Uncalibrated reconstruction: an adaptation to structured light vision

To solve the missing data problem that is caused by reasons, such as occlusion, frame reconstruction by a two-level strategy in multiple images was considered. The method first performed a projective reconstruction combining singular value decomposition (SVD) and subspace method with missing data, which estimated projective shape, projection matrices, projective depths and missing data iteratively. Then it converted the projective solution to a Euclidean one with the unknown focal length and the constant principal point by enforcing constraints. Using the constraints and the fact that scale measurement matrix can recover numberless projection matrices and point matrices, the set equations of the transformation matrix from the projective reconstruction to Euclidean reconstruction were obtained. Experimental results using real images are provided to illustrate the performance of the proposed method.

A factorization-based 3D reconstruction system is realized to recover 3D scene from an image sequence. The image sequence is captured from uncalibrated perspective camera from several views. Many matched feature points over all images are obtained by feature tracking method. Then, these data are supplied to the 3D reconstruction module to obtain the projective reconstruction. Projective reconstruction is converted to Euclidean reconstruction by enforcing several metric constraints. After many triangular meshes are obtained, realistic reconstruction of 3D models are finished by texture mapping. The developed system is implemented in C++, and Qt library is used to implement the system user interface. OpenGL graphics library is used to realize the texture mapping routine and the model visualization program. Experimental results using synthetic and real image data are included to demonstrate the effectiveness of the developed system.Keywords:Image-based Modeling, Projective Reconstruction, Euclidean Reconstruction, Structure From Motion, Texture Mapping

A new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters as well as the Euclidean reconstruction from at least three images. The novelty of our approach is that we build our calculation on a projective reconstruction obtained without the assumption on constant intrinsic parameters. This assumption simplifies the analysis, because a projective reconstruction is already obtained and we need “only” to find the correct Euclidean reconstruction among all possible projective reconstructions

We present generalizations of the classic theorem of projective reconstruction as a tool for the design and analysis of the projective reconstruction algorithms. Our main focus is algorithms such as bundle adjustment and factorization-based techniques, which try to solve the projective equations directly for the structure points and projection matrices, rather than the so called tensor-based approaches. First, we consider the classic case of 3D to 2D projections. Our new theorem shows that projective reconstruction is possible under a much weaker restriction than requiring, a priori, that all estimated projective depths are nonzero. By completely specifying possible forms of wrong configurations when some of the projective depths are allowed to be zero, the theory enables us to present a class of depth constraints under which any reconstruction of cameras and points projecting into given image points is projectively equivalent to the true camera-point configuration. This is very useful for the design and analysis of different factorization-based algorithms. Here, we analyse several constraints used in the literature using our theory, and also demonstrate how our theory can be used for the design of new constraints with desirable properties. The next part of the thesis is devoted to projective reconstruction in arbitrary dimensions, which is important due to its applications in the analysis of dynamical scenes. The current theory, due to Hartley and Schaffalitzky, is based on the Grassmann tensor, generalizing the notions of Fundamental matrix, trifocal tensor and quardifocal tensor used for 3D to 2D projections. We extend their work by giving a theory whose point of departure is the projective equations rather than the Grassmann tensor. First, we prove the uniqueness of the Grassmann tensor corresponding to each set of image points, a question that remained open in the work of Hartley and Schaffalitzky. Then, we show that projective equivalence follows from the set of projective equations, provided that the depths are all nonzero. Finally, we classify possible wrong solutions to the projective factorization problem, where not all the projective depths are restricted to be nonzero. We test our theory experimentally by running the factorization based algorithms for rigid structure and motion in the case of 3D to 2D projections. We further run simulations for projections from higher dimensions. In each case, we present examples demonstrating how the algorithm can converge to the degenerate solutions introduced in the earlier chapters. We also show how the use of proper constraints can result in a better performance in terms of finding a correct solution.

This paper describes a method to upgrade projective reconstruction to affine and to metric reconstructions using rigid general motions of a stereo rig. We make clear the algebraic relationships between projective reconstruction, the plane at infinity (affine reconstruction), camera calibration, and metric reconstruction. We show that all the computations can be carried out using standard linear resolution methods and that these methods compare favorably with nonlinear optimization, methods in the presence of Gaussian noise. We carry out a theoretical error analysis which quantify the relative importance of the accuracies of projective-to-affine conversion and affine-to-Euclidean conversion. Experiments with with real data are consistent with the theoretical error analysis and with a sensitivity analysis performed with simulated data.

In AR systems, registration is one of the most difficult problems currently limiting its applications. In this paper, we proposed a simple registration method using projective reconstruction. This method includes two steps: embedding and tracking. Embedding involves specifying four points to build the world coordinate system on which a virtual object will be superimposed. In tracking, a projective reconstruction technique in computer vision is used to track these specified four points to compute the modelview transformation for augmentation. This method is simple as only four points need to be specified at the embedding stage, and the virtual object can then be easily augmented onto a real video sequence. In addition, it can be extended to a general scenario using a generic projective matrix. The proposed method has three advantages: (1) It is fast because the linear least square method can be used to estimate the related matrix in the algorithm and it is not necessary to calculate the fundamental matrix in the extended case; (2) A virtual object can still be superimposed on a related area even if some parts of the specified area are occluded during the whole process; (3) This method is robust because it remains effective even when not all the reference points are detected during the whole process (in the rendering process), if at least six pairs of related reference point correspondences can be found. Several projective matrices obtained from the authors' previous work, which is unrelated with the present AR system, have been tested on this extended registration method. Experiments showed that these projective matrices can also be utilized for tracking the specified points.

Euclidean upgrading from segment lengths: DLT-like algorithm and its variants

In the present paper, we will focus on a new approach for efficient and reliable tridimensional reconstruction of objects from flat images. Our approach allows the realisation of tridimensional reconstruction without passing through the calibration and self-calibration phase of the camera, but based on the estimation of the fundamental matrix and the homography at infinity to have the projective, affine and Euclidean projection. Our method is based firstly on a very important step in the 3D reconstruction that is the detection of interest points using the Harris detector to have a sufficient number of matches distributed on the images, these matches are used to estimate the 3D points, and secondly to estimate the projection matrices that are made from different existing relationships between the three types of tridimensional reconstruction (projective reconstruction, affine reconstruction, Euclidean reconstruction). Experimental results prove that this method is practical and gives satisfying results without going through the calibration step.

In the present paper, we will focus on a new approach for efficient and reliable tridimensional reconstruction of objects from flat images. Our approach allows the realisation of tridimensional reconstruction without passing through the calibration and self-calibration phase of the camera, but based on the estimation of the fundamental matrix and the homography at infinity to have the projective, affine and Euclidean projection. Our method is based firstly on a very important step in the 3D reconstruction that is the detection of interest points using the Harris detector to have a sufficient number of matches distributed on the images, these matches are used to estimate the 3D points, and secondly to estimate the projection matrices that are made from different existing relationships between the three types of tridimensional reconstruction (projective reconstruction, affine reconstruction, Euclidean reconstruction). Experimental results prove that this method is practical and gives satisfying results without going through the calibration step.

Using 3D building models is extremely helpful throughout the architecture engineering and construction (AEC) lifecycle. Such models coupled with virtual walk through can enable customers to decide and be satisfied with their dream building. Manually creating a polygonal 3D model of a set of floor plans is nontrivial and requires skill and time. This project introduces and reviews a mechanism for applying interior and exterior design constructs after the conversion of 2D drawings into 3D Building Information Model (BIM). This research demonstrates an automated 3D model reconstruction of real world object from an un-calibrated image sequence targeting the same scene, which can be used for interior and exterior design. There are many key techniques in 3D reconstruction from image sequences, including feature matching, fundamental matrix estimation, projective reconstruction, camera self-calibration, dense stereo matching and Euclidean reconstruction. The effectiveness of the algorithms was evaluated in the experiments with many real image sequences.

Finding the Collineation between Two Projective Reconstructions

3D scene reconstruction is an important technique in the computer vision field. Our system can give the user a platform to reconstruct a 3D model of scene from a set of uncalibrated images which are gained by a commonly used camera. There are many key techniques in 3D reconstruction from uncalibrated image sequences, including feature matching, fundamental matrix estimation, projective reconstruction, camera self-calibration, dense stereo matching and Euclidean reconstruction. The paper is focused on above associated issues and improved some key algorithms. The effectiveness of our algorithms is evaluated in the experiments with many real image sequences.

A method of fusing data from a Global Positioning System (GPS) and a Dead Reckoning (DR) system for outdoor navigation of a Wheeled Mobile Robot (WMR) is proposed. The low-cost GPS receiver cannot be utilized by itself for navigating the mobile robot. Since, it produces an error of approximately 10–20 meters. DR can provide precise navigation data to the mobile robot but its errors accumulate over time. Since, all the previous data are utilized to calculate the current position information. DR needs to be complemented by other navigation sensors to navigate the mobile robot. The proposed GPS/DR data fusion method is based on the characteristics of the single GPS receiver output. The fused data provides accurate and robust navigation information to the outdoor mobile robot. Simulations were conducted using real GPS data which were then compared with the results using a Kalman filter that verified the potential of the proposed GPS/DR data fusion method.

In research on machine vision, the theory and technique of recovering 3D scenes are important research subjects. They have been developed from 3D reconstruction method with calibrated cameras to uncalibrated cameras. Generally speaking, in order to reconstruct a 3D scene, at least three images must be needed. These images are grabbed at three different viewpoints with a moving camera keeping its internal parameters constant. In this paper, however, it is carried out in metric space with an uncalibrated camera and a single image of the scene. It is based on active machine vision system including a color encoded pseudo-random array pattern projector. In the paper, we focus on the uncalibrated 3D reconstruction algorithm for a scene. The algorithm is divided into three steps: projection reconstruction, affine reconstruction and Euclidean reconstruction up to a scale.

In this paper, we propose a new factorization-based algorithm for projective reconstruction from multiple views by minimizing the 2D reprojection error in the images. In our algorithm, the projective reconstruction problem is formulated as a constrained minimization problem, which minimizes the 2D reprojection error in multiple images. To solve this constrained minimization problem, we use the augmented Lagrangian approach to generate a sequence of unconstrained minimization problems, which can be readily solved by standard least-squares technique. Thus we can estimate the projective depths, the projection matrices and the positions of 3D points simultaneously by iteratively solving a sequence of unconstrained minimization problems. The proposed algorithm does not require the projective depths as prior knowledge, unlike bundle adjustment techniques. It converges more robustly and rapidly than the penalty based method. Furthermore, it readily handles the case of partial occlusion, where some points cannot be observed in some images.