소실점을 이용한 3차원 재구성

Camera calibration is the process of determining the intrinsic or internal parameters (i.e. focal length and principal point) of a camera, and is important for both motion estimation and metric reconstruction of 3D models. This paper addresses the problem of calibrating a pinhole camera from images of profile of a revolution. In this paper, the symmetry of images of profiles of revolution has been extensively exploited and a practical and accurate technique of camera calibration from profiles alone has been developed. Compared with traditional techniques for camera calibration which may involve taking images of some precisely machined calibration pattern (such as a calibration grid), or edge detection for determining vanish points which are often far from images center or even don't physically exist, or calculation of fundamental matrix and Kruppa equations which can be numerically unstable, the method presented here used just profiles of revolution, which are commonly found in daily life (e.g. bowls and vases), to make the process easier as a result of the reduced cost and increased accessibility of the calibration objects. This paper firstly analyzed the relationship between the symmetry property of profile of revolution and the intrinsic parameters of a camera, and then showed how to use images of profile of revolution to provide enough information for determining intrinsic parameters. During the process, high-accurate profile extraction algorithm has also been used. Finally, results from real data are presented, demonstrating the efficiency and accuracy of the proposed methods.

The process of solving camera intrinsic and extrinsic parameters has been presented by using geometric techniques. In contrast with traditional method, which is a pure algebra process, the geometric technique accomplishes the camera parameters more intuitively and easily. If the perspective projection matrix is given, according to the geometric meaning of perspective projection camera model, the coordinates of optical centre can be directly estimated in the world coordinate system. Then rotation matrix and translation vector can be obtained from the matrix. Finally, we can derive camera intrinsic parameters. During the process of derivation, for any given 3 by 4 matrix, the constraint conditions have been discussed in another way when the matrix could be described as a perspective projection transformation. Although it has the same result as pure algebra progress, it's of great significance to understand the geometric meaning among the intrinsic and extrinsic camera parameters

Camera pose estimation under dynamic intrinsic parameter change for augmented reality

Camera calibration using one-dimensional information and its applications in both controlled and uncontrolled environments

An improved outdoor camera calibration method based on Extended Kalman Filter (EKF) is proposed in this paper. GPS coordinate system is introduced to establish world coordinate system in the calibration procedure. According to the characteristics of GPS coordinate converted to plane coordinate and the camera calibration model, we establish the mapping relations of reference points between image plane coordinate and the world coordinate. Further, we consider the world coordinate error, set the world coordinates as the measure quantities, use the method of EKF to get the optimal estimation of intrinsic and extrinsic camera parameters, in EKF the camera's intrinsic and extrinsic parameters are set as state variables, the transformation equations of image coordinate to the world coordinate are set as the measurement equations, and we let the observed feature points' image coordinates and corresponding world coordinates as the input of the filter. Experimental results confirmed that the proposed method with high precision. Index Terms - camera calibration, GPS coordinate, EKF, world coordinate error

Features of leaves can be more precisely captured using 3D imaging. A 3D leaf image is reconstructed using two 2D images taken using stereo cameras. Reconstructing 3D from 2D images is not straightforward. One of the important steps to improve accuracy is to perform camera calibration correctly. By calibrating camera precisely, it is possible to project measurement of distances in real world to the image plane. To maintain the accuracy of the reconstruction, the camera must also use correct parameter settings. This paper aims at designing a method to calibrate a camera to obtain its parameters and then using the method in the reconstruction of 3D images. Camera calibration is performed using region-based correlation methods. There are several steps necessary to follow. First, the world coordinate and the 2D image coordinate are measured. Extraction of intrinsic and extrinsic camera parameters are then performed using singular value decomposition. Using the available disparity image and the parameters obtained through camera calibration, 3D leafimage reconstruction can finally be performed. Furthermore, the results of the experimental depth-map reconstruction using the intrinsic parameters of the camera show a rough surface, so that a smoothing process is necessary to improve the depth map.

It is proposed a method for camera calibration that could be used in stereo systems as well as in stereo head navigation in this paper. A pinhole camera model and two-dimensional planar target are considered. An Iterated Extended Kalman Filter (IEKF) is used to estimate camera parameters. The met hod takes the observed feature points of images as the filter input and the estimated value of the intrinsic and extrinsic camera parameters as the filter output. Both computer simulation and real data experiments have been used to test the proposed method, and good results have been obtained. The RMS error of absolute distance between reprojection feature points is about 0.09 pixels in real experiments. The experimental results show IEKF is also a feasible optimization algorithm for on-line camera calibration. Key words: Camera Calibration, Iterated Extended Kalman Filter, planar target 1. INTRODUCTION Camera calibration is a crucial phase in most vision systems and a first step in 3D reconstruction. It has been broadly applied in machine vision, virtual reality, and three-dimensional reconstruction and so on. Generally, in order to obtain higher calibration precision, in trinsic and extrinsic camera para meters are estimated through nonlinear optimization methods with information acquired from images. Starting from the simplest method we could mention the Least Square Error (LSE)

3D reconstruction serves as a fundamental technology for comprehensively understanding and perceiving the physical world, with significant applications in computer vision fields such as industrial automation, autonomous navigation, and medical imaging. A critical challenge in monocular 3D reconstruction lies in the accurate and efficient estimation of camera intrinsic and extrinsic parameters, which are essential for determining precise positional information in each image. In this context, this paper proposes an improved PMVS (Patch-based Multi-view Stereo) 3D reconstruction assisted by union camera-turntable calibration, which can not only reduce manual effort and improve reconstruction efficiency but also capture rich surface details and accurate target localization, enabling the reconstruction of complex geometries. This study employs a cubic chessboard as a calibration object, replacing the traditional planar chessboard, which is positioned on a controllable turntable for calibration. This innovation allows for the determination of both intrinsic and extrinsic camera parameters from a single image while maintaining high accuracy. By integrating the rotary table, we can precisely control the inter-rotation angle to capture positional information and local texture from multiple perspectives. Furthermore, we utilize a transformer attention mechanism in place of conventional neural network (CNN) convolution to effectively capture global context and long-range dependencies within the images, thereby enhancing the quality of object surface reconstruction. Experimental results demonstrate that the proposed method significantly outperforms COLMAP and traditional PMVS 3D reconstruction techniques, yielding a 21.67% increase in the number of reconstructed point clouds and an ∼30% improvement in the structural similarity index (SSIM). In addition, this method reduces processing time by 24.67% while enhancing the visualization of complex surface reconstructions.

A method for camera calibration in robotic binocular stereo vision is introduced in this paper. Camera calibration is a necessary step in 3D computer vision in order to extract metric information from 2D images. Being different from with single camera calibration, binocular stereo vision system not only need to ascertain intrinsic parameters, but also the relative position relation of two cameras. We compute it in two steps: first, we compute the intrinsic and initial extrinsic parameters of camera by Zhang Plane-based Calibration Method; Second, we suppose the intrinsic parameter is invariable, camera's moving parameters can be computed by self-calibration method, through finding the stereo matching point and calculating the fundamental matrix and essential matrix.

Novel view synthesis using neural radiance fields (NeRF) is the state-of-the-art technique for generating high-quality images from novel viewpoints. Existing methods require a priori knowledge about extrinsic and intrinsic camera parameters. This limits their applicability to synthetic scenes, or real-world scenarios with the necessity of a preprocessing step. Current research on the joint optimization of camera parameters and NeRF focuses on refining noisy extrinsic camera parameters and often relies on the preprocessing of intrinsic camera parameters. Further approaches are limited to cover only one single camera intrinsic. To address these limitations, we propose a novel end-to-end trainable approach called NeRFtrinsic Four. We utilize Gaussian Fourier features to estimate extrinsic camera parameters and dynamically predict varying intrinsic camera parameters through the supervision of the projection error. Our approach outperforms existing joint optimization methods on LLFF and BLEFF. In addition to these existing datasets, we introduce a new dataset called iFF with varying intrinsic camera parameters. NeRFtrinsic Four is a step forward in joint optimization NeRF-based view synthesis and enables more realistic and flexible rendering in real-world scenarios with varying camera parameters.

Scenes that contain every-day man-made objects often possess sets of parallel lines and orthogonal planes, the projective features of which possess enough structural information to constrain possible scene element geometries as well as a camera's intrinsic and extrinsic parameters. In particular, in a scene with three mutually orthogonal sets of parallel lines, detection of the corresponding three vanishing points of the imaged lines allows us to determine the camera's image-relative principal point and effective focal length. In this paper we introduce a new technique to solve for radial and decentering lens distortion directly from the results of vanishing point estimation, thus precluding the need for special calibration templates. This is accomplished by using an iterative method to solve for the parameters that minimize vanishing point dispersion. Dispersion here is measured as covariance of vanishing point estimation error projected on the Gaussian sphere whose origin is the estimated center of projection. Having found a complete model for each camera's intrinsic parameters, corresponding points are used in the relative orientation technique to determine the camera's extrinsic parameters as well as point-wise structure. Surfaces inherit planar geometry and extent from manually identified coplanar lines and points. View independent textures are created for each surface by finding the 2-D homographic texture transformation which corrects for planar perspective foreshortening. We utilize the local Jacobian of this transformation in two important ways: to prevent aliasing in the plane's texture space and to merge correctly texture data arising from varying sampling resolutions in multiple views.

In general, video see-through based augmented reality (AR) cannot change the magnification of camera zooming parameter due to the difficulty of dealing with changes in intrinsic camera parameters. To realize the usage of camera zooming in AR, we propose a novel simultaneous intrinsic and extrinsic camera parameter estimation method based on an energy minimization framework. Our method is composed of the online and offline stages. An intrinsic camera parameter change depending on the zoom values is calibrated in the offline stage. Intrinsic and extrinsic camera parameters are then estimated based on the energy minimization framework in the online stage. In our method, two energy terms are added to the conventional marker-based camera parameter estimation method. One is reprojection errors based on the epipolar constraint. The other is the constraint of continuity of zoom values. By using a novel energy function, our method can estimate accurate intrinsic and extrinsic camera parameters. In an experiment, we confirmed that the proposed method can achieve accurate camera parameter estimation during camera zooming.

Calibration of the transformation between two planes, the image plane and the 2D platform, is important for applications where 2D metric information on the image plane is used to compute the 3D information in a world coordinate system. Efforts have been taken in computer vision literature to perform a full-scale camera calibration, including intrinsic and extrinsic parameters. For some applications, calibration of intrinsic parameters is not required as often as that of the extrinsic parameters. This paper addresses the problem of calibrating a camera's extrinsic parameters with respect to a 2D platform to which a camera is observing. A rational approximation method is proposed. Simulation and experimental results show that the proposed rational approximation method achieves comparable accuracy with the well-known homography-based approach. This work is motivated by our mobile sensor network project. Other relevant applications include vision-based metrology.

A key limitation of all existing algorithms for shape and motion from image sequences under orthographic, weak perspective and para-perspective projection is that they require the calibration parameters of the camera. We present in this paper a new approach that allows the shape and motion to be computed from image sequences without having to know the calibration parameters. This approach is derived with the affine camera model, introduced by Mundy and Zisserman (1992), which is a more general class of projections including orthographic, weak perspective and para-perspective projection models. The concept of self-calibration, introduced by Maybank and Faugeras (1992) for the perspective camera and by Hartley (1994) for the rotating camera, is then applied for the affine camera. This paper introduces the 3 intrinsic parameters that the affine camera can have at most. The intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pin-hole perspective camera, but are different in the general case. Based on the invariance of the intrinsic parameters, methods of self-calibration of the affine camera are proposed. It is shown that with at least four views, an affine camera may be self-calibrated up to a scaling factor, leading to Euclidean (similarity) shape réconstruction up to a global scaling factor. Another consequence of the introduction of intrinsic and extrinsic parameters of the affine camera is that all existing algorithms using calibrated affine cameras can be assembled into the same framework and some of them can be easily extented to a batch solution. Experimental results are presented and compared with other methods using calibrated affine cameras.

This paper introduces the 3 intrinsic parameters that the affine camera can have at most. The intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pinhole perspective camera, but different in general case. Based on the invariance of the intrinsic parameters, the methods of self-calibration of the affine camera are proposed. It is shown that with at least four views, an affine camera may be self-calibrated up to a scaling factor. It turns out Euclidean (similarity) shape reconstruction only up to a global scaling factor. Another consequence of the introduction of intrinsic and extrinsic parameters of the affine camera is that all existing algorithm using calibrated cameras can be assembled into the same framework and some of them can be easily extented to a batch solution.