UbitrackMath

Chair for Computer Aided Medical Procedures & Augmented Reality
Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

Mathematical Background Information for Ubiquitous Tracking

This page collects some papers on the math background needed for ubiquitous tracking.

Representing Rigid Motion in 3D

An overview over the possibilities to represent rigid body motion in 3D (including the exponential map) is given in:

One application of the exponential map is given here:

Uncertainty Models

(from Tom Drummond)

A paper which describes most of the early work including tracking of articulated structures (ie imposing constraints) is the PAMI paper:

The ECCV paper talks more about uncertainties and presents a linear time algorithm for optimising over long kinematic chains (this could be applied to resolving ubitrack graphs):

Finally the recent ICCV paper describes the uncertainty models much more carefully and gives more detail on propagaing uncertainties along a chain (through time in this instance):

And two more:

Interpolating between Rotations

Smooth interpolation between rotations is usually done using quaternion representations:

Edit | Attach | Refresh | Diffs | More | Revision r1.7 - 23 Mar 2005 - 20:51 - NikolasDoerfler

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