Canonical Representation and Multi-View Geometry of Cylinders

Navab, Nassir; Appel, M.

doi:10.1007/s11263-006-7935-4

Cited by 26 publications

(10 citation statements)

References 17 publications

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“…In consequence, determining the exact features of the 3-D object using solely its projection is not a trivial matter. The 3-D reconstruction (also called pose estimation) of a cylinder using its projected contour is a problem investigated by several computer vision studies due to its difficulty and numerous applications (Huang et al 1996;Doignon & de Mathelin 2007;Shiu & Huang 1993;Navab & Appel 2006). Huang et al (1996) presented a pose determination method using only the straight line projection of the sides of the cylinder, based on the image from a single camera.…”

Section: Resultsmentioning

confidence: 99%

Kinematics and wake of freely falling cylinders at moderate Reynolds numbers

2019

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We investigated experimentally the motion of elongated finite-length cylinders (length $L$, diameter $d$) freely falling under the effect of buoyancy in a low-viscosity fluid otherwise at rest. For cylinders with densities $\unicode[STIX]{x1D70C}_{c}$ close to the density $\unicode[STIX]{x1D70C}_{f}$ of the fluid ($\overline{\unicode[STIX]{x1D70C}}=\unicode[STIX]{x1D70C}_{c}/\unicode[STIX]{x1D70C}_{f}\simeq 1.16$), we explored the effect of the body volume by varying the Archimedes number $Ar$ (based on the body equivalent diameter) between 200 and 1100, as well as the effect of their length-to-diameter ratios $L/d$ ranging from 2 to 20. A shadowgraphy technique involving two cameras mounted on a travelling cart was used to track the cylinders along their fall over a distance longer than $30L$. A dedicated image processing algorithm was further implemented to properly reconstruct the position and orientation of the cylinders in the three-dimensional space. In the range of parameters explored, we identified three main types of paths, matching regimes known to exist for three-dimensional bodies (short-length cylinders, disks and spheres). Two of these are stationary, namely, the rectilinear motion and the large-amplitude oscillatory motion (also referred to as fluttering or zigzag motion), and their characterization is the focus of the present paper. Furthermore, in the transitional region between these two regimes, we observed irregular low-amplitude oscillatory motions, that may be assimilated to the A-regimes or quasi-vertical regimes of the literature. Flow visualization using dye released from the bodies uncovered the existence of different types of vortex shedding in the wake of the cylinders, according to the style of path. The detailed analysis of the body kinematics in the fluttering regime brought to light a series of remarkable properties. In particular, when normalized with the characteristic velocity scale $u_{0}=\sqrt{(\overline{\unicode[STIX]{x1D70C}}-1)gd}$ and the characteristic length scale $l_{0}=\sqrt{dL}$, the mean vertical velocity $\overline{u_{Z}}$ and the frequency $f$ of the oscillations become almost independent of $L/d$ and $Ar$. The use of the length scale $l_{0}$ and of the gravitational velocity scale to build the Strouhal number $St^{\ast }=fl_{0}/u_{0}$ allowed us to generalize to short ($0.1\leqslant L/d\leqslant 0.5$) and elongated cylinders ($2\leqslant L/d\leqslant 12$), the result $St^{\ast }\simeq 0.1$. An interpretation of $l_{0}$ as a characteristic length scale associated with the oscillatory recirculation thickness generated near the body ends is proposed. In addition, the rotation rate of the cylinders scales with $u_{0}/L$, for all $L/d$ and $Ar$ investigated. Furthermore, the phase difference between the oscillations of the velocity component $u$ along the cylinder axis and of the inclination angle $\unicode[STIX]{x1D703}$ of the cylinder is approximately constant, whatever the elongation ratio $L/d$ and the Archimedes number $Ar$.

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Section: Resultsmentioning

confidence: 99%

Kinematics and wake of freely falling cylinders at moderate Reynolds numbers

2019

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“…According to the mapping relationship, the 3D model of a tube can be reconstructed. Jones and Navab proposed a mathematical model of a cylinder centerline to represent a straight tube [28], [29]. The model parameters are solved from the edge points in each image.…”

Section: B Related Workmentioning

confidence: 99%

A Universal, Rapid and Accurate Measurement for Bend Tubes Based on Multi-View Vision

Liu

et al. 2019

IEEE Access

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Non-circular-cross-section tubes are widely used as heat exchange components throughout the industry, including in fields such as aerospace, automobiles, and vessels. Tube manufacturing in these fields is a highly complex process; to manufacture the needed tubes and guarantee a precise and stress-free assembly, the geometric parameters should be measured during manufacturing and before assembly. However, current studies and manufacturing instrumentation focus on tubes of circular cross section. This study proposes an extraction method for the tubular 3D skeleton of non-circular-cross-section tubes based on multi-view vision. Then, non-circular-cross-section tubes can be measured based on the proposed method. The experimental results show that the average deviation does not exceed 0.3 mm with 3σ reliability and the measuring time is fewer than 5 s. The accuracy and efficiency of this method are sufficient to satisfy the requirements for industrial applications.

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“…In the context of this paper, approaches trying to recover pose from conics, cylinders, or quadrics are closely related. An extensive survey can be found in [23], but the closest and most specialized treatment is in [24] and [25]. The projection geometry of conics and the decomposition of conic projections in intrinsic and extrinsic parameters is introduced in [26], [27], and Augmented Reality based tracking using circles and cylinder projections was accomplished in [28].…”

Section: Introductionmentioning

confidence: 99%

“…We assume that the radius of the cylinder is known (perhaps using the approach in [29]), and we focus on the problem of estimating the pose of the cylinder in a camera fixed frame. The closest concise treatment of a relative cylinder pose can be found in [25].…”

Section: Introductionmentioning

confidence: 99%

Visual Servoing of Quadrotors for Perching by Hanging From Cylindrical Objects

Thomas

Loianno

Daniilidis

et al. 2016

IEEE Robot. Autom. Lett.

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This paper addresses vision-based localization and servoing for quadrotors to enable autonomous perching by hanging from cylindrical structures using only a monocular camera. We focus on the problems of relative pose estimation, control, and trajectory planning for maneuvering a robot relative to cylinders with unknown orientations. We first develop a geometric model that describes the pose of the robot relative to a cylinder. Then, we derive the dynamics of the system, expressed in terms of the image features. Based on the dynamics, we present a controller which guarantees asymptotic convergence to the desired image space coordinates. Finally, we develop an effective method to plan dynamically-feasible trajectories in the image space, and we provide experimental results to demonstrate the proposed method under different operating conditions such as hovering, trajectory tracking, and perching. Abstract-This paper addresses vision-based localization and servoing for quadrotors to enable autonomous perching by hanging from cylindrical structures using only a monocular camera. We focus on the problems of relative pose estimation, control, and trajectory planning for maneuvering a robot relative to cylinders with unknown orientations. We first develop a geometric model that describes the pose of the robot relative to a cylinder. Then, we derive the dynamics of the system, expressed in terms of the image features. Based on the dynamics, we present a controller which guarantees asymptotic convergence to the desired image space coordinates. Finally, we develop an effective method to plan dynamically-feasible trajectories in the image space, and we provide experimental results to demonstrate the proposed method under different operating conditions such as hovering, trajectory tracking, and perching.

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Canonical Representation and Multi-View Geometry of Cylinders

Cited by 26 publications

References 17 publications

Kinematics and wake of freely falling cylinders at moderate Reynolds numbers

Kinematics and wake of freely falling cylinders at moderate Reynolds numbers

A Universal, Rapid and Accurate Measurement for Bend Tubes Based on Multi-View Vision

Visual Servoing of Quadrotors for Perching by Hanging From Cylindrical Objects

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