Projector Calibration Research Articles

单周期条纹双四步相移投影仪的标定方法

单周期条纹双四步相移投影仪的标定方法

Novel projector calibration method for monocular structured light system based on digital image correlation

Monocular structured light system, which consists of one camera and one digital light processing (DLP) projector, is a simple and effective tool to acquire accurate three-dimensional (3D) shapes. But such high precision is only possible if the projector is accurately calibrated. Many of the existing projector calibration methods have complicated procedures or low calibration precision. In this paper, an accurate speckle-based feature points matching method is proposed to estimate the image coordinates of feature points in projection chip (digital micro-mirror device or DMD) plane. The method relies on an uncalibrated camera and makes use of affine transformation theory and two-dimensional digital image correlation (2D-DIC) method to reach sub-pixel matching precision. Considering the skew of the projection chip, a full-parameter calibration model is presented to describe the projector. A novel system is developed and series of validation tests were carried out to demonstrate the performance of the proposed method.

Flexible digital projector calibration method based on per-pixel distortion measurement and correction

When a digital projector is applied in high precision applications, the intrinsic parameters and distortion characteristics should be calibrated precisely. In this paper, a flexible full-field projector calibration method is proposed without any approximate distortion model. With planar homography theory and fringe projection technique, the projector distortion characteristic on each pixel can be measured independently and an initial distortion map is generated. The intrinsic parameters are calibrated afterwards. Then, the initial distortion map can be refined by correcting the non-perpendicularity between the optical axis and image plane. The original pattern to be projected is corrected with the refined distortion map. Thus, the calibrated projector can be regarded as an ideal projector conforming to the pinhole model. Experimental results show a nearly ideal residual map for the corrected projection pattern. In addition, the proposed calibration method is flexible without any sophisticated ancillary equipment or complicated procedure.

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.

Precise full-field distortion rectification and evaluation method for a digital projector

Digital projectors have been widely used in many accuracy-sensitive fields. Although some calibration methods have been proposed to obtain the intrinsic parameters for a digital projector, especially the radial and tangential distortion, there are few studies on how to rectify the projected image to obtain an ideal projection pattern and further evaluate the results. In this paper, a precise full-field image rectification technique is proposed based on the principle of projector calibration. The pixel remapping and interpolation techniques are detailed step by step. All of the method’s steps maintain subpixel accuracy. Moreover, a full-field verification method is presented to evaluate the effectiveness of the projector distortion procedure using a full-field phase map. A full-field non-linear distortion distribution map can be generated to represent distortion characteristics of nearly all the pixels of a projector in a very intuitive way. The experimental results validate and show the effectiveness of the proposed full-field rectification technique and evaluation method.

Auto‐calibration of a projector–camera stereo system for projection mapping

AbstractStandard camera and projector calibration techniques use a checkerboard that is manually shown at different poses to determine the calibration parameters. Furthermore, when image geometric correction must be performed on a three‐dimensional (3D) surface, such as projection mapping, the surface geometry must be determined. Camera calibration and 3D surface estimation can be costly, error prone, and time‐consuming when performed manually. To address this issue, we use an auto‐calibration technique that projects a series of Gray code structured light patterns. These patterns are captured by the camera to build a dense pixel correspondence between the projector and camera, which are used to calibrate the stereo system using an objective function, which embeds the calibration parameters together with the undistorted points. Minimization is carried out by a greedy algorithm that minimizes the cost at each iteration with respect to both calibration parameters and noisy image points. We test the auto‐calibration on different scenes and show that the results closely match a manual calibration of the system. We show that this technique can be used to build a 3D model of the scene, which in turn with the dense pixel correspondence can be used for geometric screen correction on any arbitrary surface.

Scene Depth Perception Based on Omnidirectional Structured Light.

A depth perception method combining omnidirectional images and encoding structured light was proposed. First, a new structured light pattern was presented by using monochromatic light. The primitive of the pattern consists of four-direction sand clock-like (FDSC) image. FDSC can provide more robust and accurate position compared with conventional pattern primitive. Second, on the basis of multiple reference planes, a calibration method of projector was proposed to significantly simplify projector calibration in the constructed omnidirectional imaging system. Third, a depth point cloud matching algorithm based on the principle of prior constraint iterative closest point under mobile condition was proposed to avoid the effect of occlusion. The experimental results demonstrated that the proposed method can acquire omnidirectional depth information about large-scale scenes. The error analysis of 16 groups of depth data reported a maximum measuring error of 0.53 mm and an average measuring error of 0.25 mm.

Accurate calibration method for camera and projector in fringe patterns measurement system.

The 3D measurement system based on fringe patterns is widely applied in diverse fields. The measurement accuracy is mainly determined by camera and projector calibration accuracy. In the existing methods, the system is calibrated by a dot calibration board with traditional image process algorithms. In this paper, an improved calibration method is proposed to increase camera and projector calibration accuracy simultaneously. To this end, first, a subpixel edge detection method is proposed to improve the detection accuracy of reference features for coarse calibration; second, an iterative compensation algorithm is developed to improve the detection accuracy of the reference feature centers for fine calibration. The experimental results demonstrate that the proposed calibration method can improve the calibration accuracy and measurement accuracy.

Projector recalibration of three-dimensional profilometry system.

In three-dimensional profilometry, the primary disadvantage of the monocular system equipped with a projector and a camera is that it is often highly dependent on the projector calibration. The projector calibration errors of the principal point and focal length are analyzed in this paper, and result in measuring the object deviation, including not only the rigid transformation, but also the scale transformation. Unfortunately, the deviation cannot be revealed by reprojection, the normal error analysis method. Here, a systematic recalibration method is proposed to correct the projector calibration errors of the principal point and focal length, where an accurate binocular three-dimensional measurement system is applied. The experimental results show that the method is effective. The three-dimensional measurement accuracy of the monocular system is improved approximately from 1.0 mm before projector recalibration to 0.10 mm afterward.

An accurate projector calibration method based on polynomial distortion representation.

In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. This paper proposes a new projector calibration approach that makes use of photodiodes to directly detect the light emitted from a digital projector. By analyzing the output sequence of the photoelectric module, the pixel coordinates can be accurately obtained by the curve fitting method. A polynomial distortion representation is employed to reduce the residuals of the traditional distortion representation model. Experimental results and performance evaluation show that the proposed calibration method is able to avoid most of the disadvantages in traditional methods and achieves a higher accuracy. This proposed method is also practically applicable to evaluate the geometric optical performance of other optical projection system.

Three stepped calibration of structured light system with adaptive thresholding for 3D measurements

Structured light (SL) methods are widely used in 3D measurement systems because of their speed and contactless operation. These methods provide high resolution 3D modeling. Phase shifting is one of the SL algorithms that give high resolution with less number of pattern requirements. Since reflected patterns and obtained results are commonly distorted due to the lenses in cameras and projector systems, system calibration must be fulfilled before starting 3D modeling with SL system. Uncalibrated SL system may model the object much greater/smaller than the real dimension of it. In this study, a three step calibration system is proposed for an SL system that uses a three phase shifting algorithm with automatic thresholding. These calibration steps include camera calibration, projector calibration and depth calibration. Experimental studies showed that proposed calibrated system reduces the camera and projector lens errors. Depth calibration is applied as a last calibration step provided a 3D modeling of the object with accurate dimension. Dimensions of the objects and their 3D models are compared to have accuracy of the proposed 3D modeling system. After system calibration, obtained results showed that proposed 3D modeling system gives high accuracy with acceptable depth measurements.

Flexible calibration method for microscopic structured light system using telecentric lens.

This research presents a novel method to calibrate a microscopic structured light system using a camera with a telecentric lens. The pin-hole projector calibration follows the standard pin-hole camera calibration procedures. With the calibrated projector, the 3D coordinates of those feature points used for projector calibration are then estimated through iterative Levenberg-Marquardt optimization. Those 3D feature points are further used to calibrate the camera with a telecentric lens. We will describe the mathematical model of a telecentric lens, and demonstrate that the proposed calibration framework can achieve very high accuracy: approximately 10 μm with a volume of approximately 10(H) mm × 8(W) mm × 5(D) mm.

Multi-projector auto-calibration and placement optimization for non-planar surfaces

Non-planar projection has been widely applied in virtual reality and digital entertainment and exhibitions because of its flexible layout and immersive display effects. Compared with planar projection, a non-planar projection is more difficult to achieve because projector calibration and image distortion correction are difficult processes. This paper uses a cylindrical screen as an example to present a new method for automatically calibrating a multi-projector system in a non-planar environment without using 3D reconstruction. This method corrects the geometric calibration error caused by the screen’s manufactured imperfections, such as an undulating surface or a slant in the vertical plane. In addition, based on actual projection demand, this paper presents the overall performance evaluation criteria for the multi-projector system. According to these criteria, we determined the optimal placement for the projectors. This method also extends to surfaces that can be parameterized, such as spheres, ellipsoids, and paraboloids, and demonstrates a broad applicability.

35.1: Distinguished Paper: Auto‐Calibration for Screen Correction and Point Cloud Generation

Showing a checkerboard at different poses for camera projector calibration is impractical for large scale applications such as projection mapping onto buildings. We use an automatic calibration technique that projects Gray code structured light patterns, which, extracted by the camera, build a dense correspondence for calibration. Two applications benefit from automatic calibration: 3D model generation and screen correction.

Improving the accuracy of phase-shifting techniques

The traditional phase-shifting profilometry technique is based on the projection of digital interference patterns and computation of the absolute phase map. Recently, a method was proposed that used phase interpolation to the corner detection, at subpixel accuracy in the projector image for improving the camera–projector calibration. We propose a general strategy to improve the accuracy in the search for correspondence that can be used to obtain high precision three-dimensional reconstruction. Experimental results show that our strategy can outperform the precision of the phase-shifting method.

Accurate projector calibration method by using an optical coaxial camera.

Digital light processing (DLP) projectors have been widely utilized to project digital structured-light patterns in 3D imaging systems. In order to obtain accurate 3D shape data, it is important to calibrate DLP projectors to obtain the internal parameters. The existing projector calibration methods have complicated procedures or low accuracy of the obtained parameters. This paper presents a novel method to accurately calibrate a DLP projector by using an optical coaxial camera. The optical coaxial geometry is realized by a plate beam splitter, so the DLP projector can be treated as a true inverse camera. A plate having discrete markers on the surface is used to calibrate the projector. The corresponding projector pixel coordinate of each marker on the plate is determined by projecting vertical and horizontal sinusoidal fringe patterns on the plate surface and calculating the absolute phase. The internal parameters of the DLP projector are obtained by the corresponding point pair between the projector pixel coordinate and the world coordinate of discrete markers. Experimental results show that the proposed method can accurately calibrate the internal parameters of a DLP projector.

Accurate projector calibration based on a new point-to-point mapping relationship between the camera and projector images

The mapping relationship between the charge-coupled device (CCD) of a camera and the digital micro-mirror device (DMD) of a projector, together with the algorithm to estimate the parameters of the projector, determines the accuracy of projector calibration. In this paper, a new method is presented to achieve sub-pixel-level mapping between the camera and projector images. Instead of directly mapping the circle centers from the CCD to the DMD, which is pixel-precision-based, a set of pixels on the circle edge are extracted on the CCD and mapped onto the DMD. The locations of the circle centers are extracted on the DMD by the least-squares fitting technique, thus achieving sub-pixel precision. Compared with existing approaches based on the direct mapping of the circle centers on the camera image to the projector image, the proposed method is characterized by higher accuracy in mapping the points and thus the projector calibration. The experimental results are presented to show the effectiveness of the proposed method in the improvement of the accuracy of the projector calibration.

Projector Calibration Method using Orthogonal Gray Code Combined with Trapezoid Phase Shift Code

In coded-structured light three dimensional measurement system, system calibration plays an important role for the measurement accuracy. Projector calibration is an important part of the system calibration. Therefore, this paper proposes a projector calibration method with simple calibration process and high accuracy. This method combines Zhang’s plane model calibration method with orthogonal Gray code + trapezoid phase shift code. During the calibration process, this paper uses Gray code pattern and trapezoid phase shift code pattern to establish the relation of projector image and camera point coordinates, the corner extraction accuracy of this paper’s method is higher than the traditional orthogonal Gray code. According to the image coordinates in the projector’s perspective, we program and calculate the projector’s internal and external parameters matrix based on the Zhang’s plane model calibration toolbox. The results show that this paper’s method is simple and flexible, the maximum relative error of the calibration parameters is 0.027%, and it meets the requirements of system calibration in engineering or industrial fields.

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.

Coded-Structured Light System Calibration Using Orthogonal Phase Shift Coding Combined with Zhang’s Method

In coded-structured light three dimensional system, system calibration plays a vital role for the measurement accuracy. The camera calibration method is very mature, but the study about projector calibration is less. Therefore, this paper proposes a projector calibration method with simple calibration process and high accuracy. This method combines the Zhang’?s plane model calibration method with orthogonal phase shift coding. In calibration process, this paper uses phase shift coding pattern to establish the relationship of projector image and camera corner point coordinates. According to the image coordinates in the projector’?s perspective, we program and calculate the projector’?s internal and external parameters matrix based on the Zhang’?s plane model calibration toolbox. The results show that the proposed method is simple and flexible, the maximum relative error of the calibration parameters is 0.03%, and it meets the requirements of system calibration in medical or industrial fields.