Optimum Fiducials Under Weak Perspective Projection

International Journal of Computer VisionPublished 1 December 1999

Alfred M. Bruckstein⋆, Robert J. Holt, Thomas S. Huang, Arun N. Netravali

DOI10.1023/a:1008156210387

Source URL

Citations32

SJR quartileQ1

SJR score3.14

SNIP5.15

TL;DR

It is shown that optimum solutions are obtained when the points form concentric complete regular polyhedra and a worst-case error analysis is provided and used to analyze the effects of weak perspective approximation to true perspective viewing.

Abstract

We investigate how a given fixed number of points should be located in space so that the pose of a camera viewing them from unknown locations can be estimated with the greatest accuracy. We show that optimum solutions are obtained when the points form concentric complete regular polyhedra. For the case of optimal configurations we provide a worst-case error analysis and use it to analyze the effects of weak perspective approximation to true perspective viewing. Comprehensive computer simulations validate the theoretical results.

Keywords

Computer ScienceEngineering

International Journal of Computer VisionShape and motion from image streams under orthography: a factorization method

2,884 Citations1992Carlo Tomasi, Takeo Kanade

A factorization method is developed that can overcome the difficulty by recovering shape and motion under orthography without computing depth as an intermediate step, and gives accurate results.

International Journal of Computer VisionModel-based object pose in 25 lines of code

996 Citations1995Daniel DeMenthon, Larry S. Davis

Compared to classic approaches making use of Newton's method, POSIT does not require starting from an initial guess, and computes the pose using an order of magnitude fewer floating point operations; it may therefore be a useful alternative for real-time operation.

IEEE Transactions on Pattern Analysis and Machine IntelligenceRecognition by linear combinations of models

817 Citations1991Shimon Ullman, Ronen Basri

An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed and it is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views.

International Journal of Computer VisionRecognizing solid objects by alignment with an image

531 Citations1990Daniel P. Huttenlocher, Shimon Ullman

A new method for computing a transformation from a three-dimensional model coordinate frame to the two-dimensional image coordinate frame, using three pairs of model and image points, is developed, showing that this transformation always exists for three noncollinear points, and is unique up to a reflective ambiguity.

IEEE Transactions on Pattern Analysis and Machine IntelligenceMotion and structure from orthographic projections

180 Citations1989Thomas S. Huang, C.H. Lee

International Journal of Computer VisionObject Pose: The Link between Weak Perspective, Paraperspective, and Full Perspective

144 Citations1997Radu Horaud, Fadi Dornaika +1 more

An algebraic derivation of DeMenthon and Davis' method is given and it is shown that it belongs to a larger class of methods where the perspective camera model is approximated either at zero order (weak perspective) or first order (paraperspective).

View PDF

IEEE Transactions on Pattern Analysis and Machine Intelligence3-D pose from 3 points using weak-perspective

51 Citations1994T.D. Alter

This correspondence discusses computing the pose of a model from three matching point pairs under weak-perspective projection with a new approach to the problem that is motivated geometrically.

IEEE Transactions on Pattern Analysis and Machine IntelligenceUniqueness of 3D pose under weak perspective: a geometrical proof

20 Citations1995Thomas S. Huang, Alfred M. Bruckstein⋆ +2 more

It is presented a purely geometrical proof that under the weak perspective model, the 3D pose of a 3-point configuration is determined uniquely up to a reflection by its 2D projection.