Project Parameters Research Articles

A Coupled Calibration Method for Dual Cameras-Projector System with Sub-Pixel Accuracy Feature Extraction.

Binocular structured light systems are widely used in 3D measurements. In the condition of complex and local highly reflective scenes, to obtain more 3D information, binocular systems are usually divided into two pairs of devices, each having a Single Camera and a Projector (SCP). In this case, the binocular system can be seen as Dual Cameras-Projector (DCP) system. In the DCP calibration, the Left-SCP and Right-SCP need to be calibrated separately, which leads to inconsistent parameters for the same projector, thus reducing the measurement accuracy. To solve this problem and improve manoeuvrability, a coupled calibration method using an orthogonal phase target is proposed. The 3D coordinates on a phase target are uniquely determined by the binocular camera in DCP, rather than being calculated separately in each SCP. This ensures the consistency of the projector parameters. The coordinates of the projector image plane are calculated through the unwrapped phase, while the parameters are calibrated by the plane calibration method. In order to extract sub-pixel accuracy feature points, a method based on polynomial fitting using an orthogonal phase target is exploited. The experimental results show that the reprojection error of our method is less than 0.033 pixels, which improves the calibration accuracy.

INFLUENCE ANALYSIS OF THREE DIFFERENT CAMERA CALIBRATION METHODS ON A CAMERA-PROJECTOR MEASURING SYSTEM

The challenges arising from mass production with high quality level require advanced error measurement systems and optical metrology systems. Nowadays, it is more frequent to find this type of controls at the manufacturing industry into the quality control procedures as long as the need for a faster capture speed and precision has increased. However, these techniques can be improved. The accuracy of 3D measurement systems formed by a camera-projector pair depends directly on the calibration procedure used. The projector is usually modelled as the inverse projection of a pin-hole camera, which presents the option to calibrate the system by two different approaches: as a whole system or separately. The most common approach is the use of a camera previously calibrated, followed by the calibration of the projector. Studies show that the uncertainty of the camera parameters from its calibration propagates to the projector parameters and several authors conclude that the three most widespread are: Tsai, Zhang and Direct Linear Calibration. The objective of this study is to have a clear comprehension of the relationships between the camera and projector parameters and of how uncertainty is propagated to the measurement system error. Therefore, the three calibration methods previously mentioned and some of them possible combinations are analyzed.

A method for simultaneously calibrating projectors and correcting nonlinearities

In FPP, projector nonlinearity is a significant factor affecting calibration accuracy and the reconstruction effect. Existing techniques frequently separate system calibration from nonlinearity correction, and the majority of these correction techniques necessitate the acquisition of additional images, making the process laborious. In this study, we provide a technique for solving both the nonlinear error function and the projector parameters at the same time. The parameters of the nonlinear error function are first estimated using a theoretical calculation of the phase error due to nonlinearity, based on the distribution relationship between the reprojection error and the phase of the characteristic points. The resulting nonlinear error function is then used to correct for the wrapped phase. It was shown that the projector reprojection error was decreased by 14.7 percent (RMS) and the object reconstruction quality was enhanced after two iterations.

30‐3: A Moving Camera and Synthetic Calibration Target Solution for Non‐Planar Scene Estimation and Projector Calibration

The automatic calibration of projector systems improves the possible environments available to this technology which relies on exact scene calibration. This paper explores the challenge of projector calibration and non‐planar scene estimation. This formulation assumes no prior information on the moving camera or fixed projector. Limited scene understanding provides the basis for constructing synthetic calibration targets to perform a geometric recovery through bundle adjustment. Synthetic data are generated from ground‐truth camera and projector parameters to explore the method's performance over varying properties of the synthetic calibration targets.

Automated Geometric Registration for Multi-Projector Displays on Arbitrary 3D Shapes Using Uncalibrated Devices.

In this article we present a completely automated and scalable multi-projector registration system that allows multiple uncalibrated projectors and cameras on arbitrary shape surfaces. Our method estimates the parameters of multiple uncalibrated tiled or superimposed projectors, the extrinsic parameters of the observing cameras (with known intrinsic parameters), the shape of the illuminated 3D geometry and geometrically registers the projectors on it. This is achieved without using any fiducials, even if part of the surface is visible to only one camera. The method uses a completely automatic approach for cross-correlation and cross-validation of the device parameters and the surface geometry resulting in an accurate registration on the arbitrary unknown geometry that does not need an accurate prior calibration of each of the uncalibrated devices using physical patterns or fiducials. Estimating projector parameters allows for quick recalibration of the system in the face of projector movements, by re-estimating only the parameters of the moved projector and not the entire system. Thus, our work can enable easy deployment of spatially augmented reality environments of different sizes (from small table top objects to large immersive environments), different shapes (inside-looking-out or outside-looking in), and different configurations (tiled or superimposed) using the same proposed method.

Evaluation of Solving Methods for the Fundamental Matrix Computation


 Solving the fundamental matrix is a key step in many image calibration and 3D reconstruction systems. The goal of this paper is to study the performance of non-linear solvers for estimating the fundamental matrix in projector-camera calibration. To prevent measurements errors from distorting our understanding, synthetic data are created from ground-truth camera and projector parameters and then used for the assessment of four nonlinear solving strategies.

Iterative calibration method for measurement system having lens distortions in fringe projection profilometry.

In fringe projection profilometry, system calibration is crucial for guaranteeing the measurement accuracies. Its difficulty lies in calibrating projector parameters, especially when the projector lens has distortions, since the projector, unlike a camera, cannot capture images, leading to an obstacle to knowing the correspondences between its pixels and object points. For solving this issue, this paper, exploiting the fact that the fringe phases on a plane board theoretically have a distribution of rational function, proposes an iterative calibration method based on phase measuring. Projecting fringes onto the calibration board and fitting the measured phases with a rational function allow us to determine projector pixels corresponding to the featured points on the calibration board. Using these correspondences, the projector parameters are easy to estimate. Noting that the projector lens distortions may deform the fitted phase map thus inducing errors in the estimates of the projector parameters, this paper suggests an iterative strategy to overcome this problem. By implementing the phase fitting and the parameter estimating alternately, the intrinsic and extrinsic parameters of the projector, as well as its lens distortion coefficients, are determined accurately. For compensating for the effects of the lens distortions on measurement, this paper gives two solutions. The pre-compensation actively curves the fringes in computer when generating them; whereas when using the post-compensation, the lens distortion correction is performed in the data processing stage. Both methods are experimentally verified to be effective in improving the measurement accuracies.

Flexible camera-projector calibration using superposed color checkerboards

Camera-projector calibration is essential in structured-light systems for three-dimensional imaging. A prevalent difficulty for calibration is that two different checkerboards must be captured. First, a physical checkerboard on the reference plane is required to obtain the camera parameters. Second, the physical checkerboard must be removed because it interferes with the projected pattern required to obtain the projector parameters. These requirements can be reduced if the camera is previously calibrated or specific arrangements are considered. However, the calibration procedure is very impractical and susceptible to misalignment errors. In this paper, a flexible camera-projector calibration method without any constraint on the position and orientation of the camera, the projector, and the reference plane, is proposed. For this, a physical checkerboard of a specific color is placed on the reference plane while the projector device projects another checkerboard with a different color. From an image captured by the camera, the two superposed checkerboards are recovered using the color information. In this way, the homographies required for calibration of both the camera and the projector are obtained simultaneously. The performance of the proposed method is verified experimentally by measuring the three-dimensional surface of three objects. Because of its high flexibility and accuracy, the proposed method is useful for in situ calibration of structured-light systems for three-dimensional imaging applications.

Analysis of different camera calibration methods on a camera-projector measuring system

The accuracy of metrology equipment formed by a camera-projector pair depends directly on the calibration procedure used. This kind of equipment allows to perform the calibration by two different approaches: as a whole system or separately. The most common approach is the second one: conventional calibration. Studies show that the uncertainty of the camera parameters from its calibration propagates to the projector parameters. The objective of this study is to have a clear comprehension of the relationships between the camera and projector parameters and of how uncertainty is propagated. This will be done by using a camera previously calibrated by Tsai, Zhang or Direct Linear Calibration (DLC) methods, followed by the calibration of the projector using DLC.

Depth recovering method immune to projector errors in fringe projection profilometry by use of cross-ratio invariance

In fringe projection profilometry, the projector parameters are difficult to calibrate accurately thus inducing errors in measurement results. To solve this problem, this paper analyzes the epipolar geometry of the fringe projection system, revealing that, on an epipolar plane, the depth variation along an incident ray induces the pixel movement along the epipolar line on the image plane of the camera. The depth variation and the pixel movement can be related to each other by using projective transformations. Under this condition, their cross-ratio keeps invariant. By use of this cross-ratio invariance, we suggest a depth recovering method immune to projector errors. To calibrate the measurement system, we shift a reference board perpendicularly to three positions with known depths and measure its phase maps as the reference phase maps. When measuring an object, we calculate the object depth at each pixel by equating the cross-ratio of the depths to that of the corresponding pixels having the same phase. Experimental results demonstrate that, with this technique, the errors associated with the projector, including its errors in geometry parameters, its lens distortions, and its luminance nonlinearity, do not affect the measurement results.

Robust geometric, phase and colour structured light projection system calibration

This paper introduces a new comprehensive procedure for both geometric and colour calibration of structured light system. In order to perform both geometric and colour calibration procedure, a new calibration artifact is proposed. The intrinsic and extrinsic parameters of projector and camera are estimated by using an extended pinhole camera model with a tangential and radial distortion. Camera image plane coordinates are obtained by extracting features from images of a calibration artifact. Projector image plane coordinates are calculated on the basis of continuous phase maps obtained from a fringe pattern phase reconstruction procedure. In order to stereo calibrate camera-projector system, pairs of corresponding image plane points are calculated with subpixel accuracy. In addition, one of three pattern views is used in colour calibration. RGB values of a colour field pattern detected by camera and their reference values are compared. This comparison leads to derivation of a colour transformation matrix. The performance of the proposed method is tested by measuring plane, sphere and distance reference. Also 360 degrees complex object 3D model from a set of measurements is obtained. Residual mean errors for all tests performed are calculated.

Deviation rectification for dynamic measurement of rail wear based on coordinate sets projection

Dynamic measurement of rail wear using a laser imaging system suffers from random vibrations in the laser-based imaging sensor which cause distorted rail profiles. In this paper, a simple and effective method for rectifying profile deviation is presented to address this issue. There are two main steps: profile recognition and distortion calibration. According to the constant camera and projector parameters, efficient recognition of measured profiles is achieved by analyzing the geometric difference between normal profiles and distorted ones. For a distorted profile, by constructing coordinate sets projecting from it to the standard one on triple projecting primitives, including the rail head inner line, rail waist curve and rail jaw, iterative extrinsic camera parameter self-compensation is implemented. The distortion is calibrated by projecting the distorted profile onto the x–y plane of a measuring coordinate frame, which is parallel to the rail cross section, to eliminate the influence of random vibrations in the laser-based imaging sensor. As well as evaluating the implementation with comprehensive experiments, we also compare our method with other published works. The results exhibit the effectiveness and superiority of our method for the dynamic measurement of rail wear.

Reconstruction method for fringe projection profilometry based on light beams.

A novel reconstruction method for fringe projection profilometry, based on light beams, is proposed and verified by experiments. Commonly used calibration techniques require the parameters of projector calibration or the reference planes placed in many known positions. Obviously, introducing the projector calibration can reduce the accuracy of the reconstruction result, and setting the reference planes to many known positions is a time-consuming process. Therefore, in this paper, a reconstruction method without projector's parameters is proposed and only two reference planes are introduced. A series of light beams determined by the subpixel point-to-point map on the two reference planes combined with their reflected light beams determined by the camera model are used to calculate the 3D coordinates of reconstruction points. Furthermore, the bundle adjustment strategy and the complementary gray-code phase-shifting method are utilized to ensure the accuracy and stability. Qualitative and quantitative comparisons as well as experimental tests demonstrate the performance of our proposed approach, and the measurement accuracy can reach about 0.0454 mm.

Generic precise augmented reality guiding system and its calibration method based on 3D virtual model.

Augmented reality system can be applied to provide precise guidance for various kinds of manual works. The adaptability and guiding accuracy of such systems are decided by the computational model and the corresponding calibration method. In this paper, a novel type of augmented reality guiding system and the corresponding designing scheme are proposed. Guided by external positioning equipment, the proposed system can achieve high relative indication accuracy in a large working space. Meanwhile, the proposed system is realized with a digital projector and the general back projection model is derived with geometry relationship between digitized 3D model and the projector in free space. The corresponding calibration method is also designed for the proposed system to obtain the parameters of projector. To validate the proposed back projection model, the coordinate data collected by a 3D positioning equipment is used to calculate and optimize the extrinsic parameters. The final projecting indication accuracy of the system is verified with subpixel pattern projecting technique.

A New Calibration Method of the Projector in Structured Light Measurement Technology

The calibration of the projector is necessary in the structured light measurement system with only single projector and single camera. A new calibration method of the projector with a checkerboard calibration target and a specific projecting grid pattern is proposed. The method is divided into the following steps. First, during the calibrating process, at each position of the target, one photo is captured for the checkerboard target, and another is taken with the projector projecting the specific grid pattern on the target. Second, the camera is calibrated by Zhang Z's method using the captured photos of checkerboard target. Third, image binarization, skeletonization, Hough transform and corner detection are used to obtain the pixel coordinates of feature points in the photos of grid pattern. Further, the 3D world coordinates of feature points can be calculated by the pinhole imaging model based on results acquired by Step 2 and Step 3. Since the coordinates of the feature points in the pattern are previously configured, the parameters of projector are finally calculated via the 3D world and configured pixel coordinates of the feature points. The calibration device is easy to setup and the calibrating speed is fast. Experimental results prove the effectiveness and accuracy of the method.

The Projector Calibration Based on ZHANG’s Self-Calibration Method

Projector calibration can be seen as a special case of the camera calibration. It can establish the relationship of the three dimensional space coordinates for points and projector image coordinates for points DMD by using a projector to project coding pattern. In camera calibration, ZHANG’s self-calibration was conducted in the maximum likelihood linear refinement. Operation process takes the lens distortion factors into account finding out the camera internal and external parameters finally. Using this algorithm to the projector calibration can solve the traditional linear calibration algorithm which is complex and poor robustness. Otherwise, it can improve the practicability of calibration method. This method can both calibrate the internal and external parameters of projector, which can solve the problem of independently inside or outside calibration.

Latin American Decolonial Thought, or Making the Subaltern Speak

AbstractThe Modernity/Coloniality/Decoloniality (MCD) research program is a collective project associated with Latin America. In addition to a critique of Eurocentric “colonial modernity,” the project highlights non‐Eurocentric forms of knowing and being in the world. It also aims to foster alternative or decolonial thinking emerging from the lived colonial experiences of those situated “outside” Europe. This last is what MCD proponents claim differentiates it from postcolonial critiques of modernity with their emphasis on deconstruction. This review provides a brief but critical overview of the MCD project's parameters and claims. It makes a cautionary call to those tempted by “alternatives to modernity,” who might want to uncritically adopt alternative decolonial thinking. It concludes with a call for a closer and critical engagement with Latin American decolonial ideas and those they contest.

Accurate calibration for 3D shape measurement system using a binary defocusing technique

This paper introduces a novel method to calibrate 3D shape measurement systems that use the binary defocusing technique. Specifically, this method calibrates the pixelwise z as low-order polynomial functions of absolute phase; (x, y) coordinates are calculated from camera calibration with known z value; and the camera is calibrated using the standard flat checkerboard method. Because this method does not require estimation of the projector's parameters, it can be adopted for any phase measurement system including those employing out-of-focus projectors. Our experiment found that the root-mean-squared (rms) error for the depth measurement is less than 70μm when the measurement depth range is about 100mm, which is at the same level of the calibration stage ±50μm.

Estimating Minimum Toll Rates in Public Private Partnerships

Public private partnership (PPP) is a project delivery method which is used in many countries. The main advantage of this method compared with traditional methods is in the allocation of private funds which are used for providing public services and delivery of projects such as hospitals, schools, roads, and bridges. Under road PPP projects, a commonly used mechanism for the repayment of the private investment is the user charge system, i.e., charging tolls to the facility users. Although the toll rate may be set by the government, there are certain constraints which the minimum toll rate has to meet. These constraints are mainly related to financial parameters such as project's financial internal rate of return (IRR) and debt service coverage ratio (DSCR) which private investors evaluate during the decision making process. In other words, there is a minimum toll rate required to attract private investments. In addition to the financial constraints, other project's parameters such as construction cost, concession life, or level of government subsidies also have an impact on toll rates. The objective of this paper is to investigate the relationship between the level of toll rates and several project technical and financial parameters. A financial model included in the Toolkit for PPP in Roads and Highways, developed by the World Bank and the Public-Private Infrastructure Advisory Facility (PPIAF), is used as a tool to calculate toll rates for various sets of input values. The approach which was chosen to test sensitivity of selected parameters to potential changes in input values (e.g., technical and financial parameters) is by estimation of elasticities.

Projector calibration from the camera image point of view

The traditional projector calibration always assumes that the reprojection errors on the projector image are independent and identically distributed and utilize the same method as the camera calibration. Actually, even if the measured points on the camera image are independent and identically distributed Gaussian variables, it is impossible to obtain the statistical characteristics of the reprojection errors on the projector image, because the relation between the original measurement error and the reprojection error is nonlinear. We propose a method to estimate the projector parameters according to the camera image reprojection error. It does not require us to know the statistical characteristics of the projector image point and makes full use of the background knowledge of the camera image noise, because our cost function does not concern the reprojection error on the projector image as is the case in the traditional method. The simulations and experiments affirm that this method has higher precision, even if the real noise is not normal.