Lens Distortion Correction Research Articles

A New Model of Bundle Adjustment Used in Camera Calibration

The calibration of the internal and external parameters of each camera is a crucial step for free-form surface measurement based on stereo vision. The nonlinear optimization method of bundle adjustment is usually used in the camera calibration. The model of bundle adjustment can be derived from the nonlinear collinearity equations which contains the nonlinear distortions of camera lens. As the internal parameters of camera, the distortion parameters are implied in the projective transformation matrix, and difficult to be explicitly expressed by an equation. But the establishment of the model of bundle adjustment needs to calculate the first-order partial derivative of each parameter. At present, there is no effective method to decompose the implicit parameters which are taken as a whole in the expansion of first-order partial derivative. The existing bundle adjustment models are not comprehensive and easy to cause ill-conditioned matrix problems. In this paper, we discuss the methods of the nonlinear camera lens distortion correction, establish a new lens distortion expression, and propose a new model of bundle adjustment based on the new distortion expression. Experiments results indicate that the new bundle adjustment model can obtain high camera calibration accuracy, and avoid the ill-conditioned matrix problems.

An Automatic Approach for Radial Lens Distortion Correction From a Single Image

Radial lens distortion correction is a fundamental task in photogrammetry and computer vision disciplines, mainly when metric and quality results are required. Radial lens distortion estimation plays an essential role in several photogrammetric tasks such as: registration of sensors, 3-D reconstruction, and mapping of textures. This paper presents an iterative numerical approach for the automatic estimation and correction of radial lens distortion using only a single image. To this end, several geometric constraints (rectilinear elements and vanishing points) are considered. The reported experimental tests indicate that within certain limits, results from a single image can stand the comparison with those from multiple image bundle adjustment.

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.

Correcting radial distortion of document images by morphology

Document image captured by hand-held camera suffers from lens distortion more or less,and a mathematic morphology based lens correction algorithm was proposed according to the text line of document images.First,it used adaptive thresholding algorithm to segment the document image,and clustered connected components into text lines with morphology closing algorithm.Then,it used second order polynomial to fit the central line of text line,and constructed the object function of lens distortion.It warped the curved text line to the straight text line,thus,to solve the distortion parameters of document image.The experimental results show this method can effectively correct lens distortion of document image with various degrees.

基于共面点直接线性变换的摄像机畸变校正

基于共面点直接线性变换的摄像机畸变校正

Computational tasks in computer-assisted transbronchial biopsy

The paper presents algorithmic solutions dedicated to computer navigation system which is to assist bronchoscope positioning during transbronchial needle-aspiration biopsy. The navigation exploits the principle of on-line registration of real images from endoscope camera and the virtual ones generated on the base of computed tomography (CT) data of a patient. When these images are similar an assumption is made, that the bronchoscope and virtual camera have approximately the same position and view direction. In this paper the following computational aspects are described: correction of camera lens distortion, fast approximate estimation of endoscope ego-motion, reconstruction of bronchial tree from the CT data by means of their segmentation and its centerline calculation, virtual views generation, registration of real and virtual images via maximization of their mutual information and, finally, efficient parallel and network implementation of the navigation system which is under development at present.

Lens distortion correction using ideal image coordinates

This paper proposes a fast and simple mapping method for lens distortion correction. Typical correction methods use a distortion model defined on distorted coordinates. They need inverse mapping for distortion correction. Inverse mapping of distortion equations is not trivial; approximation must be taken for real time applications. We propose a distortion model defined on ideal undistorted coordinates, so that we can reduce computation time and maintain the high accuracy. We verify accuracy and efficiency of the proposed method from experiments.

Beyond bandlimited sampling

Digital applications have developed rapidly over the last few decades. Since many sources of information are of analog or continuous-time nature, discrete-time signal processing (DSP) inherently relies on sampling a continuous-time signal to obtain a discrete-time representation. Consequently, sampling theories lie at the heart of signal processing devices and communication systems. Examples include sampling rate conversion for software radio and between audio formats, biomedical imaging, lens distortion correction and the formation of image mosaics, and super-resolution of image sequences.

Real–Time Correction of Cameras’ Geometric Distortions using GPGPU

Lens distortion correction is very important for machine vision applications. Estimation of internal camera parameters is necessary for precise 2D or 3D scene measurements. Nonlinear image warping operation needs a lot of computational effort and is critical for real–time systems. Modern GPGPU devices give the possibility processing such data but needs fast algorithm for calculations result. In this paper optimized coalescence algorithm for best GPGPU performance is proposed.

3D curve structure reconstruction from a sparse set of unordered images

A flexible and portable approach to reconstructing 3D curve structures of free-form objects from a sparse set of unordered images taken by a hand-held CCD camera is presented. To make the whole pipeline robust and accurate, we mark the interested curves on the object to make them visually outstand from the background. Some specifically designed markers are distributed around the object as well. Followed by an automatic camera pose recovery and camera lens distortion correction step, a user-friendly semi-automatic method is put forward to extract the curves in the images. The curve correspondences in stereo image pairs are then optimally established and the 3D curve structures are recovered by using the stereo triangulation method. Experiments show that the method is applicable for reverse modeling of freeform objects with moderate accuracy requirements.

Multiview Trajectory Mapping Using Homography with Lens Distortion Correction

We present a trajectory mapping algorithm for a distributed camera setting that is based on statistical homography estimation accounting for the distortion introduced by camera lenses. Unlike traditional approaches based on the direct linear transformation (DLT) algorithm and singular value decomposition (SVD), the planar homography estimation is derived from renormalization. In addition to this, the algorithm explicitly introduces a correction parameter to account for the nonlinear radial lens distortion, thus improving the accuracy of the transformation. We demonstrate the proposed algorithm by generating mosaics of the observed scenes and by registering the spatial locations of moving objects (trajectories) from multiple cameras on the mosaics. Moreover, we objectively compare the transformed trajectories with those obtained by SVD and least mean square (LMS) methods on standard datasets and demonstrate the advantages of the renormalization and the lens distortion correction.

Photogrammetric fingerprint unwrapping

Fingerprints are important biometric cues. Compared to conventional fingerprint sensors the use of contact-free stereoscopic image acquisition of the front-most finger segment has a set of advantages: Finger deformation is avoided, the entire relevant area for biometric use is covered, some technical aspects like sensor maintenance and cleaning are facilitated, and access to a three-dimensional reconstruction of the covered area is possible. We describe a photogrammetric workflow for nail-to-nail fingerprint reconstruction: A calibrated sensor setup with typically 5 cameras and dedicated illumination acquires adjacent stereo pairs. Using the silhouettes of the segmented finger a raw cylindrical model is generated. After preprocessing (shading correction, dust removal, lens distortion correction), each individual camera texture is projected onto the model. Image-to-image matching on these pseudo ortho images and dense 3D reconstruction obtains a textured cylindrical digital surface model with radial distances around the major axis and a grid size in the range of 25–50 µm. The model allows for objective fingerprint unwrapping and novel fingerprint matching algorithms since 3D relations between fingerprint features are available as additional cues. Moreover, covering the entire region with relevant fingerprint texture is particularly important for establishing a comprehensive forensic database. The workflow has been implemented in portable C and is ready for industrial exploitation. Further improvement issues are code optimization, unwrapping method, illumination strategy to avoid highlights and to improve the initial segmentation, and the comparison of the unwrapping result to conventional fingerprint acquisition technology.

Novel Calibration and Lens Distortion Correction of 3D Reconstruction Systems

A novel calibration and lens distortion correction of 3D reconstruction systems is introduced in this paper. Assuming zero distortion at the center of image, the parameter calibration and lens distortion correction of CCD camera and DLP projector is separated with the points in center and all the rest points. Furthermore, identification and correspondence of the interest points is done automatically because of the designed target with standard circles and multicolor code of pseudo-random array during the calibration. The experiments show that it is a fast and convenient method to carry out the calibration for lens distortion.

Single view metrology of wide-angle lens images

This paper presents a framework and the associated algorithms to perform 3D scene analysis from a single image with lens distortion. Previous work focuses on either making 3D measurements under the assumption of one or more ideal pinhole cameras or correcting the lens distortion up to a projective transformation with no additional metric analyses. In this work, we bridge the gap between these two areas of work by incorporating metric constraints into lens distortion correction to achieve metric calibration. Lens distortion parameters, especially the lens distortion center, can be precisely recovered with this approach. Subsequent 3D measurements can be made from the corrected image to recover scene structures. In addition, we propose an algorithm based on hybrid backward and forward covariance propagation to yield a quantitative analysis of the confidence of the results. Experimental results show that our approach simultaneously performs image correction and 3D scene analysis.

Lens distortion correction for digital image correlation by measuring rigid body displacement

A method of lens distortion correction is proposed in order to improve the measurement accuracy of digital image correlation for two-dimensional displacement measurement. The amounts of lens distortion are evaluated from displacement distributions obtained in a rigid body in-plane translation or rotation test. After detecting the lens distortion, its coefficient is determined using the method of least squares. Then, the corrected displacement distributions are obtained. The effectiveness of the proposed method is demonstrated by applying the correction method to an in-plane translation test and tension tests. The experimental results show that the proposed distortion correction method eliminates the effect of lens distortion from measured displacements.

In-Plane Displacement Measurement Using Digital Image Correlation with Lens Distortion Correction

Two-dimensional displacement measurement using digital image correlation with lens distortion correction is described in this paper. A single cross-grating is used as a calibration reference. Using two-dimensional Fourier transform, the phases of the grating pattern are analyzed and lens distortion distribution is obtained from the unwrapped phase maps. After detecting lens distortion, the coefficients of lens distortion are determined using the least-squares method. Then, the displacement distributions without the lens distortion are obtained. The effectiveness of the method is demonstrated by applying the proposed method to the rigid body translation test and the uniaxial tension test. The results show that the proposed distortion correction method removes the effect of lens distortion from the measured displacements. By the proposed method, accurate measurements can be performed even if images are deformed by lens distortion.

A practical method to detect and correct for lens distortion in the TEM

A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images. The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry.

Tracing traffic dynamics with remote sensing

Science has not yet been completely successful in explaining the various puzzling but interesting phenomena of congested traffic flows. The reasons that these phenomena are poorly understood are mainly due to the lack of adequate data needed to develop this theory. Common measurement methods collect only ‘snapshots’ of the situation (i.e. at a limited number of cross-sections, or a single, instrumented vehicle). Such data do not provide sufficient information to study the dynamics of individual drivers in their continuously changing traffic and roadway environment. This paper presents a new innovative traffic data collection system to detect and track vehicles from aerial image sequences. Besides the longitudinal and lateral positions as a function of time, the system can also determine the vehicle lengths and widths. Before vehicle detection and tracking can be achieved, the software handles correction for lens distortion, radiometric correction, and orthorectification of the image. Vehicle detection occurs approximately each tenth of a second, after which vehicles are tracked both forward and backward in time (10 frames in each direction). The resulting data redundancy is then used to improve accuracy and reliability of the traffic data. Post-processing furthermore entails using Iterative Extended Kalman filtering to improve data quality. The software was tested on data collected from a helicopter, using a digital camera gathering high-resolution monochrome images of a Dutch motorway near the city of Utrecht. From the test, it is concluded that the techniques for analyzing the digital images can be applied automatically without many problems, while nearly 100% of all vehicles could be detected and tracked.

Wide-angle camera distortions and non-uniform illumination in mobile robot tracking

In this paper some fundamentals and solutions to accompanying problems in vision system design for mobile robot tracking are presented. The main topics are correction of camera lens distortion and compensation of non-uniform illumination. Both correction methods contribute to vision system performance if implemented in the appropriate manner. Their applicability is demonstrated by applying them to vision for robot soccer. The lens correction method successfully corrects the distortion caused by the camera lens, thus achieving a more accurate and precise estimation of object position. The illumination compensation improves robustness to irregular and non-uniform illumination that is nearly always present in real conditions.

An embedded camera lens distortion correction method for mobile computing applications

This paper describes a lens geometric and photometric distortion correction method to obtain a high quality image with low cost digital cameras. Lens geometric distortion coefficient of a digital camera is estimated using a simplified camera calibration technique, which is extended to calibration-free estimation method. Based on the estimate of the lens geometric distortion coefficient, image warping adapted for DSP architecture is applied. Photometric distortion, on the other hand, is corrected by a nonlinear model fitting of a proposed photometric distortion model function. Light intensity profile distribution is obtained without precisely controlled illumination and memory requirement is considerably reduced compared with traditional lookup table (LUT) methods.