CGAL users discussion list

[ganders <>]

Hi Pierre,

thanks for your reply, but I read this manual and it confuses me a bit and
thus I had - and still have - this question. Looking at figure 1 on page 3

I. Markovsky and S. Van Huffel, Overview of total least squares methods,
Signal Processing, Volume 87, pages 2283-2302, 2007.
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/markovsky/reports/05-34.pdf

the difference between LS and TLS is clearly described and obvious. The
right TLS picture has a orthogonal projection, the left LS one does not.
This CGAL manual is mentioning a LS - but not explicitely a TLS - with
orthogonal projection. Interpreting your answer, I guess it is a TLS, right?
Thanks in advance.

Cheers,
Gerd


Pierre Alliez wrote:
> 
> hi Gerd,
> 
> the documentation of the PCA component (user manual 
> <http://www.cgal.org/Manual/last/doc_html/cgal_manual/Principal_component_analysis/Chapter_main.html>)
>  
> says:
> Given a set of objects, /linear least squares fitting/ amounts to 
> finding the linear sub-space which minimizes the sum of squared 
> distances from all points composing the objects of the set, to their 
> projection onto this linear sub-space. Such linear sub-space is obtained 
> by so-called principal component analysis (PCA). PCA is defined as a 
> transformation that transforms the objects to a new coordinate system 
> such that the greatest variance by orthogonal projection of the objects 
> comes to lie on the first coordinate (called the first principal 
> component), the second greatest variance on the second coordinate, and 
> so on.
> 
> pierre
> 
> Pierre Alliez
> INRIA Sophia Antipolis - Mediterranee 
> Project-team GEOMETRICA 
> http://www-sop.inria.fr/members/Pierre.Alliez/
> Tel: +33 4 92 38 76 77
> Fax: +33 4 97 15 53 95
> 
> 
> 
> ganders a écrit :
>> Dear CGAL-team,
>>
>> I am searching for a method that calculates a fitting line in terms of a
>> total-least-squares (TLS) approach for 3D points. As input I would like
>> to
>> provide a matrix with the x/y/z coordinates and as output I would like to
>> receive two points describing the straight line. It looks that
>> linear_least_squares_fitting_3 is exactly that what I am looking for. But
>> I
>> am not sure if it really calculates the TLS or the different
>> linear-least-squares (LLS) solution. May I ask you to tell me what
>> approach
>> is implemented (TLS or LLS)? Thanks a lot in advance.
>>
>> Cheers,
>> Gerd 
>>   
> 
> -- 
> You are currently subscribed to cgal-discuss.
> To unsubscribe or access the archives, go to
> https://lists-sop.inria.fr/wws/info/cgal-discuss
> 
> 
> 

-- 
View this message in context: 
http://n4.nabble.com/linear-least-squares-23-tp1013139p1014093.html
Sent from the cgal-discuss mailing list archive at Nabble.com.