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).

Sketching with projective 2D strokes

Abstract: Freehand sketching has long had appeal as an artistic medium for conceptual design because of its immediacy in capturing and communicating design intent and visual experience. We present a sketching paradigm that supports the early stages of design by preserving the fluidity of traditional freehand drawings. In addition, it attempts to fill the gap between 2D drawing programs, which have fixed views, and 3D modeling programs that allow arbitrary views. We implement our application as a two-dimensional drawing program that utilizes a projective representation of points — i.e. points that lie on the surface of a unit sphere centered at the viewpoint. This representation facilitates the production of novel re-projections generated from an initial perspective sketch and gives the user the impression of being immersed in the drawing or space. We describe a method for aligning a sketch drawn outside the system using its vanishing points, allowing the integration of computer sketching and freehand sketching on paper in an iterative manner. The user interface provides a virtual camera, projective grids to guide in the construction of proportionate scenes, and the ability to underlay sketches with other drawings or photographic panoramas.

Finding point correspondences and determining motion of rigid object from two weak perspective views

Abstract: Given two images of an n-point configuration which undergoes 3D rotation, translation, and scaling, our problems are (i) How can we match the corresponding points in the two images? Can all the possible mapping be found? (ii) What underlying motions and associated depth components of these points could account for the two images? (iii) Can the object be recovered uniquely? This formulation of the n-point problem is in the most general setting and does not assume attributes or features. A natural question to ask is whether an n-point problem is equivalent to a set of fewer-point problems. This paper presents a method which reduces an n-point problem to a set of 4-point problems. The effort of reduction takes O(n) steps and it also takes O(n) steps to construct all possible mappings of an n-point set from the solution to a 4-point problem. Other results include (1) coplanarity condition of four points in two views, (2) recovering the tilt direction of the rotational axis using four points in two views, (3) recovering the scaling factor.

Matching perspective views of coplanar structures using projective unwarping and similarity matching

Abstract: The problem of matching perspective views of coplanar structures composed of line segments is considered. Both model-to-image and image-to-image correspondence matching are given a consistent treatment. These matching scenarios generally require discovery of an eight-parameter projective mapping. When the horizon line of the object plane can be found in the image, which is accomplished in this case by using vanishing point analysis, these problems reduce to a simpler six-parameter affine matching problem. When the intrinsic lens parameters of the camera are known, the problem further reduces to four-parameter affine similarity matching. >

A linear algorithm for camera self-calibration, motion and structure recovery for multi-planar scenes from two perspective images

Abstract: In this paper we show that given two homography matrices for two planes in space, there is a linear algorithm for the rotation and translation between the two cameras, the focal lengths of the two cameras and the plane equations in the space. Using the estimates as an initial guess, we can further optimize the solution by minimizing the difference between observations and reprojections. Experimental results are shown. We also provide a discussion about the relationship between this approach and the Kruppa equation.

Methods and Apparatuses for Informing an Occupant of a Vehicle of Surroundings of the Vehicle

Abstract: Methods and apparatuses for informing an occupant of a vehicle of surroundings of the vehicle are provided. A recording unit of the vehicle generates at least two images, which contain different road sections of a road plane in the surroundings of the vehicle. The at least two images are processed by an image processing unit, which generates a depiction in which the at least two images are imaged on a virtual road plane that is displayed in perspective. The depiction is displayed on a display unit in the interior of the vehicle.