scholarly journals A Hilbert Scheme in Computer Vision

2013 ◽  
Vol 65 (5) ◽  
pp. 961-988 ◽  
Author(s):  
Chris Aholt ◽  
Bernd Sturmfels ◽  
Rekha Thomas
Keyword(s):  
Computer Vision ◽  
Fixed Point ◽  
Hilbert Scheme ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Grobner Basis ◽  
Multiview Geometry ◽  
Universal Gröbner Basis ◽  
Two Dimensional Images

AbstractMultiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gröbner basis for the multiview ideal of ngeneric cameras. As the cameras move, the multiview varieties vary in a family of dimension 11n − 15. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

scholarly journals Visual Depth Perception of three dimensional images and two dimensional images

1990 ◽  
Vol 26 (Supplement) ◽  
pp. 248-249
Author(s):  
Am CHO ◽  
Kageyu NORO ◽  
Shinya KOSHIE ◽  
Atsuko HONDO ◽  
Sakae YAMAMOTO
Keyword(s):  
Depth Perception ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Visual Depth ◽  
Three Dimensional Images ◽  
Two Dimensional Images

SBART 2.4: An IEC Tool for Creating Two-Dimensional Images, Movies and Collages

Leonardo ◽  
2002 ◽  
Vol 35 (2) ◽  
pp. 189-191 ◽  
Author(s):  
Tatsuo Unemi
Keyword(s):  
User Interface ◽  
Three Dimensional ◽  
Interactive System ◽  
Small Computer ◽  
Two Dimensional ◽  
The Creation ◽  
Color Value ◽  
Two Dimensional Images

In this article, the author gives an overview of SBART 2.4, an interactive system used to create abstract two-dimensional images, collages and movies. The system, one of the successors of Karl Sims's system, runs on a small computer that uses a function to calculate the color value of each pixel as a genotype. All of the ranges and domains are three-dimensional vectors. The system utilizes a multi-field user interface to enhance the diversity of production and has optional facilities that allow the creation of collages of external images or short movies.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

Advances in Two-Dimensional and Three-Dimensional Computer Vision

2007 ◽  
pp. 323-372 ◽  
Author(s):  
Michael A. Sutton ◽  
Stephen R. McNeill ◽  
Jeffrey D. Helm ◽  
Yuh J. Chao
Keyword(s):  
Computer Vision ◽  
Three Dimensional ◽  
Two Dimensional

scholarly journals The Algorithm for Determining the Coordinates of a Point in Three-Dimensional Space by Using the Auxiliary Point

2013 ◽  
Vol 48 (4) ◽  
pp. 141-145 ◽  
Author(s):  
Bartlomiej Oszczak ◽  
Eliza Sitnik
Keyword(s):  
Fixed Point ◽  
Precise Measurement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Satellite Navigation ◽  
Reference Points ◽  
Two Dimensional ◽  
Approximate Location ◽  
The Many ◽  
Three Dimensional Space

ABSTRACT During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.

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