Camera Calibration Based on the Common Self-polar Triangle of Sphere Images

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

doi:10.1007/978-3-319-16808-1_2

Cited by 6 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ∝ indicates equality up to a non-zero scale factor. For matrix Q −1 2 Q 1 , if there exists a transformation from Q −1 2 Q 1 to HQ −1 2 Q 1 H −1 , the eigenvalues of Q −1 2 Q 1 are preserved [19]. According to Eq.…”

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

confidence: 99%

“…The three vertices w 1 , w 2 , w 3 of a common self-polar triangle are located on line l w , and vertex w 2 (w 3 ) is the common tangent (double) point of two conics c 1 , c 2 . In this case, there is no calibration method in the literature [19], [33] that can be utilized to distinguish the vanishing point and the projection of the sphere centre. Due to lack of space, we demonstrate only a degenerate case in which no common self-polar triangles exist for conics c 1 , c 2 in this paper.…”

Section: G Singularitiesmentioning

confidence: 99%

“…Specifically, they explained the geometric and algebraic properties between the sphere image and IAC using the doublecontact theorem such that the IAC can be determined linearly by using three sphere images. Huang et al [19] explored a new linear calibration algorithm based on the properties of the common self-polar triangle of sphere images. They found that for two separate sphere images, there exists a unique common self-polar triangle that can be determined from the eigenvector of the two sphere images, and one of the vertices of the common self-polar triangle is an infinity point.…”

Section: Introductionmentioning

confidence: 99%

“…(2) There is no quartic equation solving. 3The linear approach runs faster than non-linear calibration algorithms while maintaining comparable accuracy [18], [19]. 4Without considering the algebraic relation between the sphere images and IAC [16], [17], [20], we initiated a new perspective to complete the camera calibration using the projective invariants of sphere images.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Camera Calibration Using Projective Invariants of Sphere Images

2020

View full text Add to dashboard Cite

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.

show abstract

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

confidence: 99%

Section: G Singularitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Camera Calibration Using Projective Invariants of Sphere Images

2020

View full text Add to dashboard Cite

show abstract

“…Huang et al [17] explored a new linear calibration algorithm based on the properties of the common self-polar triangle of sphere images. They found that, for two separate sphere images, there exists a unique common self-polar triangle, which can be determined from the generalised eigenvectors of the two sphere images, with one of the vertices of the common self-polar triangle being an infinity point.…”

Section: Introductionmentioning

confidence: 99%

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

2020

View full text Add to dashboard Cite

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.

show abstract