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).

Plane exploration method based on panoramic image depth map

Abstract: The invention discloses a plane exploration method based on a panoramic image depth map, belonging to the field of measurable street view images. According to the method, the ground exploration plane of a depth map is used, thus uphill and downhill road section detection results are more accurate, at the same time, since the depth map is automatically produced by using point cloud, the degree of automation is high, the manual intervention is not needed, and the data production cost is low. For a building facade area plane exploration result, a target panorama is selected according to the principle of maximum perspective, and the method is more in accordance with the actual situation.

Integration Between Perspective Images and BIM Models: Projective Geometry Is Still Alive

Abstract: The large diffusion of BIM modeling within the study of historic buildings makes often necessary for researchers to integrate automatically models and graphic documentation (analogical and digital photographs, paintings, lithographs, etc.) derived from historical analysis. The study here presented study how to intersect three-dimensional digital models and analogical images using the basics of Projective Geometry. As already highlighted, within the process of virtual prefiguration of architecture, geometry has always acted as an indispensable scientific tool for the designer. It allows not only a correct and effective representation of structures and complex spatial configurations, but, above all, it inspires every creative design operation. In this way, the geometry reintroduces the ancient binomial between art and science. From an educational perspective, nowadays it is possible to proceed with a re-actualization of the projective processes, combined with the multiple attempts to “narrate” events on surfaces, (not only flat but also curves, narrations in which a person looks, for example, beyond the painted wall in a forerunner attempt that today we consider virtual reality). The study of Projective Geometry is central, making operative the well-established practice in the perspective, but in the opposite direction. In the digital space, it will be possible to project, from the point of view, the graphic information, existing on the image (representation plane), on the BIM objects. The advantage for the end user lies precisely in the projection by category of the information, which can therefore refer to the walls, some frescoes, the vaults, already modelled.

Estimation of Depth Information from a Single View in an Image.

Abstract: Distance measurement in real world has always been one of the challenging tasks to be performed in the field of computer vision. Photographic images are twodimensional depiction of three-dimensional real space. On methodical observation of the same, one can identify some third dimensional properties (like depth information). In this paper we have proposed a method, which employs perspective projective geometrical tool, and henceforth bring out a new idea of computing the distances between the edges in the object, which are parallel to the image plane in photographs of actual scene. The technique presented employs uncalibrated images with no knowledge of the internal parameters of the camera (as focal length & aspect ratio) or it’s pose (position & orientation with respect to viewed scene). Geometric characteristics (perspective projections) of the scene are employed.

Cameras, Shapes, and Contours: Geometric Models in Computer Vision

Abstract: This thesis studies mathematical models for describing the geometry of imaging processes in computer vision. Our approach is rooted in the language of projective geometry, which provides the most general setting for studying properties of lines and incidences that are at the heart of geometric vision. We also apply some tools from algebraic geometry, since many of the objects that we encounter are described by polynomial equations. For example, the multi-view geometry of $n$ pinhole cameras (or in fact any type of cameras) can be encoded in the "joint image", that is an algebraic variety in $(\mathbb P^2)^n$ formed by all point correspondences. The Grassmannian of lines ${\rm Gr}(1,\mathbb P^3)$ also plays a central role in our study. In particular, surfaces in the Grassmannian (or "line congruences") can be used to represent abstract cameras, that are mappings from points to viewing lines. In addition to modeling cameras, we investigate the relationship between 3D shapes and their images. For arbitrary sets projecting onto opaque silhouettes, the image is determined by the set of viewing lines that meet the observed object; for smooth surfaces, the "image contour" is determined by the set viewing lines that are tangent to the surface. This perspective is applied to the study of "visual hulls" and "visual events".

Classical Configurations in Affine Planes 1

Abstract: Summary. The classical sequence of implications which hold between Desargues and Pappus Axioms id proved. Formally Minor and Major Desargues Axiom (as suitable properties - predicates - of an affine plane) together with all its indirect forms are introduced; the same procedure is applied to Pappus Axioms. The so called Trapezium Desargues Axiom is also considered.