krautz - Trac king Ove rvie w and Mathe m atics Tracking...

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Tracking Overview and Mathematics
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Christoph Krautz 2 Motivation Technologies – Advantages and Disadvantages Common Problems and Errors Acoustic Tracking Mechanical Tracking Inertial Tracking Magnetic Tracking Optical Tracking Inside-out versus Outside-in Mathematics Transformations in the 2D-space Transformations in the 3D-space Discussion Motivation Technologies Tracking Mathematics Content
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Christoph Krautz 3 What is tracking? The repeated localization of the position and orientation (pose)  of one or several real physical objects Why is tracking needed in AR? Integration of virtual objects into real world (images) Motivation Technologies Tracking Mathematics Motivation
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Christoph Krautz 4 Motivation Technologies – Advantages and Disadvantages Common Problems and Errors Acoustic Tracking Mechanical Tracking Inertial Tracking Magnetic Tracking Optical Tracking Inside-out versus Outside-in Mathematics Transformations in the 2D-space Transformations in the 3D-space Discussion Motivation Technologies Tracking Mathematics Content
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Christoph Krautz 5 Motivation Technologies Tracking Mathematics Common Problems and Errors High update rate required (usually in real-time  systems) Dynamic tracker error, e.g. sensor‘s motion Distortion due to environmental influences, e.g. noise Long-term variations Cause readings to change from one day to the next day
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Christoph Krautz 6 Motivation Technologies Tracking Mathematics Acoustic Tracking The Geometry The intersection of two spheres is a circle. The intersection of three spheres is two points. One of the two points can easily be eliminated. Ultrasonic 40 [kHz] typical (Slide taken from SIGGRAPH 2001 Course 11 –  Slides by Allen, Bishop, Welch) From [1]
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Christoph Krautz 7 Motivation Technologies Tracking Mathematics Acoustic Tracking - Methods Time of Flight Measures the time required for a sonic pulse to travel from a  transmitter to a receiver. d  [m] =  v  [m/s] *  t  [s],  v  = speed of sound Absolute range measurement Phase Coherence Measures phase difference between transmitted and  received sound waves Relative to previous measurement still absolute!! (Slide taken from SIGGRAPH 2001 Course 11 –  Slides by Allen, Bishop, Welch)
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Christoph Krautz 8 Motivation Technologies Tracking Mathematics Acoustic Tracking – Discussion Advantages Small and lightweight (miniaturization of transmitters and  receivers) Only sensitive to influences by noise in the ultrasonic range Disadvantages Speed of Sound (~331 [m/s] in air at 0°C) Varies with temperature, pressure and humidity  Slow   Low update rate
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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krautz - Trac king Ove rvie w and Mathe m atics Tracking...

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