Showing papers on "Perspective (geometry) published in 2017"

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.

Perspective correction for curved display screens

Abstract: One embodiment of the present invention sets forth a technique for performing perspective correction on one or more test images. The technique includes analyzing a first test image to detect a set of outer points and calculating a geometric plane equation based on the set of outer points. The technique further includes projecting a first set of points associated with a first curved screen model based on the geometric plane equation to generate a second set of points. The technique further includes comparing the second set of points to a set of inner points included in the first test image to determine at least one error value, and determining a screen curvature value based on the at least one error value.

W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion

Abstract: Camera calibration is a key problem in 3D computer vision since the late 80’s. Most of the calibration methods deal with the (perspective) pinhole camera model. This is not a simple goal: the problem is nonlinear due to the perspectivity. The strategy of these methods is to estimate the intrinsic camera parameters first; then the extrinsic ones are computed by the so-called PnP method. Finally, the accurate camera parameters are obtained by slow numerical optimization. In this paper, we show that the weak-perspective camera model can be optimally calibrated without numerical optimization if the L2 norm is used. The solution is given by a closed-form formula, thus the estimation is very fast. We call this method as the Weak-Perspective n-Point (W-PnP) algorithm. Its advantage is that it simultaneously estimates the two intrinsic weak-perspective camera parameters and the extrinsic ones. We show that the proposed calibration method can be utilized as the solution for a subproblem of 3D reconstruction with missing data. An alternating least squares method is also defined that optimizes the camera motion using the proposed optimal calibration method.

Images of the Scenic Space between Reality and Illusion. Projective Transformations of the Scene in the Renaissance Theatre

Abstract: This study focuses on an analysis of perceiving the infinite “solid images” derived from the projective transformations of space in a relief perspective, with particular reference to Renaissance theatre scenery. Today it is possible to simulate the projective transformations of the scenic space in a parametric environment, dynamically. This parameterization allows to analyze the effects of visual perception of the scene, through the dynamic control of its projective transformations. The main objective of this study is the exploration of the places of the projective transformation straddling reality and illusion, where the metamorphosis of the space triggers changeable processes of perception. changeable processes of perception.

Complex perspective for the projective heat map acting on pentagons

Abstract: We place Schwartz's work on the real dynamics of the projective heat map $H$ into the complex perspective by computing its first dynamical degree and gleaning some corollaries about the dynamics of $H$.

Anti-perspective plane transformation-based ultrasonic plane wave imaging method

Abstract: The invention discloses an anti-perspective plane transformation-based ultrasonic plane wave imaging method. The method comprises the following steps of (1) collecting data; (2) preprocessing the data: converting imaging points on an original imaging plane into imaging points on a new plane by utilizing plane conversion, calculating delay time according to the imaging points on the new plane to obtain corrected delay time, then receiving and focusing the imaging points on the original imaging plane by utilizing a synthetic aperture focusing technology according to the corrected delay time, and obtaining a value of each imaging point on the original imaging plane; and (3) post-processing the data: performing envelope detection, logarithmic compression and grayscale mapping in sequence, and finally obtaining an ultrasonic plane wave imaging image. According to the method, a key delay time calculation mode is improved and matched with the synthetic aperture focusing technology, so that compared with the prior art, the problem of low plane wave imaging quality can be effectively solved and the ultrasonic plane wave imaging resolution is effectively increased.

Application of dandelin’s theorem to drawing circles in parallel perspective

Abstract: The paper analyses a problem of great theoretical importance in practice of perspective: thenature of the perspective of a circle from the horizontal plane according to the relative position betweenthe spectator plane (parallel to the picture plane) and the given circle. Depending on the position of theneutral line to the circle, the nature of the perspective of a point describing the circle can be determined,because the corresponding visual radius generates a conical surface, and the perspective of the mobilepoint becomes the conical section made in the conical surface by the picture plane. The paper intends tohighlight the validity of Dandelin's theorem when putting a circle into perspective. A discussion ofexamples characteristic for this problem is offered. Several conclusions distinguish the main points andresults of the paper.

Path-Tracking of service robot with iterative learning control in perspective dynamic system

Abstract: Due to the iteration-varying initial position, it is complicated in path-tracking for the mobile service robot. Perspective dynamic system (PDS) provides a theory to formulate the system, which transmits from the apparent motion to the image plane and provides a good control theoretic framework to estimate motion problem. The proposed iterative learning control (ILC) algorithms not only consider errors on the object plane but also includes errors on the imagine plane. Besides, it is allowed that the initial error at each iteration is iteration-varying in the ILC process. Experimental results show that the designed framework performs well and the proposed method improve the trajectory precision of the mobile service robot.

Ballistic Research Laboratory (BRL) paper

Abstract: The mathematical ABSTRACT The mathematical solution for the true positions of features in space from the position of their images on pairs of radiographs has been discussed in Ballistic Research Labora­ tory reports by Grabarek and Herr (BRL TN 1634, September 1966, AD 807619), and by Henry C. Dubin (BRL MR 2470, April 1975, AD B003797L, now available for unlimited distribu­ tion). A truly general solution should not require, or be limited to, orthogonality of the image pairs. Dubin provides such a solution. Because of errors in setup and measure­ ment, the two lines presumed to connect the respective source and image points through the common object point do not necessarily intersect. Using vector notation and partial deriv­ atives, he obtains the line of minimum length between these two vectors. The midpoint of this line is the best estimate for the object position, and the length is a measure of the error of the estimate. The redundant image coordinate in Dubin1s method contributes to increasing the accuracy of the estimate of the position of features. The solution of Gra­ barek and Herr uses analytic geometry and the assumption that the two lines between the respective sources and images intersect, and requires an orthogonal radiographic setup. This approach forgoes generality and some available accuracy. Driven by the need to provide as simple an approach as possible, this paper presents two similar derivations. The author uses analytic geometry to re-derive the equations of Grabarek and Herr from a simpler perspective. The form of the solution provides a concep­ tual bridge to a more direct derivation by the author, using trigonometry. Both deriva­ tions are for orthogonal radiographic setups. The trigonometric approach does not require complicated computation of magnification factors, is more easily understood in terms of the geometry of the setup, and is easily implemented in computer or calculator programs to reduce orthogonal radiographs. Flash radiography is a specialized technique widely used in ballistic experimentation to produce stop-motion images of extremely fast events. A small x-ray source of brief duration produces a stereographic projection of intervening objects to form a shadowgraph on a recording medium. The source luminosity and frequency spectrum are tailored to produce a shadowgraph of usable image quality. When geometric information is desired, the source and image positions are carefully controlled. Timing, too, is carefully control­ led, if kinematic information is sought. The true position of an object must be calcula­ ted from the measurements of its image on film, and from the known positions of sources and film. The goal of this paper is to make the mathematical basis of the data reduction understandable to as many people involved in the process as possible. This paper presents two new means of deriving the reduction equations in common use. One approach is based on analytic geometry, but takes a more straightforward approach than in past works. The second approach is to attack the problem from a simpler perspective, using trigonometry. The resulting trigonometric formulae are mathematically equivalent to those currently used. However, the form in which they are presented is quite simple, making implementa­ tion easy. I hope that by making several different approaches available, this paper will be helpful to those having to learn the subject. 2. BACKGROUND To those with a good background in mathematics, there already exists a very simple and elegant approach to the reduction of flash x-rays, but one which is apparently not in wide use. The procedure has the added advantage of being extremely general. It is given in a Ballistic Research Laboratory (BRL) paper by Henry C. Dubin . In Dubin's method, the pair of tube heads which are flashed simultaneously may be located anywhere, as long as the coordinates of their source points are known. For any feature recorded in any pair of non-parallel shadowgraphs, there are two sets of two orthogonal measurements of position that can be made, but only three independent spatial coordinates to be determined. Dubin's procedure utilizes this redundancy to improve on the accuracy of the estimate of the features1 positions. The equations for two lines are found, one from each source to its respective image point. Due to uncertainties in setup and measurement, these lines do not

Perfect Polygons and Geometric Triple Systems

Abstract: A perfect n-gon is an abstraction of a regular n-gon when regarded in the real projective plane. The vertices of a regular n-gon P lie on n parallel classes of lines. The lines in any parallel class meet at a point at infinity. We call these points the perspective points of P. The vertices of P lie on a circle and the perspective points of P lie on the line at infinity in the projective plane, so we can say that the combined set of vertices and perspective points lie on a (reducible) cubic curve consisting of a line and a circle. In our Main Theorem we show that the combined set of vertices and perspective points of any perfect polygon lie on a cubic curve which may be irreducible. In case the cubic is irreducible, a well-known algebra which we call a geometric triple system can be defined on its points. We show that perfect polygons can be obtained as translates of these algebras.

Navigation service apparatus and control method thereof

Abstract: The present invention provides a navigation service apparatus, and a method of operating the same. The present invention relates to a navigation service, dividing map data into a map plane and a periodic plane to control a perspective of a period, and controlling a distance between the map plane and the periodic plane based on an output size of the period in order to control the perspective on the map plane; and additionally controlling the perspective of the period without using an additional calculating formula to control the size of the period to reinforce visibility of the period. The present invention comprises: a checking unit checking a position of an object on the map plane; a determination unit; and a control unit.