Efficient algorithms for determining 3D biplane imaging geometry
type: Item
instance of: scholarly article
title: Efficient algorithms for determining 3D biplane imaging geometry
zbMATH Open document ID: 1088.65018
author: Jinhui Xu
author: Guang Xu
author: Zhenming Chen
author: Kenneth R. Hoffmann
author: V. V. Singh
published in: Journal of Combinatorial Optimization
publication date: 2006-02-08T00:00:00Z
review text: A key problem in biplane projection imaging is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, the authors present new algorithmic solutions for this problem: given two sets of 2D points \(A=\{a_1,\dots,a_n \}\) and \(B=\{b_1,\dots,b_n \}\) on two image screens (or planes) resp. with each corresponding pair of points \(a_i\) and \(b_i\) being the approximations of the projections of an unknown 3-D point \(p_i\), also given the 3D coordinate system of \(A\), find the most likely position of the origin of \(o_B\) and the orientation of the 3D coordinate system of \(B\) in the coordinate system of \(A\). The authors' approach first reduces the imaging geometry determination problem to an optimal cell search problem in an arrangement of surfaces in \(\mathbb R^6\), then each of surfaces is simplified in aim to obtain explicit expression by an equation (in general non-algebraic). Comparing with existing optimization-based approaches, the presented techniques yield better accuracy and have bounded execution time, thus is more suitable for online applications.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 5005137
zbMATH Keywords: bi-plane imaging geometry
zbMATH Keywords: computational geometry
zbMATH Keywords: arrangement
zbMATH Keywords: plane sweep
reviewed by: Vladimir Yu. Rovenskij
MaRDI profile type: Publication
full work available at URL: s10878-005-2266-x
OpenAlex ID: W2063980224
Wikidata QID: Q43084531
cites work: Q4952690
cites work: WALKING IN AN ARRANGEMENT TOPOLOGICALLY
cites work: Q4474113
cites work: Applying Parallel Computation Algorithms in the Design of Serial Algorithms
DBLP publication ID: journals/jco/XuXCSH05
DOI: 10.1007/S10878-005-2266-X
description: scientific article; zbMATH DE number 5005137