The Experts below are selected from a list of 21294 Experts worldwide ranked by ideXlab platform
Olivier Faugeras - One of the best experts on this subject based on the ideXlab platform.
-
oriented Projective Geometry for computer vision
European Conference on Computer Vision, 1996Co-Authors: Stephane Laveau, Olivier FaugerasAbstract:We present an extension of the usual Projective geometric framework for computer vision which can nicely take into account an information that was previously not used, i.e. the fact that the pixels in an image correspond to points which lie in front of the camera. This framework, called the oriented Projective Geometry, retains all the advantages of the unoriented Projective Geometry, namely its simplicity for expressing the viewing Geometry of a system of cameras, while extending its adequation to model realistic situations.
-
ECCV (1) - Oriented Projective Geometry for Computer Vision
Lecture Notes in Computer Science, 1996Co-Authors: Stephane Laveau, Olivier FaugerasAbstract:We present an extension of the usual Projective geometric framework for computer vision which can nicely take into account an information that was previously not used, i.e. the fact that the pixels in an image correspond to points which lie in front of the camera. This framework, called the oriented Projective Geometry, retains all the advantages of the unoriented Projective Geometry, namely its simplicity for expressing the viewing Geometry of a system of cameras, while extending its adequation to model realistic situations.
Stephane Laveau - One of the best experts on this subject based on the ideXlab platform.
-
oriented Projective Geometry for computer vision
European Conference on Computer Vision, 1996Co-Authors: Stephane Laveau, Olivier FaugerasAbstract:We present an extension of the usual Projective geometric framework for computer vision which can nicely take into account an information that was previously not used, i.e. the fact that the pixels in an image correspond to points which lie in front of the camera. This framework, called the oriented Projective Geometry, retains all the advantages of the unoriented Projective Geometry, namely its simplicity for expressing the viewing Geometry of a system of cameras, while extending its adequation to model realistic situations.
-
ECCV (1) - Oriented Projective Geometry for Computer Vision
Lecture Notes in Computer Science, 1996Co-Authors: Stephane Laveau, Olivier FaugerasAbstract:We present an extension of the usual Projective geometric framework for computer vision which can nicely take into account an information that was previously not used, i.e. the fact that the pixels in an image correspond to points which lie in front of the camera. This framework, called the oriented Projective Geometry, retains all the advantages of the unoriented Projective Geometry, namely its simplicity for expressing the viewing Geometry of a system of cameras, while extending its adequation to model realistic situations.
Jorge Stolfi - One of the best experts on this subject based on the ideXlab platform.
-
oriented Projective Geometry a framework for geometric computations
2014Co-Authors: Jorge StolfiAbstract:Part 1 Projective Geometry: the classic Projective plane advantages of Projective Geometry drawbacks of classical Projective Geometry oriented Projective Geometry related work. Part 2 Oriented Projective spaces: models of two-sided space central projection. Part 3 Flats: definition points lines planes three-spaces ranks incidence and dependence. Part 4 Simplices and orientation: simplices simplex equivalence point location relative to a simplex the vector space model. Part 5 The join operation: the join of two points the join of a point and a line the join of two arbitrary flats properties of join null objects complementary flats. Part 6 The meeting operation: the meeting point of two lines the general meet operation meet in three dimensions properties of meet. Part 7 Relative orientation: the two sides of a line relative position of arbitrary flats the separation theorem the coefficients of a hyperplane. Part 8 Projective maps: formal definition examples properties of Projective maps the matrix of a map. Part 9 General: two-sided spaces - formal definition subspaces. Part 10 Duality: duomorphisms the polar complement polar complements as duomorphisms relative polar complements general duomorphisms the power of duality. Part 11 Generalized Projective maps: Projective functions computer representation. Part 12 Projective frames: nature of Projective frames classification of frames standard frames coordinates relative to a frame. Part 13 Cross ratio: cross ratio in unoriented Geometry cross ratio in the oriented framework. Part 14 Convexity: convexity in classical Projective space convexity in oriented Projective spaces properties of convex sets the half-space property the convex hull convexity and duality. Part 15 Affine geomerty: the Cartesian connection two-sided affine spaces. Part 16 Vector albegra: two-sided vector spaces translations vector algebra the two-sided real line linear maps. Part 17 Euclidean Geometry on the two-sided plane: perpendicularity two-sided Euclidean spaces Euclidean maps length and distance angular measure and congruence non-Euclidean geometries. Part 18 Representing flats by simplices: the simplex representation the dual simplex representation the reduced simplex representation. Part 19 Plucker coordinates: the canonical embedding Plucker coefficients storage efficiency the Grassmann manifolds. Part 20 Formulas for Plucker coordinates: algebraic formulas formulas for computers Projective maps in Plucker coordinates directions and parallelism.
-
Oriented Projective Geometry
1991Co-Authors: Jorge StolfiAbstract:Oriented Projective Geometry is a model for geometric computation that combines the elegance of classical Projective Geometry with the ability to talk about oriented lines and planes, signed angles, line segments, convex figures, and many other concepts that cannot be defined within the classical version. Classical Projective Geometry is the implicit framework of many geometric computations, since it underlies the well-known homogeneous coordinate representation. It is argued here that oriented Projective Geometry — and its analytic model, based on signed homogeneous coordinates — provide a better foundation for computational Geometry than their classical counterparts. The differences between the classical and oriented versions are largely confined to the mathematical formalism and its interpretation. Computationally, the changes are minimal and do not increase the cost and complexity of geometric algorithms. Geometric algorithms that use homogeneous coordinates can be easily converted to the oriented framework at little cost. The necessary changes are largely a matter of paying attention to the order of operands and to the signs of coordinates, which are frequently ignored or left unspecified in the classical framework.
-
Chapter 1 – Projective Geometry
Oriented Projective Geometry, 1991Co-Authors: Jorge StolfiAbstract:Publisher Summary This chapter provides an overview of the standard (unsigned) homogeneous coordinates for the plane, and the classical (unoriented) Projective Geometry which they implicitly define. It also discusses the advantages and disadvantages of homogeneous coordinates as a computational model, compared to ordinary Cartesian coordinates. The Projective plane can be defined either by a means of a concrete model, borrowing concepts from linear algebra or Euclidean Geometry, or as an abstract structure satisfying certain axioms. The axiomatic approaches have the advantage of being concise and elegant, but unfortunately they cannot be generalized easily to spaces of arbitrary dimension. To avoid the axiomatic approach and to base all definitions, four concrete models of Projective space have been chosen: the straight, spherical, analytic, and vector space models. The use of homogeneous coordinates generally leads to simpler formulas that involve only the basic operations of linear algebra: determinants, dot and cross products, matrix multiplications, and the like. Another advantage of Projective Geometry is its ability to unify seemingly disparate concepts.
Peter Nelson - One of the best experts on this subject based on the ideXlab platform.
-
The structure of matroids with a spanning clique or Projective Geometry
Journal of Combinatorial Theory Series B, 2017Co-Authors: Jim Geelen, Peter NelsonAbstract:Abstract Let s , n ≥ 2 be integers. We give a qualitative structural description of every matroid M that is spanned by a frame matroid of a complete graph and has no U s , 2 s -minor and no rank-n Projective Geometry minor, showing that every such matroid is ‘close’ to a frame matroid. We also give a similar description of every matroid M with a spanning Projective Geometry over a field GF ( q ) as a restriction and with no U s , 2 s -minor and no PG ( n , q ′ ) -minor for any q ′ > q , showing that such an M is ‘close’ to a GF ( q ) -representable matroid.
-
The structure of matroids with a spanning clique or Projective Geometry
arXiv: Combinatorics, 2016Co-Authors: Jim Geelen, Peter NelsonAbstract:Let $s,n \ge 2$ be integers. We give a qualitative structural description of every matroid $M$ that is spanned by a frame matroid of a complete graph and has no $U_{s,2s}$-minor and no rank-$n$ Projective Geometry minor, showing that every such matroid is `close' to a frame matroid. We also give a similar description of every matroid $M$ with a spanning Projective Geometry over a field GF$(q)$ as a restriction and with no $U_{s,2s}$-minor and no PG$(n,q')$-minor for any $q' > q$, showing that such an $M$ is `close' to a GF$(q)$-representable matroid.
Li Shi-ju - One of the best experts on this subject based on the ideXlab platform.
-
Constructions of Projective Geometry LDPC codes and performance analysis in MIMO-OFDM system
Journal of Circuits and Systems, 2006Co-Authors: Li Shi-juAbstract:The constructions of Projective Geometry LDPC codes are introduced.The codes are taken as the channel codes into IEEE 802.16d MIMO-OFDM system simulation and compared with RS-CC codes.Finally a conclusion is made that Projective Geometry LDPC codes may be adopted as one of the key technologies in the next wireless communication systems.
