Algebraic Aspects of Reconstruction of 3D Scenes from One or More Views (original) (raw)

Relative affine structure: theory and application to 3D reconstruction from perspective views

1994

We propose an a ne framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call relative a ne structure. Via a number of corollaries of our main results we show that our framework uni es previous work | including Euclidean, projective and a ne | in a natural and simple way. Finally, the main results were applied to a real image sequence for purpose of 3D reconstruction from 2D views.

Euclidean 3D Reconstruction of Unknown Objects from Multiple Images

Journal of Emerging Technologies in Web Intelligence, 2014

In this paper, we are interested in the problem of Euclidean 3D reconstruction of unknown objects by passive stereo vision method. Our method is based on the combination between Harris and Sift interest point detectors, to take advantage of the power of these two detectors, which will be useful when matching step, as a key step for 3D reconstruction, In order to have a sufficient number of matches distributed on the images. These matches will be used to estimate the 3D points (the projection matrices will be estimated after calibration using 3D Calibration Pattern). Finally, a 3D mesh is constructed by 3D Delaunay triangulation, applied to the 3D points reconstructed. Experimental results prove that this method is practical and gives satisfying results without going through the propagation step.

Three-dimensional reconstruction of points and lines with unknown correspondence across images

2001

Three-dimensional reconstruction from a set of images is an important and difficult problem in computer vision. In this paper, we address the problem of determining image feature correspondences while simultaneously reconstructing the corresponding 3D features, given the camera poses of disparate monocular views. First, two new affinity measures are presented that capture the degree to which candidate features from different images consistently represent the projection of the same 3D point or 3D line. An affinity measure for point features in two different views is defined with respect to their distance from a hypothetical projected 3D pseudo-intersection point. Similarly, an affinity measure for 2D image line segments across three views is defined with respect to a 3D pseudo-intersection line. These affinity measures provide a foundation for determining unknown correspondences using weighted bipartite graphs representing candidate point and line matches across different images. As a result of this graph representation, a standard graph-theoretic algorithm can provide an optimal, simultaneous matching and triangulation of points across two views, and lines across three views. Experimental results on synthetic and real data demonstrate the effectiveness of the approach.

A Nonlinear Method for Estimating the Projective Geometry of Three Views

2001

Given three partially overlapping views of a scene from which a set of point correspondences have been extracted, recover the three trifocal tensors between the three views. We give a new way of deriving the trifocal tensor based on Grassmann-Cayley algebra that sheds some new light on its structure. We show that our derivation leads to a complete characterization of its geometric and algebraic properties which is fairly intuitive, i.e. geometric. We give a set of algebraic constraints which are satisfied by the 27 coefficients of the trifocal tensor and allow to parameterize it minimally with 18 coefficients. We then describe a robust method for estimating the trifocal tensor from point and line correspondences that uses this minimal parameterization. Our experimental results show that this method is superior to the linear methods which had been previously published.

A nonlinear method for estimating the projective geometry of 3 views

1998

An Approach to Projective Reconstruction from Multiple Views

2010

We present an original multiple views method to perform a robust and detailed 3D reconstruction of a static scene from several images taken by one or more uncalibrated cameras. Making use only of fundamental matrices we are able to combine even heterogeneous video and/or photo sequences. In particular we give a characterization of camera matrices space consistent with a given fundamental matrix and provide a straightforward bottom-up method, linear in most practical uses, to fulfil the 3D reconstruction. We also describe shortly how to integrate this procedure in a standard vision system following an incremental approach.

Camera calibration and 3D reconstruction from a single view based on scene constraints

Image and Vision Computing, 2005

This paper mainly focuses on the problem of camera calibration and 3D reconstruction from a single view of structured scene. It is well known that three constraints on the intrinsic parameters of a camera can be obtained from the vanishing points of three mutually orthogonal directions. However, there usually exist one or several pairs of line segments, which are mutually orthogonal and lie in the pencil of planes defined by two of the vanishing directions in the structured scenes. It is proved in this paper that a new independent constraint to the image of the absolute conic can be obtained if the pair of line segments is of equal length or with known length ratio in space. The constraint is further studied both in terms of the vanishing points and the images of circular points. Hence, four independent constraints on a camera are obtained from one image, and the camera can be calibrated under the widely accepted assumption of zero-skew. This paper also presents a simple method for the recovery of camera extrinsic parameters and projection matrix with respect to a given world coordinate system. Furthermore, several methods are presented to estimate the positions and poses of space planar surfaces from the recovered projection matrix and scene constraints. Thus, a scene structure can be reconstructed by combining the planar patches. Extensive experiments on simulated data and real images, as well as a comparative test with other methods in the literature, validate our proposed methods.

Automatic Reconstruction of Stationary 3-D Objects from Multiple Uncalibrated Camera Views

A system for the automatic reconstruction of real world objects from multiple uncalibrated camera views is presented. The camera position and orientation for all views, the 3-D shape of the rigid object as well as associated color information are recovered from the image sequence. The system proceeds in four steps. First, the internal camera parameters describing the imaging geometry of the camera are calibrated using a reference object. Second, an initial 3-D description of the object is computed from two views. This model information is then used in a third step to estimate the camera positions for all available views using a novel linear 3-D motion and shape estimation algorithm. The main feature of this third step is the simultaneous estimation of 3-D camera motion parameters and object shape refinement with respect to the initial 3-D model. The initial 3-D shape model exhibits only a few degrees of freedom and the object shape refinement is defined as flexible deformation of the initial shape model. Our formulation of the shape deformation allows the object texture to slide on the surface, which differs from traditional flexible body modeling. This novel combined shape and motion estimation using sliding texture considerably improves the calibration data of the individual views in comparison to fixed-shape model-based camera motion estimation. Since the shape model used for model-based camera motion estimation is approximate only, a volumetric 3-D reconstruction process is initiated in the fourth step that combines the information from all views simultaneously. The recovered object consists of a set of voxels with associated color information that describe even fine structures and details of the object. New views of the object can be rendered from the recovered 3-D model, which has potential applications in virtual reality or multimedia systems and the emerging field of video coding using 3-D scene models.

Important approach to 3D reconstruction of tridimensional objects based on multiple plan images

International Journal of Computer Applications in Technology, 2017

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.

Algebraic Aspects of Reconstruction of 3D Scenes from One or More Views (original) (raw)

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