Tangential Distortion Research Articles

Subaru weak lensing measurement of a z = 0.81 cluster discovered by the Atacama Cosmology Telescope Survey★

We present a Subaru weak lensing measurement of ACT-CL J0022.2-0036, one of the most luminous, high-redshift (z=0.81) Sunyaev-Zel'dovich (SZ) clusters discovered in the 268 deg^2 equatorial region survey of the Atacama Cosmology Telescope. For the weak lensing analysis using i'-band images, we use a model-fitting (Gauss-Laguerre shapelet) method to measure shapes of galaxy images, where we fit galaxy images in different exposures simultaneously to obtain best-fit ellipticities taking into account the different PSFs in each exposure. We also take into account the astrometric distortion effect on galaxy images by performing the model fitting in the world coordinate system. To select background galaxies behind the cluster at z=0.81, we use photometric redshift (photo-z) estimates for every galaxy derived from the co-added images of multi-passband Br'i'z'Y, with PSF matching/homogenization. After a photo-z cut for background galaxy selection, we detect the tangential weak lensing distortion signal with a total signal-to-noise ratio of about 3.7. By fitting a Navarro-Frenk-White model to the measured shear profile, we find the cluster mass to be M_200\bar{\rho}_m = [7.5^+3.2_-2.8(stat.)^+1.3_-0.6(sys.)] x 10^14 M_\odot/h. The weak lensing-derived mass is consistent with previous mass estimates based on the SZ observation, with assumptions of hydrostatic equilibrium and virial theorem, as well as with scaling relations between SZ signal and mass derived from weak lensing, X-ray, and velocity dispersion, within the measurement errors. We also show that the existence of ACT-CL J0022.2-0036 at z=0.81 is consistent with the cluster abundance prediction of the \Lambda-dominated cold dark matter structure formation model. We thus demonstrate the capability of Subaru-type ground-based images for studying weak lensing of high-redshift clusters.

Quantitative imaging and measurement of cell–substrate surface deformation by digital holography

Quantitative phase microscopy by digital holography (DH-QPM) is introduced to study the cell–substrate interactions and migratory behavior of adhesive cells. A non-wrinkling elastic substrate, collagen-coated polyacrylamide (PAA) has been employed and its surface deformation due to cell adhesion and motility has been visualized as certain tangential and vertical displacement and distortion. The surface deformation on substrates of different elasticity and thickness has been quantitatively imaged and the corresponding cellular traction force of motile fibroblasts has been measured from phase profiles by DH-QPM. DH-QPM is able to yield quantitative measures directly and provide efficient and versatile means for quantitatively analyzing cellular motility.

AERIAL TERRAIN MAPPING USING UNMANNED AERIAL VEHICLE APPROACH

Abstract. This paper looks into the latest achievement in the low-cost Unmanned Aerial Vehicle (UAV) technology in their capacity to map the semi-development areas. The objectives of this study are to establish a new methodology or a new algorithm in image registration during interior orientation process and to determine the accuracy of the photogrammetric products by using UAV images. Recently, UAV technology has been used in several applications such as mapping, agriculture and surveillance. The aim of this study is to scrutinize the usage of UAV to map the semi-development areas. The performance of the low cost UAV mapping study was established on a study area with two image processing methods so that the results could be comparable. A non-metric camera was attached at the bottom of UAV and it was used to capture images at both sites after it went through several calibration steps. Calibration processes were carried out to determine focal length, principal distance, radial lens distortion, tangential lens distortion and affinity. A new method in image registration for a non-metric camera is discussed in this paper as a part of new methodology of this study. This method used the UAV Global Positioning System (GPS) onboard to register the UAV image for interior orientation process. Check points were established randomly at both sites using rapid static Global Positioning System. Ground control points are used for exterior orientation process, and check point is used for accuracy assessment of photogrammetric product. All acquired images were processed in a photogrammetric software. Two methods of image registration were applied in this study, namely, GPS onboard registration and ground control point registration. Both registrations were processed by using photogrammetric software and the result is discussed. Two results were produced in this study, which are the digital orthophoto and the digital terrain model. These results were analyzed by using the root mean square errors and mean absolute error to determine the level of accuracy and the precision of photogrammetric products. It can be concluded that the new method of image registration by using the GPS onboard of the UAV produces medium accuracy result compared to the method that uses the ground control point. This new method can be used for the medium accuracy requirements. Unmanned Aerial Vehicle can be used for several applications, which requires a medium accuracy.

A Least Squares Solution for Camera Distortion Parameters

Most applications in optical metrology need a well calibrated camera. In particular, a calibrated camera includes a distortion mapping, parameters of which are determined in a final non-linear optimization over all camera parameters. In this article we present a closed form solution for the distortion parameters provided that all other camera parameters are known. We show that for radial, tangential, and thin prism distortions the determination of the parameters form a linear least squares problem. Therefore, a part of the camera calibration error function can be minimized by linear methods in closed form: We are able to decouple the calculation of the distortion parameters from the non-linear optimization. The number of parameters in the non-linear minimization are reduced. Several experimental results confirm the benefit of the approach.

Lifting the degeneracy between geometric and dynamic distortions using the sound horizon from the cosmic microwave background

The degeneracy between geometric (Alcock-Paczynski) and dynamic (redshift space) distortions in the pattern of the galaxy distribution has been a long standing problem in the study of the large scale structure of the universe. We examine the possibility of lifting this degeneracy and constraining cosmological parameters by using the Baryon Acoustic Oscillation (BAO) scale as a feature of known physical size, the sound horizon r_s ~ 150 Mpc. We callibrate this scale with the equivalent feature in the Cosmic Microwave Background (CMB). First, we construct a toy model of a power spectrum which includes the BAO as well as geometric and dynamic distortions. By adding a prior onto the sound horizon of ~1% we show, using a Fisher matrix analysis, that error ellipses for line of sight and tangential distortion parameters shrink by a factor of two for a 20(Gpc/h)^3 `DESpec/BigBOSS'-like galaxy survey including shot noise. This improvement is even more marked in smaller surveys. We also carry out a Monte Carlo Nested Sampling analysis on our parameter space. We find that Monte Carlo and Fisher methods can agree reasonably well for surveys with large volume but differ greatly for small volume surveys.

Low-cost FPGA stereo vision system for real time disparity maps calculation

Several applications demand efficient hardware implementations of stereo vision systems in order to furnish real time three-dimensional measurements. This paper proposes a complete fast low-cost stereo vision system that performs stereo image rectification with tangential and radial distortion removal, computes dense disparity maps using the Sum of Absolute Differences as the dissimilarity metric, and, finally, exploits a novel injective consistency check purpose-designed for eliminating unreliable disparity values.The proposed system has been realized and hardware tested for several images resolutions and disparity ranges. When 1280×720 grayscale images are processed with the disparity range equal to 30, the system allows a frame rate up to 97fps@89MHz to be reached. It has been realized on a single low-cost XilinxVirtex-4 XC4VLX60 FPGA chip and it occupies 63 DSPs, 128 BRAMs and 15728 slices.

Picking Robot Camera Calibration System Based on OpenCV

Aim at the effect of the radial distortion and tangential distortion, the camera calibration principle, geometric model and complex equation solution were studied, in order to reduce the artificial participation in proofreading and error correction, then the camera’s software precise calibration module based on OpenCV was developed. The results showed that the system was quickly speed, high precision and could satisfy the requirements of robot vision navigation system and built the foundation for the next step research.

An Efficient Camera Calibration Technique Offering Robustness and Accuracy Over a Wide Range of Lens Distortion

In the field of machine vision, camera calibration refers to the experimental determination of a set of parameters that describe the image formation process for a given analytical model of the machine vision system. Researchers working with low-cost digital cameras and off-the-shelf lenses generally favor camera calibration techniques that do not rely on specialized optical equipment, modifications to the hardware, or an a priori knowledge of the vision system. Most of the commonly used calibration techniques are based on the observation of a single 3-D target or multiple planar (2-D) targets with a large number of control points. This paper presents a novel calibration technique that offers improved accuracy, robustness, and efficiency over a wide range of lens distortion. This technique operates by minimizing the error between the reconstructed image points and their experimentally determined counterparts in "distortion free" space. This facilitates the incorporation of the exact lens distortion model. In addition, expressing spatial orientation in terms of unit quaternions greatly enhances the proposed calibration solution by formulating a minimally redundant system of equations that is free of singularities. Extensive performance benchmarking consisting of both computer simulation and experiments confirmed higher accuracy in calibration regardless of the amount of lens distortion present in the optics of the camera. This paper also experimentally confirmed that a comprehensive lens distortion model including higher order radial and tangential distortion terms improves calibration accuracy.

Measurement of shaft diameters by machine vision

A machine vision method for accurately measuring the diameters of cylindrical shafts is presented. Perspective projection and the geometrical features of cylindrical shafts are modeled in order to enable accurate measurement of shaft diameters. Some of the model parameters are determined using a shaft of known diameter. The camera model itself includes radial and tangential distortions terms. Experiments were used to measure the accuracy of the proposed method and the effect of the position of the camera relative to the shaft, as well as other factors.

Lens distortion models evaluation

Many lens distortion models exist with several variations, and each distortion model is calibrated by using a different technique. If someone wants to correct lens distortion, choosing the right model could represent a very difficult task. Calibration depends on the chosen model, and some methods have unstable results. Normally, the distortion model containing radial, tangential, and prism distortion is used, but it does not represent high distortion accurately. The aim of this paper is to compare different lens distortion models to define the one that obtains better results under some conditions and to explore if some model can represent high and low distortion adequately. Also, we propose a calibration technique to calibrate several models under stable conditions. Since performance is hard conditioned with the calibration technique, the metric lens distortion calibration method is used to calibrate all the evaluated models.

LoCuSS: Subaru Weak Lensing Study of 30 Galaxy Clusters

We use high-quality Subaru/Suprime-Cam imaging data to conduct a detailed weak lensing study of the distribution of dark matter in a sample of 30 X-ray luminous galaxy clusters at 0.15 $\le z \le$ 0.3. A weak lensing signal is detected at high statistical significance in each cluster, the total signal-to-noise ratio of the detections ranging from 5 to 13. Comparing spherical models to the tangential distortion profiles of the clusters individually, we are unable to discriminate statistically between a singular isothermal sphere (SIS) and Navarro, Frenk, and White (NFW) models. However, when the tangential distortion profiles are combined and then models are fitted to the stacked profile, the SIS model is rejected at 6$\ \sigma$ and 11$\ \sigma$, respectively, for low ($M_{\rm vir}\lt$ 6 $\times$ 10$^{14}\ h^{-1}\ M_\odot$) and high ($M_{\rm vir} \gt $ 6 $\times$ 10$^{14}\ h^{-1}\ M_\odot$) mass bins. We also used individual cluster NFW model fits to investigate the relationship between the cluster mass and the concentration, finding that the concentration ($c_{\rm vir}$) decreases with increasing cluster mass ($M_{\rm vir}$). The best-fit $c_{\rm vir}$–$M_{\rm vir}$ relation is: $c_{\rm vir}$($M_{\rm vir}$) $=$ 8.75$^{+4.13}_{-2.89} \times$ ($M_{\rm vir}/$10$^{14}\ h^{-1}\ M_\odot$)$^{-\alpha}$ with $\alpha \approx$ 0.40$\ \pm\ $0.19: i.e., a non-zero slope is detected at 2$\ \sigma$ significance. This relation gives a concentration of $c_{\rm vir} =$ 3.48$^{+1.65}_{-1.15}$ for clusters with $M_{\rm vir} =$ 10$^{15}\ h^{-1}M_\odot$, which is inconsistent at 4$\ \sigma$ significance with the values of $c_{\rm vir} \sim$ 10 reported for strong-lensing-selected clusters. We have found that the measurement error on the cluster mass is smaller at higher over-densities, $\Delta \simeq$ 500–2000, than at the virial over-density, $\Delta_{\rm vir} \simeq$ 110; typical fractional errors at $\Delta \simeq$ 500–2000 are improved to $\ \sigma$($M_\Delta$)$/M_{\Delta } \simeq$ 0.1–0.2 compared with 0.2–0.3 at $\Delta_{\rm vir}$. Furthermore, comparing the 3D spherical mass with the 2D cylinder mass, obtained from the aperture mass method at a given aperture radius, $\theta_\Delta$, reveals $M_{\rm 2D}$($\lt \theta_{\Delta}$)$/M_{\rm 3D}$($\lt r_\Delta = D_{\rm l}\theta_{\Delta}$) $\simeq$ 1.46 and 1.32 for $\Delta =$ 500 and $\Delta_{\rm vir}$, respectively. The amplitude of this offset agrees well with that predicted by integrating an NFW model of cluster-scale halos along the line-of-sight.

Impact of a ball on a surface with tangential compliance

A simple model is presented to explain how the spin of a ball can be enhanced when the ball is incident obliquely on a flexible surface. The mechanism involves tangential distortion of the surface and a return of the elastic energy stored in the surface via the action of the static friction force on the ball. As an example, we consider the enhancement of the spin that is possible using an appropriate type of tennis racquet string.

WEAK-LENSING MASS MEASUREMENTS OF SUBSTRUCTURES IN COMA CLUSTER WITH SUBARU/SUPRIME-CAM

We obtain the projected mass distributions for two Subaru/Suprime-Cam fields in the southwest region (r\simlt 60') of the Coma cluster (z=0.0236) by weak lensing analysis and detect eight subclump candidates. We quantify the contribution of background large-scale structure (LSS) on the projected mass distributions using SDSS multi-bands and photometric data, under the assumption of mass-to-light ratio for field galaxies. We find that one of eight subclump candidates, which is not associated with any member galaxies, is significantly affected by LSS lensing. The mean projected mass for seven subclumps extracted from the main cluster potential is <M_2D^(corr)> = (5.06\pm1.30)10^12h^-1 M_sun after a LSS correction. A tangential distortion profile over an ensemble of subclumps is well described by a truncated singular-isothermal sphere model and a truncated NFW model. A typical truncated radius of subclumps, r_t\simeq 35 h^-1 kpc, is derived without assuming any relations between mass and light for member galaxies. The radius coincides well with the tidal radius, \sim42 h^-1 kpc, of the gravitational force of the main cluster. Taking into account the incompleteness of data area, a projection effect and spurious lensing peaks, it is expected that mass of cluster substructures account for 19 percent of the virial mass, with 13 percent statistical error. The mass fraction of cluster substructures is in rough agreement with numerical simulations.

Wide-angle camera technology for automotive applications: a review

The development of electronic vision systems for the automotive market is a strongly growing field, driven in particular by customer demand to increase the safety of vehicles both for drivers and for other road users, including vulnerable road users (VRUs), such as pedestrians. Customer demand is matched by legislative developments in a number of key automotive markets; for example Europe, Japan and the US are in the process of introducing legislation to aid in the prevention of fatalities to VRUs, with emphasis on the use of vision systems. The authors discuss some of the factors that motivate the use of wide-angle and fish-eye camera technologies in vehicles. The authors describe the benefits of using wide-angle lens camera systems to display areas of a vehicle's surroundings that the driver would, otherwise, be unaware of (i.e. a vehicle's blind-zones). However, although wide- angle optics provide greater fields of view, they also introduce undesirable effects, such as radial distortion, tangential distortion and uneven illumination. These distortions have the potential to make objects difficult for the vehicle driver to recognise and, thus, potentially have a greater risk of accident. The authors describe some of the methods that can be employed to remove these unwanted effects, and digitally convert the distorted image to the ideal and intuitive rectilinear pin-hole model.

Tennis physics, anyone?

After a tennis ball lands on the court, it slows down, spins up, and squashes. Friction on the ball can even reverse direction, pushing it forward.

Accurate calibration for a camera–projector measurement system based on structured light projection

The accurate calibration for a camera–projector measurement system based on structured light projection is important to the system measurement accuracy. This study proposes an improved systematic calibration method focusing on three key factors: calibration model, calibration artifact and calibration procedures. The calibration model better describes the camera and projector imaging process by considering higher to fourth order radial and tangential lens distortion. The calibration artifact provides a sufficient number of accurate 3D reference points uniformly distributed in a common world coordinate system. And the calibration procedures calibrate the camera and projector simultaneously based on the same reference points to eliminate the influences of the camera calibration error on the projector calibration. The experiments demonstrate that our calibration method can improve the measurement accuracy by 47%.

A precise method for correcting stereo pairs collected by a new binocular device

PurposeThe paper seeks to develop a stereo vision system based on a new binocular device. It aims to present an explicit‐implicit correction method to correct radial and tangential distortion of image synchronously. It also aims to propose a step‐rotation rectification method to rectify epipolar error between stereo pairs.Design/methodology/approachLeast squares technique was used in solving the explicit‐implicit correction model. When the step‐rotation rectification method was implemented, the technology of rotating image space was used.FindingsThe paper finds that the stereo vision system based on a new binocular device can be used in different circumstances, and it can obtain more eyeshot of cameras. The explicit‐implicit correction method can eliminate radial and tangential distortion of images, and the solution to this method is so easy that it can be solved by least squares technique. The theory of step‐rotation rectification is simple, and it is effective for rectifying epipolar error.Practical implicationsThe explicit‐implicit correction method and step‐rotation rectification method can be used in correcting image distortion and epipolar error in stereo pairs collected by a stereo vision system. The new binocular device can be used in building a stereo vision system.Originality/valueA new binocular device is developed in the paper. Explicit distortion method and implicit distortion method are united to correct image distortion. A step‐rotation rectification method is proposed to rectify epipolar error.

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≤0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses ∼10 15 M ⊙ , the effect of the gravitomagnetic term is ≤0.04 per cent on strong lensing estimates and ≤0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≤1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.

Using Weak‐Lensing Dilution to Improve Measurements of the Luminous and Dark Matter in A1689

The E/SO sequence of a cluster defines a boundary redward of which a reliable weak lensing signal can be obtained from background galaxies, uncontaminated by cluster members. For bluer colors, both background and cluster members are present, reducing the distortion signal by the proportion of unlensed cluster members. In deep Subaru and HST/ACS images of A1689 the tangential distortion of galaxies with bluer colors falls rapidly toward the cluster center relative to the lensing signal of the red background. We use this dilution effect to derive the cluster light profile and luminosity function to large radius, with the advantage that no subtraction of far-field background counts is required. The light profile declines smoothly to the limit of the data, r<2Mpc/h, with a constant slope, dlog(L)/dlog(r)=-1.12+-0.06, unlike the lensing mass profile which steepens continuously with radius, so that M/L peaks at an intermediate radius, ~100kpc/h. A flatter behavior is found for the more physically meaningful ratio of dark-matter to stellar-matter, when accounting for the color-mass relation of cluster members. The cluster luminosity function has a flat slope, alpha=-1.05+-0.07, independent of radius and with no faint upturn to M_i'<-12. We establish that the very bluest objects are negligibly contaminated by the cluster V-i'<0.2, because their distortion profile rises towards the center following the red background, but offset higher by ~20%. This larger amplitude is consistent with the greater estimated depth of the faint blue galaxies, z~=2.0 compared to z~=0.85 for the red background, a purely geometric effect related to cosmological parameters. Finally, we improve upon our earlier mass profile by combining both the red and blue background populations, clearly excluding low concentration CDM profiles.

High precision camera calibration in vision measurement

In order to ensure the measurement precision for shape recovery from a stereo vision system, a novel high precision calibration method is presented. Some standard points acquired from the object of interest are used as standard world points. There are four rotation matrices and translation matrices that need to be calibrated, the first is between the left camera and the world coordinate, the second is between the right camera and the world coordinate, the third is between the left camera and the right camera, and the last is between the right camera and the left camera. The lens distortion parameters include radial and tangential distortion. The merits of the calibration method are its high precision, easy of operation, and high reliability.