Showing papers on "Perspective (geometry) published in 2005"

Distortions of perceived length in the frontoparallel plane: Tests of perspective theories

Abstract: The perceived length of a line segment in a frontoparallel plane is sometimes affected by the presence of other line segments in the visual field. Perspective theories attribute such interactions to sizeconstancy scaling: The configuration of line segments present in the visual field includes depth cues that trigger size scaling of each line segment. In three experiments, we test this claim for a range of simple configurations composed of two line segments joined at a point. These configurations include the inverted T configuration of the bisection illusion, as well as the L configuration of the horizontal— vertical illusion. We conclude that the available depth cues, even when supplemented by known biases in perspective interpretations, do not account for observed distortions in judgments of relative length.

Non-rigid 3D factorization for projective reconstruction

Abstract: In this paper we address the problem of projective reconstruction for deformable objects. Recent work in non-rigid factorization has proved that it is possible to model deformations as a linear combination of basis shapes, allowing the recovery of camera motion and 3D shape under weak perspective viewing conditions. However, the performance of these methods degrades when the object of interest is close to the camera and strong perspective distortion is present in the data. The main contribution of this work is the proposal of a practical method for the recovery of projective depths, camera motion and non-rigid 3D shape from a sequence of images under strong perspective conditions. Our approach is based on minimizing 2D reprojection errors, solving the minimization as four weighted least squares problems. Results using synthetic and real data are given to illustrate the performance of our method.

Jean Victor Poncelet, Traité des propriétés projectives des figures first edition (1822)

Abstract: Publisher Summary Poncelet's book is the source of the launch of the modern study of projective geometry, after the work of various 17th-century authors did not generate sufficient momentum to sustain the subject through the 18th century. Poncelet brought up the key idea of central projection. Central projection has a number of unexpected properties. It was a familiar fact from the theory of central focussed perspective in painting that a line in one plane may correspond to a line seemingly infinitely far away in another plane. In this way intersecting lines in one plane may appear as parallel lines in the other plane, and parallel lines may be correctly depicted as ones that intersect. Poncelet proclaimed that his law of continuity allowed him to treat two conics simultaneously in remarkable ways. The study of the central projection of two conics at once was a new idea of his, and he proclaimed that any two conics may be projected into two circles. Poncelet had shown conclusively that there was an extensive body of non-metrical results in geometry. But his methods, resting as they did on his “law of continuity” were by and large not acceptable to his contemporaries.

Geometric Fourier Analysis for Computational Vision

Abstract: Projective Fourier analysis — geometric Fourier analysis of the group SL(2,ℂ), the group identified in the conformal camera that provides image perspective transformations—is discussed in the framework of representation theory of semisimple Lie groups. The compact model of projective Fourier analysis is constructed, complementing the noncompact model proposed before. Detailed mathematical formulation of both models is presented. It is demonstrated that the projective Fourier analysis provides the data model for efficient perspectively covariant digital image representation well adapted to the retino-cortical mapping of biological visual system, and therefore, explicitly designed for the foveated sensors of a silicon retina, the use of which in active vision systems is presently limited due to the lack of such a model.

Geometric invariant theory and projective toric varieties

Abstract: This is an expository paper in which we define projective GIT quotients and introduce toric varieties from this perspective It is intended primarily for readers who are learning either invariant theory or toric geometry for the first time

Three-dimensional display

Abstract: The invention relates to a three-dimensional auto-stereoscopic display aimed at, but not restricted to domestic television applications. In this display different viewing directions in the horizontal plane are created by projecting an image on a 2D display through lenticular lenses and onto horizontal lines of to the 3D screen. These lines are scanned along the display by means of a single rotating mirror. The proposed embodiment has a large viewing angle and shows a picture with realistic parallax and perspective. Compared to other known three-dimensional displays, it uses existing components, has a simple construction and is light efficient.

Registration of Augmented Reality Based on Natural Characteristic Points

Abstract: A method of registration of augmented reality(AR) based on natural characteristics is introduced.According to a theory of computer vision,the most general transformation that can occur between a scene plane and an image plane under perspective imaging is a plane projective transformation.It is therefore concluded that a projection matrix can be computed through homography under certain condition.First,an initial projection matrix is obtained through homography between an image and a scene plane.The homograph matrix between two images,i.e.,the image plane and the scene plane,can then be calculated from matching points of these two images.Thus the projection matrix of every next frame can be calculated from homograph matrix between the current image plane and the previous one.Registration of virtual objects is finally completed.

Improvement 3-D Reconstruction Accuracy Considering Distortion in Stereovision Using a Set of Linear Spatial Filters

Abstract: This paper presents a frequency-based stereovision approach to improve the accuracy of the three-dimensional (3D) reconstruction. In view of the fact that, stereo images are obtained from the different perspective position, so that each image can have the effect of projective distortion region (half occlusion, perspective foreshortening). These effects cause problems, since the projected distortion region cannot be estimated in terms of fixed-size block matching algorithm. An alternative approach is presented, which based on the output of linear spatial filters turned to a range of orientations and scales to make the correspondence analysis more reliable and robust. The responses of these filters at a given point constitute a vector called the filter response vector (FRY) is correlated instead of correlating area in the two images. In addition, an automatic procedure is used to evaluate and optimize the filters set by using the steering theorem and the singular value decomposition (SVD). The experimental result shows that remarkable improvement is obtained in the projective distortion region

Parameter identification of a moving object based on sensor fusion

Abstract: In this paper, in order to get the better identification of motion and shape parameters of a plane dynamics, that is, in order to reduce the parameter ambiguity in the case of when we use only vision as the observation data, we now consider that we apply the laser range finder data with vision using both of a single laser range finder and a single CCD camera mounted on a mobile robot platform. The reason why we use the laser range finder is that it makes a line on the moving plane along a horizontal laser plane. Namely the laser range finder observes a cross section of the plane as a line. This line changes as the plane moves. We can add a line information for the identification problem. We show that when we use the laser range finder data with vision as the observation data the dimension of the parameter ambiguity in the only vision case can be reduced. Further, we introduce a suitable canonical form in order to identify orbits of the underlying a suitable subgroup of perspective group.