Open AccessAn Analytic Solution to Projector Pose Estimation Problem
Author(s) -
Lee JooHaeng
Publication year - 2012
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.12.0212.0089
Subject(s) - quadrilateral , rectangle , pose , projector , diagonal , mathematics , 3d pose estimation , computer vision , projection (relational algebra) , pinhole (optics) , orientation (vector space) , artificial intelligence , position (finance) , simple (philosophy) , image (mathematics) , computer science , algorithm , geometry , optics , engineering , finite element method , physics , philosophy , structural engineering , finance , epistemology , economics
We present an analytic solution to the projector pose estimation problem for the pinhole projection model in which the source image is a centered rectangle with an unknown aspect ratio. From a single quadrilateral given as a target image, our solution gives the position and orientation of a projector as well as the aspect ratio of a source image. The proposed method decomposes the problem into two pose estimation problems of coupled line projectors aligned at each diagonal of the given quadrilateral and then computes the common solution that satisfies the relevant geometric constraints. The solution is formulated as simple analytic equations. We also provide a determinant of projectability of an arbitrary quadrilateral.