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Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.
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Ubaidillah, Muhammad Izzat. "Proyeksi Geometri Fuzzy pada Ruang." CAUCHY 2, no. 3 (November 15, 2012): 139. http://dx.doi.org/10.18860/ca.v2i3.3123.
<div class="standard"><a id="magicparlabel-481">Fuzzy geometry is an outgrowth of crisp geometry, which in crisp geometry elements are exist and not exist, but also while on fuzzy geometry elements are developed by thickness which is owned by each of these elements. Crisp projective geometries is the formation of a shadow of geometries element projected on the projectors element, with perpendicular properties which are represented by their respective elemental, the discussion focused on the results of the projection coordinates. While the fuzzy projective geometries have richer discussion, which includes about coordinates of projection results, the mutual relation of each element and the thickness of each element. This research was conducted to describe and analyzing procedure fuzzy projective geometries on the plane and explain the differences between crisp projective geometries and fuzzy projective geometries on plane.</a></div>
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Calderbank, David, Michael Eastwood, Vladimir Matveev, and Katharina Neusser. "C-projective geometry." Memoirs of the American Mathematical Society 267, no. 1299 (September 2020): 0. http://dx.doi.org/10.1090/memo/1299.
Erdnüß, B. "MEASURING IN IMAGES WITH PROJECTIVE GEOMETRY." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-1 (September 26, 2018): 141–48. http://dx.doi.org/10.5194/isprs-archives-xlii-1-141-2018.
<p><strong>Abstract.</strong> There is a fundamental relationship between projective geometry and the perspective imaging geometry of a pinhole camera. Projective scales have been used to measure within images from the beginnings of photogrammetry, mostly the cross-ratio on a straight line. However, there are also projective frames in the plane with interesting connections to affine and projective geometry in three dimensional space that can be utilized for photogrammetry. This article introduces an invariant on the projective plane, describes its relation to affine geometry, and how to use it to reduce the complexity of projective transformations. It describes how the invariant can be use to measure on projectively distorted planes in images and shows applications to this in 3D reconstruction. The article follows two central ideas. One is to measure coordinates in an image relatively to each other to gain as much invariance of the viewport as possible. The other is to use the remaining variance to determine the 3D structure of the scene and to locate the camera centers. For this, the images are projected onto a common plane in the scene. 3D structure not on the plane occludes different parts of the plane in the images. From this, the position of the cameras and the 3D structure are obtained.</p>
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Song, Xiao Zhuang, Ming Liang Lu, and Tao Qin. "Projective Geometry on the Structure of Geometric Composition Analysis Application." Applied Mechanics and Materials 166-169 (May 2012): 127–30. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.127.
The analysis rule of geometry composition analysis in building structure must rely on geometry theory, while the traditional Euclidean geometry theory can not solve some building structures problems of the geometry components. This problem can be solved in the use of projective geometry theory. In this paper we introduce the proof of projective geometry in the geometry composition analysis and we discuss the application of this theory.
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Gupta, K. C., and Suryansu Ray. "Fuzzy plane projective geometry." Fuzzy Sets and Systems 54, no. 2 (March 1993): 191–206. http://dx.doi.org/10.1016/0165-0114(93)90276-n.
Wong, Tzu Yen. "Image transition techniques using projective geometry." University of Western Australia. School of Computer Science and Software Engineering, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0149.
[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.
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Romano, Raquel Andrea. "Projective minimal analysis of camera geometry." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29231.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002. Includes bibliographical references (p. 115-120). This thesis addresses the general problem of how to find globally consistent and accurate estimates of multiple-view camera geometry from uncalibrated imagery of an extended scene. After decades of study, the classic problem of recovering camera motion from image correspondences remains an active area of research. This is due to the practical difficulties of estimating many interacting camera parameters under a variety of unknown imaging conditions. Projective geometry offers a useful framework for analyzing uncalibrated imagery. However, the associated multilinear models-the fundamental matrix and trifocal tensorare redundant in that they allow a camera configuration to vary along many more degrees of freedom than are geometrically admissible. This thesis presents a novel, minimal projective model of uncalibrated view triplets in terms of the dependent epipolar geometries among view pairs. By explicitly modeling the trifocal constraints among projective bifocal parameters-the epipoles and epipolar collineations-this model guarantees a solution that lies in the valid space of projective camera configurations. We present a nonlinear incremental algorithm for fitting the trifocally constrained epipolar geometries to observed image point matches. The minimal trifocal model is a practical alternative to the trifocal tensor for commonly found image sequences in which the availability of matched point pairs varies widely among different view pairs. Experimental results on synthetic and real image sequences with typical asymmetries in view overlap demonstrate the improved accuracy of the new trifocally constrained model. (cont.) We provide an analysis of the objective function surface in the projective parameter space and examine cases in which the projective parameterization is sensitive to the Euclidean camera configuration. Finally, we present a new, numerically stable method for minimally parameterizing the epipolar geometry that gives improved estimates of minimal projective representations. by Raquel A. Romano. Ph.D.
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Contatto, Felipe. "Vortices, Painlevé integrability and projective geometry." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275099.
GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the Abelian–Higgs model is proposed in such a way that spontaneous symmetry breaking and the Bogomolny argument still hold. The Painlevé test, when applied to its soliton equations, reveals a complete list of its integrable cases. The corresponding solutions are given in terms of third Painlevé transcendents and can be interpreted as original vortices on surfaces with conical singularity. The last two chapters present the following results in projective differential geometry and Hamiltonians of hydrodynamic-type systems. It is shown that the projective structures defined by the Painlevé equations are not metrisable unless either the corresponding equations admit first integrals quadratic in first derivatives or they define projectively flat structures. The corresponding first integrals can be derived from Killing vectors associated to the metrics that solve the metrisability problem. Secondly, it is given a complete set of necessary and sufficient conditions for an arbitrary affine connection in 2D to admit, locally, 0, 1, 2 or 3 Killing forms. These conditions are tensorial and simpler than the ones in previous literature. By defining suitable affine connections, it is shown that the problem of existence of Killing forms is equivalent to the conditions of the existence of Hamiltonian structures for hydrodynamic-type systems of two components.
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Marino, Nicholas John. "Vector Bundles and Projective Varieties." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018.
Beardsley, Paul Anthony. "Applications of projective geometry to robot vision." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316854.
Six experiments tested the assumption that, in visual perception, observers have reliable and direct access to the equivalence of shapes in projective geometry (I call this "the invariance hypothesis in the theory of shape constancy"). This assumption has been made in the study of vision since Helmholtz's time. Two experiments tested recognition of the projective equivalence of planar shapes. In another four experiments, subjects estimated the apparent shape of a solid object from different perspectives. Departure from projective equivalence was assessed in each study by measuring the cross ratio for the plane. This measure of projective invariance is new to perceptual research. Projective equivalence was not found to be perceived uniformly in any of the studies. A significant effect of change in perspective was found in each study. These results were construed as supporting the classical theory of depth cues against the invariance hypothesis.
Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.
Faure, Claude-Alain, and Alfred Frölicher. Modern Projective Geometry. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9590-2.
Ostermann, Alexander, and Gerhard Wanner. "Projective Geometry." In Geometry by Its History, 319–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29163-0_11.
Arnold, Vladimir I. "Projective Geometry." In UNITEXT, 33–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36243-9_4.
Cederberg, Judith N. "Projective Geometry." In A Course in Modern Geometries, 213–313. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3490-4_4.
Kumaresan, S., and G. Santhanam. "Projective Geometry." In Texts and Readings in Mathematics, 53–98. Gurgaon: Hindustan Book Agency, 2005. http://dx.doi.org/10.1007/978-93-86279-24-8_3.
Conference papers on the topic "Geometry, Projective":
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Stolfi, J. "Oriented projective geometry." In the third annual symposium. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/41958.41966.
Bokor, J., and Z. Szabo. "Projective geometry and feedback stabilization." In 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES). IEEE, 2017. http://dx.doi.org/10.1109/ines.2017.8118537.
D'Andrea, Francesco, and Giovanni Landi. "Geometry of Quantum Projective Spaces." In Proceedings of the Noncommutative Geometry and Physics 2008, on K-Theory and D-Branes & Proceedings of the RIMS Thematic Year 2010 on Perspectives in Deformation Quantization and Noncommutative Geometry. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814425018_0014.
Li, Xiaolu, Tao He, Lijun Xu, Lulu Chen, and Zhanshe Guo. "Projective rectification of infrared image based on projective geometry." In 2012 IEEE International Conference on Imaging Systems and Techniques (IST). IEEE, 2012. http://dx.doi.org/10.1109/ist.2012.6295549.
Ge, Q. J. "Projective Convexity in Computational Kinematic Geometry." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASME, 2002. http://dx.doi.org/10.1115/detc2002/mech-34281.
Buchanan, Thomas. "Photogrammetry and projective geometry: an historical survey." In Optical Engineering and Photonics in Aerospace Sensing, edited by Eamon B. Barrett and David M. McKeown, Jr. SPIE, 1993. http://dx.doi.org/10.1117/12.155817.
Carli, Francesca Paola, and Rodolphe Sepulchre. "On the projective geometry of kalman filter." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402570.
Gubitosi, Giulia, Angel Ballesteros, and Francisco J. Herranz. "Generalized noncommutative Snyder spaces and projective geometry." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Trieste, Italy: Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0190.
Ozuag, Ersin, and Sarp Erturk. "Image sequences synchronization by using projective geometry properties." In 2015 23th Signal Processing and Communications Applications Conference (SIU). IEEE, 2015. http://dx.doi.org/10.1109/siu.2015.7130348.
Harihara, S. G., M. Girish Chandra, Tarakapraveen Uppalapati, and B. S. Adiga. "Decoding architectures for Projective Geometry based LDPC codes." In 2008 1st IFIP Wireless Days (WD). IEEE, 2008. http://dx.doi.org/10.1109/wd.2008.4812880.
Bolbat, O. B., and T. V. Andryushina. Lectures on descriptive geometry. Part 1. Methods of projection. Point. Straight. Plane: Multimedia Tutorial. OFERNIO, May 2021. http://dx.doi.org/10.12731/ofernio.2021.24809.
Rao, C. R. Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach. Fort Belvoir, VA: Defense Technical Information Center, March 1988. http://dx.doi.org/10.21236/ada197608.
Shashua, Amnon. On Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views. Fort Belvoir, VA: Defense Technical Information Center, July 1993. http://dx.doi.org/10.21236/ada270520.
