Internal Camera Parameters Research Articles

Pose-Free Structure From Motion Using Depth From Motion Constraints

Structure from motion (SFM) is the problem of recovering the geometry of a scene from a stream of images taken from unknown viewpoints. One popular approach to estimate the geometry of a scene is to track scene features on several images and reconstruct their position in 3-D. During this process, the unknown camera pose must also be recovered. Unfortunately, recovering the pose can be an ill-conditioned problem which, in turn, can make the SFM problem difficult to solve accurately. We propose an alternative formulation of the SFM problem with fixed internal camera parameters known a priori. In this formulation, obtained by algebraic variable elimination, the external camera pose parameters do not appear. As a result, the problem is better conditioned in addition to involving much fewer variables. Variable elimination is done in three steps. First, we take the standard SFM equations in projective coordinates and eliminate the camera orientations from the equations. We then further eliminate the camera center positions. Finally, we also eliminate all 3-D point positions coordinates, except for their depths with respect to the camera center, thus obtaining a set of simple polynomial equations of degree two and three. We show that, when there are merely a few points and pictures, these "depth-only equations" can be solved in a global fashion using homotopy methods. We also show that, in general, these same equations can be used to formulate a pose-free cost function to refine SFM solutions in a way that is more accurate than by minimizing the total reprojection error, as done when using the bundle adjustment method. The generalization of our approach to the case of varying internal camera parameters is briefly discussed.

Simple, flexible calibration of phase calculation-based three-dimensional imaging system

One important step of phase-based three-dimensional imaging system is calibration, which defines the relationship between phase and depth data. Existing calibration methods are complicated and hard to carry out because of using a translation stage or gauge block in a laboratory environment. This Letter introduces a new simple, flexible calibration method by using a checkerboard and a white plate having discrete markers with known separation. The checkerboard determines the internal parameters of a CCD camera. The plate gives phase and depth data of each pixel to establish their relationship. Experimental results and performance evaluation show that the proposed calibration method can reliably build up the accurate relationship between phase map and depth data in a simple, flexible way.

Research on a Single Camera Location Model and its Application

Digital cameras have been widely used in the areas of road transportation, railway transportation as well as security system. To address the position of digital camera in these fields this paper proposed a geometry calibration method based on feature point extraction of arbitrary target. Under the meaning of the questions, this paper first defines four kinds of coordinate system, that is the world coordinate system. The camera's optical center of the coordinate system is the camera coordinate system, using the same point in different coordinate system of the coordinate transformation to determine the relationship between world coordinate system and camera coordinate. And thus determine the camera's internal parameters and external parameters, available transformation matrix and translation vector indicated by the camera's internal parameters of the external parameters and the establishment of a single camera location model. According to the model, using the camera's external parameters to be on the target circle center point in the image plane coordinates.

Calibration Method and Experimental Study of the Camera Internal Parameters Based on One-Step Movement

A calibration method based on target features circle is proposed, which can determine the camera internal parameters based on the two different CCD images. One CCD image can be obtained in a position, and the other CCD image can be gotten by moving the target or camera to a new position. The principle of the calibration method based on one-step movement is expounded. The geometrical relationship and the criteria that the camera axis is orthogonal to the target plane are proven when the CCD image is circle. Finally, the experiment results verify that the method proposed is effective, and the data of the internal calibration parameters of the camera is given.

Shape reconstruction and texture sampling by active rectification and virtual view synthesis

In this paper it is shown how to obtain a three-dimensional, textured object model by relying exclusively on image warping 2D–2D transformations. To achieve this goal, a dual (laser and natural light) illumination of the scene is exploited. Shape reconstruction is not based on triangulation, but on the planar rectification and collation of laser profiles. Texture sampling uses laser profile warping and compositing rather than 3D–2D model shape reprojection, so as to synthesize a virtual view of the object at hand, that is matched against the natural light sequence to obtain color data. Shape reconstruction and texture sampling are independent from each other, and can be run in parallel, thus speeding up the process. Moreover, the approach requires only a simple manual setup, and is effective with textured or textureless objects of any shape. Experimental results demonstrate that the approach combines the high accuracy of state-of-the-art active reconstruction methods with the flexibility of uncalibrated methods, improving on both. Specifically, avoiding any intermediate 3D measurement – in particular the external camera calibration parameters – has a dramatic impact on both model shape an texture accuracy, and also adds robustness w.r.t. any estimation errors of internal camera parameters.

Localization and Trajectory Reconstruction in Surveillance Cameras with Nonoverlapping Views

This paper proposes a method that localizes two surveillance cameras and simultaneously reconstructs object trajectories in 3D space. The method is an extension of the Direct Reference Plane method, which formulates the localization and the reconstruction as a system of linear equations that is globally solvable by Singular Value Decomposition. The method's assumptions are static synchronized cameras, smooth trajectories, known camera internal parameters, and the rotation between the cameras in a world coordinate system. The paper describes the method in the context of self-calibrating cameras, where the internal parameters and the rotation can be jointly obtained assuming a man-made scene with orthogonal structures. Experiments with synthetic and real--image data show that the method can recover the camera centers with an error less than half a meter even in the presence of a 4 meter gap between the fields of view.

A new calibration method for linear CCD camera

The linear CCD camera which applies to micro-image measuring system must have been calibrated before working. The separate calibration method of linear CCD camera’s internal and external orientation parameters is proposed in the paper. The imaging model of the linear camera has been studied, and the equal parallel lines are used to calibrate internal parameters of camera in the experiment where the industrial environment is simulated. In addition, parallel lines and tri-forked stencil are used to calibrate external orientation parameters in the industrial field, such as the attitude angel. The separate calibration method has reduced the calibration task in the industry, and the calibration template is easy to make. The results show that the testing accuracy improves greatly by using the calibrated camera for measuring the gauge, and the calibrated camera can be easily applied to other measurement environment.

Measurement of Three-Dimensional Environment with a Fish-Eye Camera Based on Structure from Motion - Error Analysis

This paper proposes a method for measuring 3-dimensional (3D) environment and estimating camera movement with two fish-eye images. This method deals with large distortion of images from a fish-eye camera to calibrate internal and external camera parameters precisely by simultaneous estimation. In this paper, we analyze 3D measurement accuracy based on a theoretical model and evaluate it in practical analysis in experimental and real environments. These analyses show that the theoretical measurement error model works over a wide range of fish-eye views.

Self-Calibrating View-Invariant Gait Biometrics

We present a new method for viewpoint independent gait biometrics. The system relies on a single camera, does not require camera calibration, and works with a wide range of camera views. This is achieved by a formulation where the gait is self-calibrating. These properties make the proposed method particularly suitable for identification by gait, where the advantages of completely unobtrusiveness, remoteness, and covertness of the biometric system preclude the availability of camera information and specific walking directions. The approach has been assessed for feature extraction and recognition capabilities on the SOTON gait database and then evaluated on a multiview database to establish recognition capability with respect to view invariance. Moreover, tests on the multiview CASIA-B database, composed of more than 2270 video sequences with 65 different subjects walking freely along different walking directions, have been performed. The obtained results show that human identification by gait can be achieved without any knowledge of internal or external camera parameters with a mean correct classification rate of 73.6% across all views using purely dynamic gait features. The performance of the proposed method is particularly encouraging for application in surveillance scenarios.

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.

A geometric method for calibration of internal camera parameters of fish‐eye lenses

AbstractFish‐eye cameras (cameras with a fish‐eye lens) have a very wide view angle of about 180° and a great depth of field. Therefore, it is possible to take pictures of broad scenes with a fixed posture, and it is suitable for uses like 3D modeling and surveillance cameras for indoor and outdoor environments. Geometrical and optical calibration of the internal parameters are necessary for improvement of the measuring accuracy in the real world. In this paper, we address the geometrical calibration problem. Some geometrical methods for calibration of the internal camera parameters of fish‐eye cameras force the eye camera into a perspective model that is not applicable in wide views of 180° or more. We propose a calibration method using spherical projection and projection models, which combine the projection function of the fish‐eye lens and geometrical distortion models. Our method can perform calibration quickly and with high accuracy by using patterns of horizontal and vertical parallel lines shown on a liquid crystal display (LCD), which can display such patterns with high accuracy. We show the effectiveness of our method by an experimental evaluation with a fish‐eye camera of orthographic projection type, which obtains high resolution near the edges of the imaging area. © 2007 Wiley Periodicals, Inc. Syst Comp Jpn, 38(12): 55–65, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20685

Flexible calibration procedure for fringe projection profilometry

A novel calibration method for whole field three-dimensional shape measurement by means of fringe projection is presented. Standard calibration techniques, polynomial-and model-based, have practical limitations such as the difficulty of measuring large fields of view, the need to use precise z stages, and bad calibration results due to inaccurate calibration points. The proposed calibration procedure is a mixture of the two main standard techniques, sharing their benefits and avoiding their main problems. In the proposed method, an absolute phase is projected over marked planes placed at unknown positions. The corresponding absolute phase and marks positions are recovered for each plane location. Using Zhang's calibration method, internal camera parameters (also called intrinsic parameters) and the spatial position for each plane are computed. Later on, a polynomial fit of depth with respect to the phase is performed. To obtain the absolute position of an object point, the depth coordinate is obtained by means of the polynomial calibration and its absolute phase. Then the lateral coordinates are computed from the depth, the internal parameters, and the pixel coordinates of the imaged point. Experimental results comparing the proposed method with the standard polynomial-based calibration are shown, demonstrating the feasibility of the proposed technique.

Towards 3-D scene reconstruction from broadcast video

Three-dimensional (3-D) scene reconstruction from broadcast video is a challenging problem with many potential applications, such as 3-D TV, free-view TV, augmented reality or three-dimensionalization of two-dimensional (2-D) media archives. In this paper, a flexible and effective system capable of efficiently reconstructing 3-D scenes from broadcast video is proposed, with the assumption that there is relative motion between camera and scene/objects. The system requires no a priori information and input, other than the video sequence itself, and capable of estimating the internal and external camera parameters and performing a 3-D motion-based segmentation, as well as computing a dense depth field. The system also serves as a showcase to present some novel approaches for moving object segmentation, sparse and dense reconstruction problems. According to the simulations for both synthetic and real data, the system achieves a promising performance for typical TV content, indicating that it is a significant step towards the 3-D reconstruction of scenes from broadcast video.

Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold

A novel approach for essential matrix estimation is presented, this being a key task in stereo vision processing. We estimate the essential matrix from point correspondences between a stereo image pair, assuming that the internal camera parameters are known. The set of essential matrices forms a smooth manifold, and a suitable cost function can be defined on this manifold such that its minimum is the desired essential matrix. We seek a computationally efficient optimization scheme towards meeting the demands of on-line processing of video images. Our work extends and improves the earlier research by Ma et al., who proposed an intrinsic Riemannian Newton method for essential matrix computations. In contrast to Ma et al., we propose three Gauss-Newton type algorithms that have improved convergence properties and reduced computational cost. The first one is based on a novel intrinsic Newton method, using the normal Riemannian metric on the manifold consisting of all essential matrices. The other two methods are Newton-like methods, that are more efficient from a numerical point of view. Local quadratic convergence of the algorithms is shown, based on a careful analysis of the underlying geometry of the problem.

Self-calibration from turn-table sequences in presence of zoom and focus

This paper proposes a novel method, using constant inter-frame motion, for self-calibration from an image sequence of an object rotating around a single axis with varying camera internal parameters. Our approach makes use of the facts that in many commercial systems rotation angles are often controlled by an electromechanical system, and that the inter-frame essential matrices are invariant if the rotation angles are constant but not necessary known. Therefore, recovering camera internal parameters is possible by making use of the equivalence of essential matrices which relate the unknown calibration matrices to the fundamental matrices computed from the point correspondences. We also describe a linear method that works under restrictive conditions on camera internal parameters, the solution of which can be used as the starting point of the iterative non-linear method with looser constraints. The results are refined by enforcing the global constraints that the projected trajectory of any 3D point should be a conic after compensating for the focusing and zooming effects. Finally, using the bundle adjustment method tailored to the special case, i.e., static camera and constant object rotation, the 3D structure of the object is recovered and the camera parameters are further refined simultaneously. To determine the accuracy and the robustness of the proposed algorithm, we present the results on both synthetic and real sequences.

An image-based calibration technique of spatial domain depth-from-defocus

Depth-from-defocus (DFD) is useful in 3-D range image acquisition and automatic focusing. However, DFD needs precise calibration of internal camera parameters. Most DFD techniques use well known camera calibration techniques or specially designed vision systems to precisely measure the settings of the lens system of a camera. In this paper, we introduce an image-based defocus calibration technique. Especially we employ the Spatial domain Convolution/Deconvolution Transform Method (STM) which is introduced by Subbarao and Surya [Subbarao, M., Surya, G., 1994. Depth-from-defocus: A spatial domain approach. Internat. J. Comput. Vision 13 (3), 271–294]. STM estimates blur parameters σ 1 and σ 2 of defocused images obtained at two different lens steps of the camera. In STM, the blur difference between two defocused images is considered to be a constant value which is determined by internal camera parameters. We use the blur level of the defocused images to calibrate blur difference and camera parameters. Calibrated parameters yield consistent results in depth estimation. Experimental results of depth measurement using real objects are presented.

Metric 3D reconstruction and texture acquisition of surfaces of revolution from a single uncalibrated view

Image analysis and computer vision can be effectively employed to recover the three-dimensional structure of imaged objects, together with their surface properties. In this paper, we address the problem of metric reconstruction and texture acquisition from a single uncalibrated view of a surface of revolution (SOR). Geometric constraints induced in the image by the symmetry properties of the SOR structure are exploited to perform self-calibration of a natural camera, 3D metric reconstruction, and texture acquisition. By exploiting the analogy with the geometry of single axis motion, we demonstrate that the imaged apparent contour and the visible segments of two imaged cross sections in a single SOR view provide enough information for these tasks. Original contributions of the paper are: single view self-calibration and reconstruction based on planar rectification, previously developed for planar surfaces, has been extended to deal also with the SOR class of curved surfaces; self-calibration is obtained by estimating both camera focal length (one parameter) and principal point (two parameters) from three independent linear constraints for the SOR fixed entities; the invariant-based description of the SOR scaling function has been extended from affine to perspective projection. The solution proposed exploits both the geometric and topological properties of the transformation that relates the apparent contour to the SOR scaling function. Therefore, with this method, a metric localization of the SOR occluded parts can be made, so as to cope with them correctly. For the reconstruction of textured SORs, texture acquisition is performed without requiring the estimation of external camera calibration parameters, but only using internal camera parameters obtained from self-calibration.

Estimating Intrinsic Camera Parameters from the Fundamental Matrix Using an Evolutionary Approach

Calibration is the process of computing the intrinsic (internal) camera parameters from a series of images. Normally calibration is done by placing predefined targets in the scene or by having special camera motions, such as rotations. If these two restrictions do not hold, then this calibration process is called autocalibration because it is done automatically, without user intervention. Using autocalibration, it is possible to create 3D reconstructions from a sequence of uncalibrated images without having to rely on a formal camera calibration process. The fundamental matrix describes the epipolar geometry between a pair of images, and it can be calculated directly from 2D image correspondences. We show that autocalibration from a set of fundamental matrices can simply be transformed into a global minimization problem utilizing a cost function. We use a stochastic optimization approach taken from the field of evolutionary computing to solve this problem. A number of experiments are performed on published and standardized data sets that show the effectiveness of the approach. The basic assumption of this method is that the internal (intrinsic) camera parameters remain constant throughout the image sequence, that is, the images are taken from the same camera without varying such quantities as the focal length. We show that for the autocalibration of the focal length and aspect ratio, the evolutionary method achieves results comparable to published methods but is simpler to implement and is efficient enough to handle larger image sequences.

A system for the acquisition of reproducible digital skin lesions images

A major issue concerning the design and implementation of an image acquisition system for skin lesions is its ability to capture reproducible images. The reproducibility is considered essential for image analysis and for the comparison of sequential images during follow-up studies. This paper describes a prototype image acquisition system that includes a standardized illumination and capturing geometry with polarizing filters and a series of software corrections: Calibration to Black, White and Color for color constancy, Internal camera Parameters adjustment and Pose extraction for stereo vision, Shading correction and Noise Filtering for color quality. The validity of the calibration procedure and the images' reproducibility were tested by capturing sample images in three different lighting conditions: dark, medium and intense lighting. For each case the average values of the three color planes RGB and their standard deviations were calculated; the measured error differences ranged between 0.7 and 12.9 (in the 0-255 scale). Preliminary experiments for stereo measurements provided repeatability of about 0.3 mm. The above results demonstrate the reproducibility of the captured images at a satisfactory level. The developed prototype was also evaluated clinically, for its ability to support the construction of knowledge-based decision systems and for telemedicine, thus to support telemedical sessions in dermatology.

Design and Calibration of an Opto-mechanical Appliance for 3D Non-contact Orthopedic Measurements Part I: Mathematical Model and Laboratory Prototype

An opto-mechanical system performing fast and accurate non-contact foot measurements is proposed. By processing the measured data it is possible to get three-dimensional foot models and to design custom-made shoes. This work is subdivided into two parts: in Part I, after introducing the system operating method and describing the vision technology employed, a mathematical model of the system is developed accounting for the main internal parameters of the camera. In order to reduce scanning time and the time necessary to create the 3D foot model, the measured data have been arranged in a particular structure and a suitable acquisition procedure has been developed. A laboratory prototype has been built to test the performances of the system: a detailed analysis of its geometry and of its components is provided as well as a concise description of the simple user interface developed to run and control the system.