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).

Control based on perspective lines of a non-holonomic mobile robot with camera-on-board

Abstract: This paper addresses the control of wheeled mobile robots based on visual information of perspective lines. These lines can be generated by the projection of environment lines like those formed by the intersection of walls and floor, the structural features delimiting paths, or by painted lines on the floor. The control objective is to navigate at a desired speed along the lines, keeping a specified separating distance from them. No assumption is made on the absolute location of either the robot or the lines. A smooth time-invariant controller is proposed in order to command the angular velocity of the robot, while the linear velocity is generated to achieve a cautious and smooth motion. By invoking the LaSalle's invariance principle convergence is shown to a proper invariant set which guarantees accomplishment of the control objective. Finally, experimental results illustrating the performance of the control system are presented.

Control Implications in Tracking Moving Objects Using Time-Varying Perspective-Projective Imagery

Abstract: Control implications which arise when tracking moving objects contained in time-varying perspective-projective imagery are studied. First, a transformation is derived to relate pan/tilt camera mount movement to image plane perturbations. Ramifications of this model, particularly with respect to magnification ratio, noncentered targets and camera mount angular magnitudes are illustrated. A pan/tilt control algorithm is then developed using this transformation and a large magnification ratio assumption. Experimental results with real imagery are shown to confirm the approach validity.

Field calibration method of structural parameter of line structure light vision sensing system

Abstract: The invention provides a field calibration method of the structural parameter of a line structure light vision sensing system, comprising the following steps: (a) a movable plane target is put in a measured space, a collinear and three characteristic points with known mutual distance are arranged on the plane target, and the light plane which is projected by a line structure light projector intersects with the straight line at which the three are positioned so as to form a fixed point; (b) the collinear three characteristic points are used for setting up a three-point perspective model, and according to the mutual distances of the three characteristic points, the picpointed coordinates which are imaged on the image surface of a television camera by the three characteristic points and the fixed point, and the internal parameter of the television camera, the coordinate of the fixed point in the coordinate system of the television camera is computed; (c) the plane target is moved to many different positions within measuring range so as to respectively form a plurality of additional fixed points, and the step (b) is repeatedly carried out so as to respectively compute the coordinates of the additional fixed points in the coordinate system of the television camera; and (d) the fixed points which are obtained at many times are fitted into a plane so as to obtain the plane equation of the light plane in the coordinate system of the television camera, thereby completing the field calibration.

A Tale of Three Circles

Abstract: Everyone knows that the sum of the angles of a triangle formed by three lines in the plane is 180 ◦ , but is this still true for curvilinear triangles formed by the arcs of three circles in the plane? We invite the reader to experiment enough to see that the angle sum indeed depends on the triangle, and that no general pattern is obvious. We give a complete analysis of the situation, showing along the way, we hope, what insights can be gained by approaching the problem from several points of view and at several levels of abstraction. We begin with an elementary solution using only the most basic concepts of Euclidean geometry. While it is direct and very short, this solution is not complete, since it works only in a special case. The key to another special case turns out to be a model of hyperbolic geometry, leading us to suspect that the various manifestations of the problem lie on a continuum of models of geometries with varying curvature. This larger geometric framework reveals many beautiful unifying themes and provides a single method of proof that completely solves the original problem. Finally, we describe a very simple formulation of the solution, whose proof relies on transformations of the plane, a fitting ending we think, since a transformation may be regarded as a change in one’s point of view. The background developed earlier informs our understanding of this new perspective, and allows us to give a purely geometric description of the transformations needed. For the reader who is unfamiliar with the classical noneuclidean geometries, in which the notions of line and distance are given new interpretations, we provide an overview that is almost entirely self-contained. Such a reader will be introduced to such things as angle excess, stereographic projection, and even a sphere of imaginary radius. For the reader who is familiar with the three classical geometries, we offer some new ways of looking at them, which we are confident will reveal some surprises.

Projective structure from facial motion

Abstract: Nonrigid Structure-From-Motion is a well-known approach to estimate time-varying 3D structures from 2D input image sequences. For challenging problems such as the reconstruction of human faces, state-of-the-art approaches estimate statistical shape spaces from training data. It is common practice to use orthographic or weak-perspective camera models to map 3D to 2D points. We propose to use a projective camera model combined with a multilinear tensor-based face model, enabling approximation of a dense 3D face surface by sparse 2D landmarks. Using a projective camera is beneficial, as it is able to handle perspective projections and particular camera motions which are critical for affine models. We show how the nonlinearity of the projective model can be linearized so that its parameters can be estimated by an alternating-least-squares approach. This enables simple and fast estimation of the model parameters. The effectiveness of the proposed algorithm is demonstrated using challenging real image data.