Singular points in the optical center distribution of P3P solutions
type: Item
instance of: scholarly article
title: Singular points in the optical center distribution of P3P solutions
zbMATH Open document ID: 1394.68397
DOI: 10.1155/2015/147397
author: Lihua Hu
author: Bo Wang
author: Jifu Zhang
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Multisolution phenomenon is an important issue in P3P problem since, for many real applications, the question of how many solutions could possibly exist for a given P3P problem must at first be addressed before any real implementation. In this work we show that, given 3 control points, if the camera's optical center is close to one of the 3 toroids generated by rotating the circumcircle of the control point triangle around each one of its 3 sides, there is always an additional solution with its corresponding optical center lying in a small neighborhood of one of the control points, in addition to the original solution. In other words, there always exist at least two solutions for the P3P problem in such cases. Since, for all such additional solutions, their corresponding optical centers must lie in a small neighborhood of control points, the 3 control points constitute the singular points of the P3P solutions. The above result could act as some theoretical guide for P3P practitioners besides its academic value.
Mathematics Subject Classification ID: 68T45
Mathematics Subject Classification ID: 65D19
zbMATH DE Number: 6925581
Wikidata QID: Q59117381
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/147397
OpenAlex ID: W1549371424
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description: scientific article; zbMATH DE number 6925581