Showing papers on "Perspective (geometry) published in 1998"
23 Jun 1998
TL;DR: The novel contributions are that in a stratified context the various forms of providing metric information can be represented as circular constraints on the parameters of an affine transformation of the plane, providing a simple and uniform framework for integrating constraints.
Abstract: We describe the geometry constraints and algorithmic implementation for metric rectification of planes. The rectification allows metric properties, such as angles and length ratios, to be measured on the world plane from a perspective image. The novel contributions are: first, that in a stratified context the various forms of providing metric information, which include a known angle, two equal though unknown angles, and a known length ratio; can all be represented as circular constraints on the parameters of an affine transformation of the plane-this provides a simple and uniform framework for integrating constraints; second, direct rectification from right angles in the plane; third, it is shown that metric rectification enables calibration of the internal camera parameters; fourth, vanishing points are estimated using a Maximum Likelihood estimator; fifth, an algorithm for automatic rectification. Examples are given for a number of images, and applications demonstrated for texture map acquisition and metric measurements.
414 citations
TL;DR: Parametric and non-parametric approaches to warping, and matching criteria, are reviewed.
Abstract: Summary Image warping is a transformation which maps all positions in one image plane to positions in a second plane. It arises in many image analysis problems, whether in order to remove optical distortions introduced by a camera or a particular viewing perspective, to register an image with a map or template, or to align two or more images. The choice of warp is a compromise between a smooth distortion and one which achieves a good match. Smoothness can be ensured by assuming a parametric form for the warp or by constraining it using differential equations. Matching can be specified by points to be brought into alignment, by local measures of correlation between images, or by the coincidence of edges. Parametric and non-parametric approaches to warping, and matching criteria, are reviewed.
337 citations
01 Jan 1998
TL;DR: It is shown that structures that repeat in the world are related by particular parametrized transformations in perspective images, and these image transformations provide powerful grouping constraints, and can be used at the heart of hypothesize and verify grouping algorithms.
Abstract: The objective of this work is the automatic detection and grouping of imaged elements which repeat on a plane in a scene (for example tiled floorings). It is shown that structures that repeat on a scene plane are related by particular parametrized transformations in perspective images. These image transformations provide powerful grouping constraints, and can be used at the heart of hypothesize and verify grouping algorithms. The parametrized transformations are global across the image plane and may be computed without knowledge of the pose of the plane or camera calibration.
Parametrized transformations are given for severalcl asses of repeating operation in the world as well as groupers based on these. These groupers are demonstrated on a number of real images, where both the elements and the grouping are determined automatically.
It is shown that the repeating element can be learnt from the image, and hence provides an image descriptor. Also, information on the plane pose, such as its vanishing line, can be recovered from the grouping.
79 citations
Patent•
30 Jun 1998
TL;DR: In this article, the problem of expressing a large space with no distortion in a facility install space made compact as much as possible based on three-dimensional (3D) graphic data expressing an object space by previously correcting the distortion to be generated when extracted two-dimensional(2D) image data are projected from a viewpoint position different from viewpoint position relation with a projection plane to a projection planes having the equivalent relation with the projection plane.
Abstract: PROBLEM TO BE SOLVED: To express a large space with no distortion in a facility install space made compact as much as possible based on three-dimensional (3D) graphic data expressing an object space by previously correcting the distortion to be generated when extracted two-dimensional(2D) image data are projected from a viewpoint position different from viewpoint position relation with a projection plane to a projection plane having the equivalent relation with the projection plane. SOLUTION: First of all, the 2D image data extracted from the 3D graphic data expressing the object space as a perspective direct projection picture onto the projection plane crossing at any arbitrary angle are projected from the viewpoint position equivalent with the viewpoint position relation with the projection plane onto the projection plane having the relation equivalent with the projection plane by projection planes S1 and S2 and video projection equipment P1 and P2 . Next, the 2D image data edited to be distorted for previously avoiding the distortion, which is generated in the case of projection from the viewpoint position different from the viewpoint position relation with the projection plane onto the projection plane having the relation equivalent with the projection plane, are projected by projection planes S3 -S8 and video projection equipment P3 -P8 .
4 citations
TL;DR: In this article, Pinhole Cameras, Perspective, and Projective Geometry are discussed. But they focus on the perspective of the camera and not on the geometry of the projection space.
Abstract: (1998). Pinhole Cameras, Perspective, and Projective Geometry. The American Mathematical Monthly: Vol. 105, No. 7, pp. 618-630.
4 citations