Orthogonal matrix in Singular Value Decomposition

Article View: alt.uu.math.misc

Article #123

#123

From: Daniel Bengtsson
Date: Thu, 08 May 2003 08:44

34 lines
2219 bytes

Hi,

I am working on a surface registration problem and is trying to solve it
using singular value decomposition. The problem is set up as follows:

PR = Q

where P is [mx3], R is [3x3] and Q is [mx3]

Using the SVD on Q I get: 

P = UDV

where U is [mxm], D is [mx3] and V is [3x3]  m>>3

What I have understood I can now find the matrix R that gives the minimal
solution to PR = Q with:

R = (V*)(D+)(U*)Q 

Where (V*) means the adjoint matrix of V and (D+) means the pseudoinverse of
D.

My question 1 is: 
I want to have an orthogonal matrix R as this R should be a rigid rotation
matrix. My calculations does not seem to give an orthogonal R though, so
what should I do to add this restriction on R ?

My question 2 is:
As the U matrix gets dimensions [mxm] this can be very large for big
datasets and thus demands huge amounts of memory on my machine. Is there
anything to avoid this without reducing the dataset ? Is U sparse ?

/Daniel Bengtsson

Technical Details

Message-ID: <b9d5hf$5m9$1@maud.ifi.uio.no>

Path:

arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.icl.net!newsfeed.fjserv.net!feed.news.nacamar.de!uninett.no!uio.no!nntp.uio.no!ifi.uio.no!not-for-mail

Show Full Headers

Complete Article Headers

X-Google-Language: ENGLISH,ASCII-7-bit
X-Google-Thread: 10c88d,c6a6cbcabf57d394,start
X-Google-Attributes: gid10c88d,public
X-Google-Thread: 1077c2,c6a6cbcabf57d394,start
X-Google-Attributes: gid1077c2,public
X-Google-Thread: f4956,c6a6cbcabf57d394,start
X-Google-Attributes: gidf4956,public
X-Google-ArrivalTime: 2003-05-08 01:46:40 PST
Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.icl.net!newsfeed.fjserv.net!feed.news.nacamar.de!uninett.no!uio.no!nntp.uio.no!ifi.uio.no!not-for-mail
From: Daniel Bengtsson <danielbe@ifil.uio.no>
Newsgroups: alt.uu.math.misc,fj.sci.math,nordunet.sci.math
Subject: Orthogonal matrix in Singular Value Decomposition
Followup-To: alt.uu.math.misc
Date: Thu, 08 May 2003 10:44:25 +0200
Organization: University of Oslo
Lines: 34
Message-ID: <b9d5hf$5m9$1@maud.ifi.uio.no>
NNTP-Posting-Host: sos-dhcp088.studby.uio.no
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7Bit
X-Trace: maud.ifi.uio.no 1052383599 5833 129.240.104.118 (8 May 2003 08:46:39 GMT)
X-Complaints-To: abuse@ifi.uio.no
NNTP-Posting-Date: 8 May 2003 08:46:39 GMT
User-Agent: KNode/0.7.2