding contour circle of a sphere and the optical centre of a camera form a right circular cone, and the generalised eigenvectors of two right circular cones encode an infinity point that lies on two support planes containing the contour circle. In the image plane, a vanishing line can be determined by connecting two vanishing points. Furthermore, the direction of the diameter passing through the infinity point is orthogonal to the direction of its conjugate diameter; thus, a set of orthogonal vanishing points can be computed. The imaged circular points or orthogonal vanishing points provide constraints that enable the intrinsic parameters to be recovered completely. The results of simulations and comparison data obtained from actual experiments confirm the effectiveness and feasibility of the proposed algorithms. INDEX TERMS Camera calibration, conjugate diameters, generalized eigenvalue, right circular cone, vanishing point.

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Common Self-polar Triangle of Concentric Conics for Light Field Camera Calibration

Zhang

Wang

2019

Computer Vision – ACCV 2018

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The common self-polar triangle of separate circles: Properties and applications to camera calibration

Cited by 8 publications

References 16 publications

Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

Camera Calibration Using Projective Invariants of Sphere Images

Common Self-polar Triangle of Concentric Conics for Light Field Camera Calibration

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