Showing papers on "Perspective (geometry) published in 2003"

Simultaneous pose and correspondence determination using line features

Abstract: We present a new robust line matching algorithm for solving the model-to-image registration problem. Given a model consisting of 3D lines and a cluttered perspective image of this model, the algorithm simultaneously estimates the pose of the model and the correspondences of model lines to image lines. The algorithm combines softassign for determining correspondences and POSIT for determining pose. Integrating these algorithms into a deterministic annealing procedure allows the correspondence and pose to evolve from initially uncertain values to a joint local optimum. This research extends to line features the SoftPOSIT algorithm proposed recently for point features. Lines detected in images are typically more stable than points and are less likely to be produced by clutter and noise, especially in man-made environments. Experiments on synthetic and real imagery with high levels of clutter, occlusion, and noise demonstrate the robustness of the algorithm.

Linear Multi-View Reconstruction of Points, Lines, Planes and Cameras using a Reference Plane

Abstract: This paper presents a new linear method for reconstructingsimultaneously 3D features (points, lines and planes)and cameras from many perspective views by solving a singlelinear system. It assumes that a real or virtual referenceplane is visible in all views. We call it the Direct ReferencePlane (DRP) method. It is well known that the projection relationshipbetween uncalibrated cameras and 3D featuresis non-linear in the absence of a reference plane. With aknown reference plane, points and cameras have a linearrelationship, as shown in [16]. The main contribution ofthis paper is that lines and cameras, as well as, planes andcameras also have a linear relationship. Consequently, all3D features and all cameras can be reconstructed simultaneouslyfrom a single linear system, which handles missingimage measurements naturally. A further contribution is anextensive experimental comparison, using real data, of differentreference plane and non-reference plane reconstructionmethods. For difficult reference plane scenarios, withpoint or line features, the DRP method is superior to allcompared methods. Finally, an extensive list of referenceplane scenarios is presented, which shows the wide applicabilityof the DRP method.

Linear multiview reconstruction of points, lines, planes and cameras using a reference plane

Abstract: This paper presents a new linear method for reconstructing simultaneously 3D features (points, lines and planes) and cameras from many perspective views by solving a single linear system. It assumes that a real or virtual reference plane is visible in all views. We call it the Direct Reference Plane (DRP) method. It is well known that the projection relationship between uncalibrated cameras and 3D features is nonlinear in the absence of a reference plane. With a known reference plane, points and cameras have a linear relationship, as shown by Rother and Carlsson (2001). The main contribution of this paper is that lines and cameras, as well as, planes and cameras also have a linear relationship. Consequently, all 3D features and all cameras can be reconstructed simultaneously from a single linear system, which handles missing image measurements naturally. A further contribution is an extensive experimental comparison, using real data, of different reference plane and nonreference plane reconstruction methods. For difficult reference plane scenarios, with point or line features, the DRP method is superior to all compared methods. Finally, an extensive list of reference plane scenarios is presented, which shows the wide applicability of the DRP method.

Lines in one orthographic and two perspective views

Abstract: We introduce a linear algorithm to recover the Euclidean motion between an 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. Here, 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.

A Tale of Three Circles

Abstract: Everyone knows that the sum of the angles of a triangle formed by three lines in the plane is 180 ◦ , but is this still true for curvilinear triangles formed by the arcs of three circles in the plane? We invite the reader to experiment enough to see that the angle sum indeed depends on the triangle, and that no general pattern is obvious. We give a complete analysis of the situation, showing along the way, we hope, what insights can be gained by approaching the problem from several points of view and at several levels of abstraction. We begin with an elementary solution using only the most basic concepts of Euclidean geometry. While it is direct and very short, this solution is not complete, since it works only in a special case. The key to another special case turns out to be a model of hyperbolic geometry, leading us to suspect that the various manifestations of the problem lie on a continuum of models of geometries with varying curvature. This larger geometric framework reveals many beautiful unifying themes and provides a single method of proof that completely solves the original problem. Finally, we describe a very simple formulation of the solution, whose proof relies on transformations of the plane, a fitting ending we think, since a transformation may be regarded as a change in one’s point of view. The background developed earlier informs our understanding of this new perspective, and allows us to give a purely geometric description of the transformations needed. For the reader who is unfamiliar with the classical noneuclidean geometries, in which the notions of line and distance are given new interpretations, we provide an overview that is almost entirely self-contained. Such a reader will be introduced to such things as angle excess, stereographic projection, and even a sphere of imaginary radius. For the reader who is familiar with the three classical geometries, we offer some new ways of looking at them, which we are confident will reveal some surprises.

Simulation Studies For The Performance Analysis Of The Reconstruction Of A Line In 3-D From Two Arbitrary Perspective Views Using Two Plane Intersection Method

Abstract: Objects in nature as well as man made are bound by planar as well as curvilinear surfaces. Hence the reconstruction process of three dimensional objects involves obtaining the geometrical attributes of these planar and curvilinear surfaces, lines, points etc. If a line in 3-D space is viewed from two arbitrary positions, two different images of the same line are obtained. The correspondence between this pair of projections of the line is assumed to be established in this work. The work presented in this paper describes a method of reconstruction of a line in 3-D as an intersection of two planes containing the respective projected line images. The parameters of the line in 3-D space are obtained from the parameters of projected images of the line. Relevant mathematical formulations and analytical solutions for obtaining the parameters of the reconstructed line are given. The effect of noise in the reconstruction and the efficiency of the described reconstruction methodology are studied by simulation studies.

Distance to the Perspective Plane

Abstract: Distance is an integral concept in perspective, both ancient and modern. Tomas Garcia-Salgado provides a historical survey of the concept of distance, then goes on to draw some geometric conclusions that relate distance to theories of vision, representation, and techniques of observation in the field. This paper clarifies the principles behind methods of dealing with the perspective of space, in contrast to those dealing with the perspective of objects, and examines the perspective method of Pomponius Gauricus, contrasting it with the method of Alberti. Finally the symmetry of the perspective plane is discussed.

Determination of 3-D position of particles in perspective picture with vanishing-point theorem

Abstract: Parallel lines viewed in a picture taken with a camera appear to meet at a vanishing point. Three groups of parallel lines which are perpendicular each to other appear three vanishing-points in a perspective picture. This paper proposed an algorithm by which real 3-D position ofthe viewpoint andimaging plane of the picture (also of the focus and film of the camera) and the scale of the picture aredetermined based on positions ofthe three vanishing-points. In this paper the principle of perspective geometry, visual geometry, was also discussed, especially the vanishing-point theorem. Meanwhile, this paper also proposed a method by which real3-D positions ofthe objects are determined with a two-viewpoint imaging system.Keyword: 3-D measurement, perspective picture, vanishing point, particle determinability, determinableprobability 1. Principle Of Vision Geometry The so-called visual imaging is a mapping image on retina of a physical body in 3-D space. As far as the principle of imaging is concerned, the imaging principle and process is the same with that of acamera. Fig. 1 represents the geometry of optical system, which explains a camera's imaging. The00 '-axis is a camera's optical axis and C stands for the optical center of a group of camera lens.

An extended perspective three points problem

Abstract: In this paper, an extended P3P (Perspective Three Points) problem is investigated. It is formulated as fitting three moving vertices along their associated optical rays to a known triangle structure. This allows the three optical rays to come from one, two or three cameras respectively. The classical P3P problem for only single camera is considered as a special case of the extended P3P problem. An analysis on these different cases is given in a uniform way. Experiments with simulated data show the effectiveness of the approach.