Finite Geometries: a tool for better understanding of Euclidean Geometry by Antonio Maturo

“…The work begins with a review of Hilbert's axiomatic, starting from more general point of view adopted by Albrecht Beutelspacher and Ute Rosenbaum in their book on the fundamentals of general projective geometry (1998), defined by a system of incidence axioms.   …”
Get full text

Thrust Network Analysis : exploring three-dimensional equilibrium by Block, Philippe (Philippe Camille Vincent)

Get full text

S5-2: Shifting the Perspective on Biological Movement Perception by Zsolt Palatinus

“…Most efforts for understanding biological movement perception seem to agree in assuming a key role of some version of 2D projective geometry being the basis of either computation or invariant detection somewhere between the stimulus and perception. …”
Get full text

A multi-stage neural network approach for coronary 3D reconstruction from uncalibrated X-ray angiography images by Kritika Iyer, Brahmajee K. Nallamothu, C. Alberto Figueroa, Raj R. Nadakuditi

“…The network also led to 52% and 38% reduction in vessel centerline reconstruction errors compared to a single-stage network and projective geometry-based methods, respectively. Our method demonstrated robustness to overcome challenges such as vessel foreshortening or overlap in the input images. …”
Get full text

EPIPOLAR GEOMETRY BETWEEN PHOTOGRAMMETRY AND COMPUTER VISION – A COMPUTATIONAL GUIDE by B. Alsadik, N. A. Abdulateef

“…</p><p>A successfully reconstructed stereo image geometry is based on solving the epipolar constraint using the fundamental matrix which is based on the projective geometry in computer vision. However, in photogrammetry, the problem is well known as relative orientation and there is a different solution that is based on the euclidean geometry using collinearity or coplanarity equations.…”
Get full text

A MATHEMATICAL SENSOR MODEL FOR INDOOR USE OF A MULTI-BEAM ROTATING 3D LIDAR by L. S. Tessema, L. S. Tessema, R. Jaeger, U. Stilla

“…Our contribution presents a new perspective in the mathematical description of a rotating multi-beam LiDAR sensor, in a sense that we make use of projective geometry along with the “homogeneous general equation of the second degree” to parametrize scan lines. …”
Get full text

Mario Pieri’s View of the Symbiotic Relationship between the Foundations and the Teaching of Elementary Geometry in the Context of the Early Twentieth Century Proposals for Pedagog... by Elena Anne Corie Marchisotto, Ana Millán Gasca

“…Pieri addressed the topic of intuition in many of his axiomatizations, including those in projective geometry which was his main area of concentration in foundations. …”
Get full text

Mistletoe Berry Outline Mapping with a Path Curve Function and Recording the Circadian Rhythm of their Phenotypic Shape Change by Renatus Derbidge, Renatus Derbidge, Peter Heusser, Stephan Baumgartner, Stephan Baumgartner

“…We introduce a new approach to chronobiological research on a macro-phenotypic scale to trace changes over long periods of time (with a resolution from hours to months) by using a dynamic form-determining parameter called Lambda (λ). λ is known in projective geometry as a measure for pertinent features of the outline shapes of egg-like forms, so called path curves. …”
Get full text

Infinite secret sharing – Examples by Dibert Alexander, Csirmaz László

“…These schemes touch quite diverse areas of mathematics such as projective geometry, stochastic processes and Hilbert spaces. …”
Get full text

Geometric deep learning enables 3D kinematic profiling across species and environments by Severson, Kyle S, Wang, Fan

“…Therefore, we designed DANNCE to robustly track anatomical landmarks in 3D across species and behaviors. DANNCE uses projective geometry to construct inputs to a convolutional neural network that leverages learned 3D geometric reasoning. …”
Get full text

On Maximal Homogeneous 3-Geometries and Their Visualization by Emil Molnár, István Prok, Jeno Szirmai

“…Vice-versa, we can start with the projective geometry, namely with the classification of Coll ( P S 3 ) through linear transforms of dual pairs of real 4-vector spaces ( V 4 , V 4 , R , ∼ ) = P S 3 (up to positive real multiplicative equivalence ∼) via Jordan normal forms. …”
Get full text

Freeform surfaces adaptation using developable strips and planar quadrilateral facets by Francisco Gonzalez-Quintial, Javier Barrallo, Ana Artiz-Elkarte

“…Through the geometric concept of apparent contours and by the systematization of a process inspired by traditional projective geometry an algorithm is built, using the newest and outstanding CAD processes. …”
Get full text

Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (C<span style="font-variant: small-caps">e</span>DG) by Manuel Prado-Velasco, Laura García-Ruesgas

“…Computer-extended Descriptive Geometry (C<span style="font-variant: small-caps;">e</span>DG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. …”
Get full text

Characteristic Number: Theory and Its Application to Shape Analysis by Xin Fan, Zhongxuan Luo, Jielin Zhang, Xinchen Zhou, Qi Jia, Daiyun Luo

“…Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability to characterize the curve or surface underlying the given points. …”
Get full text

Spatial skills of preschool children from Serbia and a possible model for the typology of children’s spatial skills by Olivera J. Đokić, Marija M. Vorkapić

“…They specifically explore the significance of spatial understanding through Piaget’s primacy of topological concepts and the increasing emphasis on projective geometry. The research focuses on preschoolers in Serbia, aged 5.5–6.5, as they transition to primary school.MethodsThe study involves 103 children exposed to two distinct preschool curricula: The General Foundations of the Preschool Curriculum (GFPC) and The Foundations of the Preschool Curriculum – Years of Ascent (YA). …”
Get full text

On the Nature of Bondi–Metzner–Sachs Transformations by Zahra Mirzaiyan, Giampiero Esposito

“…Eventually, all BMS transformations are re-expressed in the homogeneous coordinates suggested by projective geometry. It is then found that BMS transformations are the restriction to a pair of unit circles of a more general set of transformations. …”
Get full text

Substantiation of the Fault-Block Structure for Effective Additional Exploration and Development of the West-Kommunarsky Field by M.A. Lobusev, A.V. Bochkarev, G.Yu. Rachkova

“…The justification of disjunctive dislocations, which have been planned but not tracked due to their uncertainty in seismic data and determination of their main characteristics, was performed by stratigraphic correlation of well sections using the rules of projective geometry and confirmed by other traditional methodical methods. …”
Get full text

TGA-based solutions map method for four-position synthesis of planar 4R linkage by Y. Zhao, L. Xue, G. Wang, G. Wang, F. Zou, Y. Song, H. Zhang, H. Zhang

“…First, the points on the center curve are obtained by using projective geometry, and those of the circle curve are obtained by vector elimination. …”
Get full text

Automatic social distance estimation for photographic studies: Performance evaluation, test benchmark, and algorithm by Mert Seker, Anssi Männistö, Alexandros Iosifidis, Jenni Raitoharju

“…Our method is a hybrid method that combines deep learning-based object detection and human pose estimation with projective geometry. The method can be applied on uncalibrated single images with known focal length and sensor size. …”
Get full text

ON-LINE COMPATIBLE ORIENTATION OF A MICRO-UAV BASED ON IMAGE TRIPLETS by M. Reich, J. Unger, F. Rottensteiner, C. Heipke

“…<br><br> Our approach combines linear projective geometry for obtaining initial values using the trifocal tensor with non-linear perspective geometry for the estimation of the unknowns. …”
Get full text