Efficient iterative solution to M-view projective reconstruction problem

2003 ◽  
Author(s):  
Qian Chen ◽  
G. Medioni
Keyword(s):  
Iterative Solution ◽  
Projective Reconstruction ◽  
Reconstruction Problem

scholarly journals Critical hypersurfaces and instability for reconstruction of scenes in high dimensional projective spaces

2020 ◽  
Vol 29 (1) ◽  
pp. 3-20
Author(s):  
Marina Bertolini ◽  
Luca Magri
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
High Dimensional ◽  
Projective Reconstruction ◽  
Algebraic Varieties ◽  
Reconstruction Problem ◽  
Complex Projective Spaces ◽  
Simulated Experiment ◽  
Complex Projective ◽  
Practical Implications

In the context of multiple view geometry, images of static scenes are modeled as linear projections from a projective space P^3 to a projective plane P^2 and, similarly, videos or images of suitable dynamic or segmented scenes can be modeled as linear projections from P^k to P^h, with k>h>=2. In those settings, the projective reconstruction of a scene consists in recovering the position of the projected objects and the projections themselves from their images, after identifying many enough correspondences between the images. A critical locus for the reconstruction problem is a configuration of points and of centers of projections, in the ambient space, where the reconstruction of a scene fails. Critical loci turn out to be suitable algebraic varieties. In this paper we investigate those critical loci which are hypersurfaces in high dimension complex projective spaces, and we determine their equations. Moreover, to give evidence of some practical implications of the existence of these critical loci, we perform a simulated experiment to test the instability phenomena for the reconstruction of a scene, near a critical hypersurface.

scholarly journals A Linear Method to Derive 3D Projective Invariants from 4 Uncalibrated Images

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
YuanBin Wang ◽  
XingWei Wang ◽  
Bin Zhang ◽  
Ying Wang
Keyword(s):  
Linear Method ◽  
Projective Reconstruction ◽  
Reconstruction Problem ◽  
Linear Transformations ◽  
Explicit Formulas ◽  
Projective Invariants ◽  
Projective Invariant ◽  
Uncalibrated Images ◽  
Bilinear Equations ◽  
2D Images

A well-known method proposed by Quan to compute projective invariants of 3D points uses six points in three 2D images. The method is nonlinear and complicated. It usually produces three possible solutions. It is noted previously that the problem can be solved directly and linearly using six points in five images. This paper presents a method to compute projective invariants of 3D points from four uncalibrated images directly. For a set of six 3D points in general position, we choose four of them as the reference basis and represent the other two points under this basis. It is known that the cross ratios of the coefficients of these representations are projective invariant. After a series of linear transformations, a system of four bilinear equations in the three unknown projective invariants is derived. Systems of nonlinear multivariable equations are usually hard to solve. We show that this form of equations can be solved linearly and uniquely. This finding is remarkable. It means that the natural configuration of the projective reconstruction problem might be six points and four images. The solutions are given in explicit formulas.

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

Parallel iterative solution-based tabu search for the obnoxious p-median problem

2021 ◽  
Vol 127 ◽  
pp. 105155
Author(s):  
Jian Chang ◽  
Lifang Wang ◽  
Jin-Kao Hao ◽  
Yang Wang
Keyword(s):  
Tabu Search ◽  
Iterative Solution ◽  
Median Problem ◽  
Parallel Iterative

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

Sign in / Sign up

Export Citation Format

Share Document