Friday, May 25. 2007
Dilated + rotated 2D Gaussian
I’ve finally improved my script that computes a dilated and rotated 2D Gaussian with respect to low memory consumption. It applies a dilation and rotation matrix to the 2D domain. I published it under the GNU GPLv2, so if you find any improvements, you are forced to share them. 
I still have the impression that it is rather slow, but I currently don’t know how to do it better. Of course, it has to be evaluated on
% Computes a non-separable (dilated + rotated) 2D Gaussian
% Usage: g = nsgauss(p, q, vdil, hdil, rot);
% Input: p,q .... size of g
% vdil ... vertical dilation factor (before rotation)
% hdil ... horizontal dilation factor (before rotation)
% rot .... rotation angle, e.g. pi/4
% Example:
% norm(nsgauss(p,q,1,1,0) - gaussnk(p)’*gaussnk(q)) == eps
%
% Version 0.2-20070525
% by Stephan Paukner {stephan+math at paukner dot cc}
% Licensed under the GNU General Public License v2
% $Id: nsgauss.m,v 1.2 2007/05/25 10:14:52 ps Exp ps $
D=[1/vdil 0; 0 1/hdil]; %dilation matrix
R=[cos(rot) -sin(rot); sin(rot) cos(rot)]’; %’%rotation matrix
sp=sqrt(p); sq=sqrt(q);
g=zeros(1,p*q);
for jp=-3:3
for jq=-3:3
[x y]=meshgrid( (0:p-1)/sp + jp*sp , (0:q-1)/sq + jq*sq );
v=D*R*[x(:)’; y(:)’];
g=g+exp(-pi*(v(1,:).^2 + v(2,:).^2));
end
end
g=reshape(g,q,p)’; %’
g=g/norm(g,’fro’);
Here’s a comparison of computing time and accuracy:
And some plots using different parameters:
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Storage capacity consideration
In my notebook, I have a 60GB disk, 27+14=41GB considered for the whole Linux system and 11.5GB left for various personal files. In my backup PC, I have a 112GB /home partition (LVM on RAID-5) and 12GB left, another 12GB are available on the /usr partition and 8.6GB in /opt, and as everything is on LVM, it might be resizable. So there’s currently no real need for additional disk space. The only drawback is that I can’t hold all music files on my notebook and that the available space is splitted into two partitions. But I can live with that, I just have to consider that some things will be in a mounted subdirectory.
When space will get small, I’ll buy a 160GB notebook-disk. And my backup PC will be a new one with two 500GB SATA-disks on RAID-1. I won’t take a kind of commercial network storage array, as these aren’t capable of rsync or the like.
I thought about taking RAID-5 again instead of RAID-1. Three 320GB disks are cheaper than two with 500GB, but data redundancy decreases from 2 to 1.5. Only one disk may fail in both cases, no matter if you’ve got two disks at RAID-1 or three disks at RAID-5. In addition, the probability that two disks fail is three(!) times higher when there are three disks as if there were only two. For me, RAID-5 is therefore just a strategy for expansion, not for starting freshly.
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