mathematical principle
 From: "Birgit.Hauser" Received: Apr 30, 2002 To artoolkit@h .................. Subject: mathematical principle ```Hello everybody, I've some information about the mathematical principle of ARToolkit, but not everything I understood. I am wondering about following things: 1. calculating of the transformationmatrix Tcm. It is said that the ideal screen coordinates are estimated. How are they estimated? Which values are "ideal"? If it is estimated, an error will be calculated - the error should be 0 if Tcm is found. What does this error mean? 2. distortion parameters: the relationship between ideal and observed screen coordinates is described as follows: p = (1 - fd) d = (x1 - x10)˛ + (y1- y10)˛ x10 = p(x1 - x10) + x10, y10 = p(y1 - y10) + y10 F ... distortion factor What do parametes d , p, x10, y10, x1, y1 mean? 3. normalized correlation (marker): What do the equation parameters mean? What does the equation calculate? Thanks a lot! Birgit ```
 From: Hirokazu Kato Received: May 1, 2002 To artoolkit@h .................. Subject: Re: mathematical principle ```Hi, >1. calculating of the transformationmatrix Tcm. It is said that the ideal >screen coordinates are estimated. How are they estimated? Which values are >"ideal"? >If it is estimated, an error will be calculated - the error should be 0 if Tcm >is found. What does this error mean? There are 4 vertices on a square. Pose and position can be calculated from 3 vertices information. When we have 4 vertices information to calculate pose and position, sometimes 4th vertex dose not fit to the pose and position which are estimated from 3 vertices. ARToolKit calculates pose and position from 4 vertices information by something like a LSM method. Then there is an error on this calculation. Actually it means sum of differences between vertices position which are detected by image processing and vertices position which can be calculated from estimated pose and position information. >2. distortion parameters: the relationship between ideal and observed >screen coordinates is described as follows: >p = (1 - fd) >d = (x1 - x10)?h + (y1- y10)?h >x10 = p(x1 - x10) + x10, >y10 = p(y1 - y10) + y10 > >F ... distortion factor > >What do parametes d , p, x10, y10, x1, y1 mean? I think you can find information from past emails in this mailinglist. >3. normalized correlation (marker): >What do the equation parameters mean? What does the equation calculate? You can use http://www.google.com/ and keyword: normalized correlation, pattern recognition Then you can find some good articles. -- ------------------------------------------------------------------ Hirokazu Kato Faculty of Information Sciences Hiroshima City University Phone: 082-830-1705 Email: kato@s ........................ Fax: 082-830-1435 URL: http://www.sys.im.hiroshima-cu.ac.jp/people/kato/ ```