Showing papers on "Perspective (geometry) published in 2000"

Iterative projective reconstruction from multiple views

Abstract: We propose an iterative method for the recovery of the projective structure and motion from multiple images. It has been recently noted that by scaling the measurement matrix by the true projective depths, recovery of the structure and motion is possible by factorization. The reliable determination of the projective depths is crucial to the success of this approach. The previous approach recovers these projective depths using pairwise constraints among images. We first discuss a few important drawbacks with this approach. We then propose an iterative method where we simultaneously recover both the projective depths as well as the structure and motion that avoids some of these drawbacks by utilizing all of the available data uniformly. The new approach makes use of a subspace constraint on the projections of a 3D point onto an arbitrary number of images. The projective depths are readily determined by solving a generalized eigenvalue problem derived from the subspace constraint. We also formulate a dual subspace constraint on all the points in a given image, which can be used for verifying the projective geometry of a scene or object that was modeled. We prove the monotonic convergence of the iterative scheme to a local maximum. We show the robustness of the approach on both synthetic and real data despite large perspective distortions and varying initializations.

3D environment labelling

Abstract: Objects (3, 4) of a three dimensional 3D virtual world that are represented on a two dimensional 2D image plane (6) are provided with labels (7, 8) which are generated in the 2D image plane (6) itself. The labels are in spatial registration with the object as represented on the 2D image plane. The generation of the labels in the 2D image plane avoids problems relating to perspective and aliasing which can occur when labels are provided in the virtual world itself and are rendered from the 3D virtual world.

A linear algorithm for camera self-calibration, motion and structure recovery for multi-planar scenes from two perspective images

Abstract: In this paper we show that given two homography matrices for two planes in space, there is a linear algorithm for the rotation and translation between the two cameras, the focal lengths of the two cameras and the plane equations in the space. Using the estimates as an initial guess, we can further optimize the solution by minimizing the difference between observations and reprojections. Experimental results are shown. We also provide a discussion about the relationship between this approach and the Kruppa equation.

A Linear Algorithm for Computing the Homography from Conics in Correspondence

Abstract: This paper presents a study, based on conic correspondences, on the relationship between two perspective images acquired by an uncalibrated camera. We show that for a pair of corresponding conics, the parameters representing the conics satisfy a linear constraint. To be more specific, the parameters that represent a conic in one image are transformed by a five-dimensional projective transformation to the parameters that represent the corresponding conic in another image. We also show that this transformation is expressed as the symmetric component of the tensor product of the transformation based on point/line correspondences and itself. In addition, we present a linear algorithm for uniquely determining the corresponding point-based transformation from a given conic-based transformation up to a scale factor. Accordingly, conic correspondences enable us to easily handle both points and lines in uncalibrated images of a planar object.

Structure from motion using points, lines, and intensities

Abstract: We present a fast factorization algorithm for estimating structure and motion simultaneously from points, lines, and/or directly from the image intensities under full perspective. It generalizes the Oliensis method for points to include lines and intensities as well.

Lines in one orthographic and two perspective views

Abstract: In this paper we introduce a linear algorithm to recover the Euclidean motion between one orthographic and two perspective cameras from straight line correspondences filling the gap in the analysis of motion estimation from line correspondences for various projection models. The general relationship between lines in three views is described by the trifocal tensor. Euclidean structure from motion for three perspective views is a special case in which the relationship is defined by a collection of three matrices. We describe the case of two calibrated perspective views and an orthographic view. Similar to the other cases, our linear algorithm requires 13 or more line correspondences to recover 27 coefficients of the trifocal tensor.