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research-article

Complete Solution Classification for the Perspective-Three-Point Problem

Authors:

Jianliang Tang,

Hang-Fei ChengAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 25, Issue 8

Pages 930 - 943

https://doi.org/10.1109/TPAMI.2003.1217599

Published: 01 August 2003 Publication History

Abstract

In this paper, we use two approaches to solve the Perspective-Three-Point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.

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cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 25, Issue 8

August 2003

112 pages

ISSN:0162-8828

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Copyright © Copyright © 2003 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 August 2003

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https://dl.acm.org/doi/10.1007/s10851-024-01228-4
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