Perspective (geometry)

About: Perspective (geometry) is a research topic. Over the lifetime, 277 publications have been published within this topic receiving 5795 citations. The topic is also known as: perspective (geometry).

Replicator system and method for digitizing the geometry of a physical object

Abstract: A system (100) for generating a three-dimensional surface model of a physical object (122) includes a computer (102) and a coordinate measuring machine (CMM) (120). The CMM provides three-dimensional coordinates of user-specified points to the computer (102). A replicator program permits the user to define a cut plane (428) that passes through the physical object, and to capture three dimensional coordinates of points that fall at the intersection of the cut plane (428) and the surface of the object. Special viewing features of the program permit the user to view the distance between incoming points from the CMM and the cut plane, and to view the captured data in three dimensions (602-608) and from any viewing perspective. Other program features are included that enable the user to capture points falling at the intersection of the two planes (325), project capture points into a user-defined plane, and detect maximum and minimum points along an object's surface with respect to a user-defined plane.

Segment based camera calibration

Abstract: The basic idea of calibrating a camera system in previous approaches is to determine camera parameters by using a set of known 3D points as calibration reference In this paper, we present a method of camera calibration in which camera parameters are determined by a set of 3D lines A set of constraints is derived on camera parameters in terms of perspective line mapping From these constraints, the same perspective transformation matrix as that for point mapping can be computed linearly The minimum number of calibration lines is 6 This result generalizes that of Liu, Huang and Faugeras[12] for camera location determination in which at least 8 line correspondences are required for linear computation of camera location Since line segments in an image can be located easily and more accurately than points, the use of lines as calibration reference tends to ease the computation in image preprocessing and to improve calibration accuracy Experimental results on the calibration along with stereo reconstruction are reported

Complete Singularity Analysis for the Perspective-Four-Point Problem

Abstract: This paper is concerned with pose estimation and visual servoing from four points. We determine the configurations for which the corresponding Jacobian matrix becomes singular, leading to inaccurate and unstable results. Using an adequate representation and algebraic geometry, it is shown that, for any orientation between the camera and the object, there are always two to six singular locations of the camera in the generic case where the points are not coplanar, corresponding to the intersection of four cylinders. The particular case where the four points are coplanar is also characterized. Furthermore, some realistic example configurations are considered to substantiate the theory and to demonstrate failure cases in pose estimation and image-based visual servoing when the camera approaches a singularity.

A general solution to the hidden-line problem

Abstract: The requirements for computer-generated perspective projections of three dimensional objects has escalated. A general solution was developed. The theoretical solution to this problem is presented. The method is very efficient as it minimizes the selection of points and comparison of line segments and hence avoids the devastation of square-law growth.

Related Solutions to the Perspective Three-Point Pose Problem

Abstract: The perspective three-point pose problem involves solving Grunert's system of quadratic equations for the distances from the center of perspective to the three control points, typically resulting in multiple mathematical solutions. Relationships between the corresponding possible camera positions in space have only rarely been studied. Several efforts have been made though to understand the number of solution points using various assumptions. In this article, the number of solutions is determined in the limiting case, where the center of perspective is far from the plane containing the control points, as compared with its distance to the danger cylinder. Moreover, concise formulas are given for the other solutions based on a knowledge of one of the solutions. It turns out that the projection onto the control points plane of the various solution points lies at the intersection points of two rectangular hyperbolas. A certain deltoid curve also plays a crucial role.