Serwis Infona wykorzystuje pliki cookies (ciasteczka). Są to wartości tekstowe, zapamiętywane przez przeglądarkę na urządzeniu użytkownika. Nasz serwis ma dostęp do tych wartości oraz wykorzystuje je do zapamiętania danych dotyczących użytkownika, takich jak np. ustawienia (typu widok ekranu, wybór języka interfejsu), zapamiętanie zalogowania. Korzystanie z serwisu Infona oznacza zgodę na zapis informacji i ich wykorzystanie dla celów korzytania z serwisu. Więcej informacji można znaleźć w Polityce prywatności oraz Regulaminie serwisu. Zamknięcie tego okienka potwierdza zapoznanie się z informacją o plikach cookies, akceptację polityki prywatności i regulaminu oraz sposobu wykorzystywania plików cookies w serwisie. Możesz zmienić ustawienia obsługi cookies w swojej przeglądarce.
This article is a general introduction to Cartan's moving frame method which is elegant, simple, and of an algorithmic nature. We have demonstrated how to use it systematically on three examples relevant to computer vision, curves in the euclidean, affine and projective planes, and derived the corresponding Frenet equations. We have then used these equations to show that the analysis of the deformation...
A uniform algebraic procedure is presented for deriving both epipolar geometry and three-dimensional object structure from general stereo imagery. The procedure assumes central-projection cameras of unknown interior and exterior orientations. The ability to determine corresponding points in the stereo images is assumed, but no prior knowledge of the scene is required. Epipolar geometry and the fundamental...
We discuss briefly a number of areas where epipolar geometry is currently central in carrying out visual tasks. In contrast we demonstrate configurations for which 3D projective invariants can be computed from perspective stereo pairs, but epipolar geometry (and full projective structure) cannot. We catalogue a number of these configurations which generally involve isotropies under the 3D projective...
Recently, a number of classes of 3D structures have been identified which permit structure recovery and 3D invariants to be measured from a single image of the structure. A large class with this property is the case of repeated structures where a structure (such as a pointset, curve or surface), and a transformed copy of the structure are both observed in a single perspective image. In general the...
We are interested in the applications of invariant theory to computer vision problems. A survey and clarification of the different invariant calculation methods are detailed in our extented technical report
This paper investigates the differences — conceptually and algorithmically — between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. The study is made by first proposing an affine framework for perspective views, captured by a single remarkably simple equation, which is based on a viewer-centered invariant we call relative affine structure...
The double algebra is a system for computations involving subspaces of a general finite dimensional vector space. If this vector space is taken as projective 3-space, the operations of the double algebra can be interpreted as joins and intersections of points, lines and planes. All computations are coordinate free and invariant over linear transformations. The double algebra is therefore a very effective...
Within an invariance framework, the recognition of plane objects under general viewpoints and perspective projection calls for the extraction of two-dimensional projective invariants. If the possible poses of the object are constrained with respect to the camera, however, simpler groups than the projective transformations become relevant, and consequently, simpler invariants exist. Several such special...
The image formed by shading depends on many variables, including the shape of the object, the lighting characteristics, the imaging system, etc. Most of these variables are not known in advance, so the calculation of shape from shading is difficult. The problem could be greatly simplified if we could find invariants of the situation, namely quantities that stay constant as some of the unknown variables...
In this paper projective normalization and projective invariants of planar curves are discussed. It is shown that there exists continuous affine invariants. It is shown that many curves can be projected arbitrarily close to a circle in a strengthened Hausdorff metric. This does not infer any limitations on projective invariants, but it is clear that projective normalization by maximizing compactness...
Size functions are integer valued functions of two real variables which represent metric and topological properties of visual shape. In this paper size functions invariant for transformations of increasing generality are presented and discussed. Experiments on synthetically generated and real images show that by means of size functions invariant for Euclidean, affine, or projective transformations...
The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalently, Euclidean structure-from-motion from an uncalibrated camera. No tractable algorithm for implementing...
It is possible to recover the three-dimensional structure of a scene using images taken with uncalibrated cameras and pixel correspondences. But such a reconstruction can only be computed up to a projective transformation of the 3D space. Therefore, constraints have to be added to the reconstructed data in order to get the reconstruction in the euclidean space. Such constraints arise from knowledge...
The three-dimensional structure of a scene consisting of at least five points whose images are identified in two perspective views taken from different positions with a relative object-camera translation in between, can be reconstructed up to a 3D affine transformation. Hence, a more detailed reconstruction is possible using less information when compared to the results reported on arbitrary stereo...
There has been much interest recently in using invariant theory in computer vision. Most work has concentrated on recognition of 3-D objects from 2-D images using algebraic or differential invariants. In this work, we address the usage of a class of projective invariants and quasi-invariants for the segmentation and 3-D recovery of generalized cylinders from a monocular image. We derive important...
In many cases, the geometric representation that a recognition system could recover is insufficient to identify objects. When object geometry is simple, it is not particularly distinctive; however, a rich representation can be obtained by mapping the surface markings of the object onto the geometry recovered. If edges are mapped, a representation that is relatively insensitive to the details of lighting...
Using three dimensional invariant representations, we address the problem of changes in appearance that result from a change in camera orientation (or change of viewpoint). This approach is based on a Euclidean invariant representation of three dimensional objects, where the metric information is kept using the Gramian of 4 basis points and the affine coordinates of the remaining points, or using...
Podaj zakres dat dla filtrowania wyświetlonych wyników. Możesz podać datę początkową, końcową lub obie daty. Daty możesz wpisać ręcznie lub wybrać za pomocą kalendarza.