scholarly journals An Efficient and Flexible Solution for Camera Autocalibration from N≥3 Views

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Rongfu Tang ◽  
Baosong Deng ◽  
Jing Li ◽  
Ye Yan
Keyword(s):  
Aspect Ratio ◽  
Focal Length ◽  
Geometric Constraints ◽  
Camera Motion ◽  
Simulation Experiments ◽  
Internal Parameters ◽  
Marquardt Algorithm ◽  
Camera Autocalibration ◽  
3D Information ◽  
Fundamental Matrices

This paper presents an efficient and flexible solution for camera autocalibration from N≥3 views, given image correspondences and zero (or known) skew only. The knowledge is not required on camera motion, 3D information, scene, or internal constraints. Our method is essentially based only on the fundamental matrices and its main virtues are threefold. Firstly, it is shown that, in the center-oriented metric coordinates, the focal length and aspect ratio can be estimated independent of considerable principle point shift (PPs). Thus, our method includes recursive steps: estimating focal length and aspect ratio and then calculating the PPs. Secondly, the optimal geometric constraints are selected for calibration by using error propagation analyses. Thirdly, the Levenberg–Marquardt algorithm is adopted for the fast final refinement of four internal parameters. Our method is fast and efficient to derive a unique calibration. Besides, this method can be applied to calibrate the focal length from two views, without requiring the prior knowledge of PPs. Good performance of our method is evaluated and confirmed in both the simulation experiments and the practical tests.

scholarly journals A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Min Kyoo Kang ◽  
Rui Huang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Variational Approach ◽  
Chemical Potential ◽  
Polymer Network ◽  
Material Model ◽  
Geometric Constraints ◽  
Free Energy Function ◽  
Finite Element Implementation

A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.

Liquid crystal lens with four driving voltages and its applications in imaging system with rectangular aperture

2021 ◽  
Author(s):  
Lvhan Xu ◽  
Yalei Zhang ◽  
Zhiqiang Liu ◽  
Mao Ye
Keyword(s):  
Liquid Crystal ◽  
Aspect Ratio ◽  
Imaging System ◽  
Focal Length ◽  
Rectangular Aperture ◽  
Liquid Crystal Lens ◽  
Four Electrodes

Abstract Liquid crystal lens has the characteristic of variable focal length. Many studies have demonstrated that electronically controlled focusing without mechanical movements can be realized by using liquid crystal lenses in imaging system. In this paper, a four-electrodes liquid crystal lens with a rectangular aperture is applied to focus. The aperture’s aspect ratio of the liquid crystal lens can be designed arbitrarily so that installing it with the periscope lens in phones becomes possible.

scholarly journals Envy-Free Division of Land

2020 ◽  
Vol 45 (3) ◽  
pp. 896-922 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Shmuel Nitzan ◽  
Avinatan Hassidim ◽  
Yonatan Aumann
Keyword(s):  
Aspect Ratio ◽  
Fair Division ◽  
Electronic Media ◽  
Geometric Shape ◽  
Geometric Constraints ◽  
Crucial Importance ◽  
One Dimensional ◽  
Individual Preferences ◽  
Cake Cutting ◽  
Natural Settings

Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (“cake”) such that the resulting division is fair according to each agent’s individual preferences. However, these algorithms either ignore the geometry of the resource altogether or assume it is one-dimensional. In practice, it is often required to divide multidimensional resources, such as land estates or advertisement spaces in print or electronic media. In such cases, the geometric shape of the allotted piece is of crucial importance. For example, when building houses or designing advertisements, in order to be useful, the allotments should be squares or rectangles with bounded aspect ratio. We, thus, introduce the problem of fair land division—fair division of a multidimensional resource wherein the allocated piece must have a prespecified geometric shape. We present constructive division algorithms that satisfy the two most prominent fairness criteria, namely envy-freeness and proportionality. In settings in which proportionality cannot be achieved because of the geometric constraints, our algorithms provide a partially proportional division, guaranteeing that the fraction allocated to each agent be at least a certain positive constant. We prove that, in many natural settings, the envy-freeness requirement is compatible with the best attainable partial-proportionality.

A Stratified Optimization Method for Camera Self-Calibration

2012 ◽  
Vol 580 ◽  
pp. 248-252
Author(s):  
Qian Sun ◽  
Dong Xu
Keyword(s):  
Aspect Ratio ◽  
Accurate Result ◽  
Focal Length ◽  
Optimization Method ◽  
Singular Value ◽  
Optimization Approach ◽  
Point Location ◽  
Principal Point ◽  
Self Calibration ◽  
Value Decomposition

We present an efficient stratified optimization approach for self-calibration of a camera in the case that its focal length and the principal point location are unknown. Generally we can assume that the two views are of the same focal length, and the pixels are nearly perfectly rectangular, also it is possible to know the aspect ratio rather accurately. In our approach, we use singular value decomposition to solve a modified Kruppa Equation to derive the focal length with the supposition that the principal point is at the center of the image, and perform an exhaustive search for the principal point near the center of the image to minimize a cost function. We can get a much accurate result with the optimized principal point location.

scholarly journals BIFOCAL STEREO FOR MULTIPATH PERSON RE-IDENTIFICATION

2017 ◽  
Vol XLII-2/W8 ◽  
pp. 37-44 ◽  
Author(s):  
G. Blott ◽  
C. Heipke
Keyword(s):  
Focal Length ◽  
Image Resolution ◽  
Field Of View ◽  
Eye Lens ◽  
Single Camera ◽  
Identification Performance ◽  
Stereo Cameras ◽  
Working Distance ◽  
3D Information ◽  
Fish Eye

This work presents an approach for the task of person re-identification by exploiting bifocal stereo cameras. Present monocular person re-identification approaches show a decreasing working distance, when increasing the image resolution to obtain a higher reidentification performance. We propose a novel 3D multipath bifocal approach, containing a rectilinear lens with larger focal length for long range distances and a fish eye lens of a smaller focal length for the near range. The person re-identification performance is at least on par with 2D re-identification approaches but the working distance of the approach is increased and on average 10% more re-identification performance can be achieved in the overlapping field of view compared to a single camera. In addition, the 3D information is exploited from the overlapping field of view to solve potential 2D ambiguities.

scholarly journals ACQUISITION OF 3D INFORMATION FOR VANISHED STRUCTURE BY USING ONLY AN ANCIENT PICTURE

2016 ◽  
Vol XLI-B5 ◽  
pp. 311-314 ◽  
Author(s):  
Y. Kunii ◽  
R. Sakamoto
Keyword(s):  
Focal Length ◽  
Body Height ◽  
3D Shape ◽  
Geometrical Information ◽  
3D Information ◽  
Camera Length

In order to acquire 3D information for reconstruction of vanished historical structure, grasp of 3D shape of such structure was attempted by using an ancient picture. Generally, 3D information of a structure is acquired by photogrammetric theory which requires two or more pictures. This paper clarifies that the geometrical information of the structure was obtained only from an ancient picture, and 3D information was acquired. This kind of method was applied for an ancient picture of the Old Imperial Theatre. The Old Imperial Theatre in the picture is constituted by two-point perspective. Therefore, estimated value of focal length of camera, length of camera to the Old Imperial Theatre and some parameters were calculated by estimation of field angle, using body height as an index of length and some geometrical information. Consequently, 3D coordinate of 120 measurement points on the surface of the Old Imperial Theatre were calculated respectively, and 3DCG modeling of the Old Imperial Theatre was realized.

High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls

2014 ◽  
Vol 764 ◽  
pp. 133-147 ◽  
Author(s):  
François Feuillebois ◽  
Maria L. Ekiel-Jeżewska ◽  
Eligiusz Wajnryb ◽  
Antoine Sellier ◽  
Jerzy Bławzdziewicz
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Intrinsic Viscosity ◽  
Effective Viscosity ◽  
Geometric Constraints ◽  
Particle Orientation ◽  
Hydrodynamic Coupling ◽  
Linear Shear ◽  
Dilute Suspension ◽  
Particle Length

AbstractA general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to $N$-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity $[{\it\mu}]$ increases monotonically when the distance $H$ between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for $H>l$, where $l$ is the particle length), where $[{\it\mu}]$ is slightly larger for smaller $H$; (ii) a ‘semi-confined’ regime, when $H$ becomes smaller than $l$, where $[{\it\mu}]$ rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when $H$ becomes smaller than 2–3 particle widths $d$, where $[{\it\mu}]$ rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

Using Single Image Parallelepipeds for Camera Calibration

2014 ◽  
Vol 496-500 ◽  
pp. 1869-1872
Author(s):  
Ye Tian ◽  
Zhen Wei Wang ◽  
Feng Chen
Keyword(s):  
Camera Calibration ◽  
Topological Structure ◽  
Geometric Constraints ◽  
Human Vision ◽  
Single Image ◽  
Paper Briefly ◽  
Self Calibration ◽  
Internal Parameters ◽  
Complicated Process ◽  
Real Objects

Human vision is generally regarded as a complicated process from feeling to consciousness. In other words, it refers to a projection form 3-D object to 2-D image, as well as a cognition of real objects according to 2-D image,The process that a real object is modeled through some images is called 3-D reconstruction. Presently, camera calibration attracts many researchers, and it includes the internal parameters and the external parameters, such as coordinate of main point, parameters of rotation and translation. Some researchers have pointed out that parallelepiped has a strict topological structure and geometric constraints. Therefore, it is suitable for the self-calibration of camera. This paper briefly explains parallelepiped methodsand tries to apply this method to deal with self-calibration. The experiments show that this method is flexible and available. image.

Fabrication and Testing of Micro Corona Motor and Micro Gas Bearings

2004 ◽  
Author(s):  
Daejong Kim ◽  
Sanghoon Lee ◽  
Michael D. Bryant
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Geometric Constraints ◽  
Test Results ◽  
X Ray ◽  
Gas Bearings ◽  
Performance Requirements ◽  
Tall Structures ◽  
Gas Bearing ◽  
Bearing System

The paper introduces fabrication processes of a micro corona motor and micro gas bearings via X-ray lithography. The micro corona motor was fabricated using a membrane-less built-on X-ray mask. The motor principle requires axially thick sharp stator electrodes. Therefore, X-ray lithography was adopted for precise, high aspect ratio characteristics. To minimize diffraction, a built-on X-ray mask (conformal mask) technique was employed with negative toned SU-8 photo resist. This technique may be suitable for fast fabrication of prototypes or very tall structures, which can be largely affected by printing gaps. Micro gas bearings were fabricated as a viable bearing system for the micro corona motor. Timembrane mask was fabricated to meet the strict performance requirements and geometric constraints of the micro gas bearing. Test results of the micro gas bearings and micro corona motor are also presented.

scholarly journals Funnel libraries for real-time robust feedback motion planning

2017 ◽  
Vol 36 (8) ◽  
pp. 947-982 ◽  
Author(s):  
Anirudha Majumdar ◽  
Russ Tedrake
Keyword(s):  
Real Time ◽  
Model Uncertainty ◽  
High Speed ◽  
Parametric Model ◽  
Geometric Constraints ◽  
Robotic Systems ◽  
Simulation Experiments ◽  
Cluttered Environments ◽  
Ground Vehicle ◽  
Bounded Disturbances

We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of “funnels” along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. We leverage powerful computational machinery from convex optimization (sums-of-squares programming in particular) to compute these funnels. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, these demonstrations constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real time in environments with complex geometric constraints.

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