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).

Almost perfect and planar functions

Abstract: In this article I survey some recent results on planar functions, almost planar functions and modified planar functions from the perspective of difference sets.

Geometric Grouping of Repeated Elements within Images

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.

Projective geometry and its applications to computer graphics

Abstract: The goal of the book is to support the design of solutions to computer graphic problems through an understanding of the underlying elements of projective geometry. Some of the topics discussed are: How to view the structure of two and three dimensional graphic libraries, how to create two dimensional perspective and parallel images of a three dimensional object, how to draw the graph of a function of two real variables, and more

A Perspective Theory for Motion and Shape Estimation in Machine Vision

Abstract: In this paper, we consider the problem of motion and shape estimation of a moving body with the aid of a monocular camera. We show that the estimation problem reduces to a specific parameter estimation of a perspective dynamical system. Surprisingly, the above reduction is independent of whether the data measured is the brightness pattern which the object produces on the image plane or whether the data observed are points, lines, or curves on the image plane produced as a result of discontinuities in the brightness pattern. Many cases of the perspective parameter estimation problem have been analyzed in this paper. These cases include a fairly complete analysis of a planar textured surface undergoing a rigid flow and an affine flow. These two cases have been analyzed for orthographic, pseudo-orthographic, and image-centered projections. The basic procedure introduced for parameter estimation is to subdivide the problem into two modules, one for "spatial averaging" and the other for "time averaging." The estimation procedure is carried out with the aid of a new "realization theory for perspective systems" introduced for systems described in discrete time and in continuous time. Finally, much of our analysis has been substantiated by computer simulation of specific algorithms developed in order to explicitly compute the parameters. Detailed simulation that would answer the perspective realizability question is a subject of future research.

Geometric Grouping of Repeated Elements within Images.

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.