Showing papers on "Perspective (geometry) published in 2002"

A perspective factorization method for Euclidean reconstruction with uncalibrated cameras

Abstract: Structure from motion (SFM), which is recovering camera motion and scene structure from image sequences, has various applications, such as scene modelling, robot navigation, object recognition and virtual reality. Most of previous research on SFM requires the use of intrinsically calibrated cameras. In this paper we describe a factorization-based method to recover Euclidean structure from multiple perspective views with uncalibrated cameras. The method first performs a projective reconstruction using a bilinear factorization algorithm, and then converts the projective solution to a Euclidean one by enforcing metric constraints. The process of updating a projective solution to a full metric one is referred as normalization in most factorization-based SFM methods. We present three normalization algorithms which enforce Euclidean constraints on camera calibration parameters to recover the scene structure and the camera calibration simultaneously, assuming zero skew cameras. The first two algorithms are linear, one for dealing with the case that only the focal lengths are unknown, and another for the case that the focal lengths and the constant principal point are unknown. The third algorithm is bilinear, dealing with the case that the focal lengths, the principal points and the aspect ratios are all unknown. The results of experiments are presented. Copyright © 2002 John Wiley & Sons, Ltd.

On Pencils of Tangent Planes and the Recognition of Smooth 3D Shapes from Silhouettes

Abstract: This paper presents a geometric approach to recognizing smooth objects from their outlines We define a signature function that associates feature vectors with objects and baselines connecting pairs of possible viewpoints Feature vectors, which can be projective, affine, or Euclidean, are computed using the planes that pass through a fixed baseline and are also tangent to the object's surface In the proposed framework, matching a test outline to a set of training outlines is equivalent to finding intersections in feature space between the images of the training and the test signature functions The paper presents experimental results for the case of internally calibrated perspective cameras, where the feature vectors are angles between epipolar tangent planes

Semi-metric Formal 3D Reconstruction from Perspective Sketches

Abstract: We present a new approach for accurate and fast reconstruction of 3D models from hand-drawn perspective sketches and imposed geometric constraints. A distinctive feature of the approach is the decomposition of the reconstruction process into the stages of correction of the 2D sketch and elevation of the 3D model. All 3D constraints that describe the spatial structure of the model are strictly satisfied, while preferences that describe the model projection are treated in relaxed manner. The constraints are subdivided into the projective, affine and metric ones and expressed in algebraic form by using the Grassmann-Cayley algebra. The constraints are resolved one by another following the order of their types by using the local propagation methods. The preferences allow to apply linear approximations and to systematically use formal methods.

A User-Focused Reference Model for Wireless Systems Beyond 3G

Abstract: This whitepaper describes a proposal from Working Group 1, the Human Perspective of the Wireless World, for a user-focused reference model for systems beyond 3G. The general structure of the proposed model involves two "planes": the Value Plane and the Capability Plane. The characteristics of these planes are discussed in detail and an example application of the model to a specific scenario for the wireless world is provided.

Simulation studies for the reconstruction of a straight line in 3D from two arbitrary perspective views using epipolar line method

Abstract: Reconstruction of a line in 3-D space using arbitrary perspective views involves the problem of obtaining the set of parameters representing the line. This is widely used for many applications of 3-D object recognition and machine inspection. A performance analysis of the reconstruction process in the presence of noise in the image planes is necessary in certain applications which require a large degree of accuracy. In this paper, a methodology, which is based on the concept of epipolar line, for the reconstruction of a 3-D line, from two arbitrary perspective views is given. In this problem the points in the second image plane, which correspond to points in the first image plane are found by using epipolar line method, by considering all the points in the first image plane. Then triangulation law is used to find the points in 3-D space. Using least square regression in 3-D, the parameters of a line in 3-D space are found. This least square regression problem is solved by two different methods. Simulation study results of this epipolar line based method, in presence of noise, as well as results of error analysis are given.

Simulation studies for the reconstruction of a straight line in 3-D from two arbitrary perspective views using Epipolar line method

Abstract: Reconstuction of a line in 3-D space using arbitrary perspectve views involves the problem of obtaining the set of parameters representing the line. This is widely used for many applications of 3-D object recognition and machine inspection. A performance analysis of the reconstruction process in the presence of noise in the image planes is necessary in certain applications which require a large degree of accuarcy. In this paper, a methodology, which is based on the concept of epipolar line, for the reconstruction of a 3-D line, from two arbitrary perspective views is given. In this problem the points in the second image plane, which correspond to points in the first image plane are found by using epipolar line method, by considering all the points in the first image plane. Then triangulation law is used to find the points in 3-D space. Using least square regression in 3-D, the parameters of a line in 3-D space are found. This least square regression problem is solved by two different methods. Simulation study results of this epipolar line based method, in presence of noise, as well as results of error analysis are given.

Recovering Non-rigid 3D Shape Using a Plane+Parallax Approach

Abstract: The recovering of 3D shape from video sequences has been one of the most important computer vision problems in the last ten years. For the case of rigid scenes, linear and factorization approaches have been developed. However, for non-rigid scenes only factorization methods for parallel projection, based on the Tomasi-Kanade's factorization method, have been proposed. In this paper we study the case of perspective cameras for non-rigid scenes. Our approach makes use of recent results of the plane+parallax representation for rigid scene. We show that it is possible, from a reference system defined on a particular plane of the scene, to estimate the 3D Euclidean coordinates of the moving points and the camera center.