zigzag scan: Image processing function
Muthiah Annamalai <[email protected]> Thu, 05 Oct 2006 11:58:32 -0500
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Hello there,
I have a function zigzag() which walks-off a (square)matrix and reads
its elements in a zigzag fashion. It is useful for image processing.
Example:
octave --eval "x=[1:4]'*[1:4];eval('x');tic;printf('%d
\n',zigzagscan(x));toc()" -q
x =
1 2 3 4
2 4 6 8
3 6 9 12
4 8 12 16
1
2
2
3
4
3
4
6
6
4
8
9
8
12
12
16
Elapsed time is 0.177223 seconds.
However I dont know where I should commit it to in Octave-forge.
Someone please suggest the right place.
Code is attached.
Cheers
Muthu
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Hello there,<BR>
I have a function zigzag() which walks-off a (square)matrix and reads its elements in a zigzag fashion. It is useful for image processing.<BR>
<BR>
Example:<BR>
octave --eval "x=[1:4]'*[1:4];eval('x');tic;printf('%d\n',zigzagscan(x));toc()" -q<BR>
x =<BR>
<BR>
1 2 3 4<BR>
2 4 6 8<BR>
3 6 9 12<BR>
4 8 12 16<BR>
<BR>
1<BR>
2<BR>
2<BR>
3<BR>
4<BR>
3<BR>
4<BR>
6<BR>
6<BR>
4<BR>
8<BR>
9<BR>
8<BR>
12<BR>
12<BR>
16<BR>
Elapsed time is 0.177223 seconds.<BR>
<BR>
<BR>
However I dont know where I should commit it to in Octave-forge.<BR>
Someone please suggest the right place. <BR>
<BR>
Code is attached.<BR>
<BR>
Cheers<BR>
Muthu<BR>
<BR>
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## Copyright (C) 2006, June, Muthiah Annamalai, <[email protected]>
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
##
## -*- texinfo -*-
## @deftypefn {Function File} {} zigzag (@var{M})
##
## Returns the zig-zag scanned coefficients of given matrix @var{M}.
## Function of ZigZag scan is to accumulate the transform (DCT like)
## coefficients in the LF->HF in that order, from a square matrix.
##
## An exmaple of the use of @code{zigzag} is
## @example
## @group
## x=[1:4]'*[1:4];
## zigzag(x)
## @end group
## @end example
## @end deftypefn
% (C) 2006 June, Muthiah Annamalai, <[email protected]>
%
% For a simple case_ we can use a ZZ scan using many loops, to
% generate the indices.
% eg: case_ 4x4 we have ZZ scan indices being (in that order)
% (each of the rows have sums of 2:8) i.e 2:2S)
% (each row of t=2:2S has sum= (t-1) elements if_ t<S+2, and sum=2S+1-t, elsewhere)
% (each row contains all the permutations summing up to t, in that order)
% (permutations are equidistant)
% (permutations are ordered as oddrows have descending in x)
% (even rows have ascending in x)
% (if_ even row & non-multiple of 3, increase y index, else_ x index \
% for_ first element of row.)
% (all odd rows have to increase x component first)
% (if_ only with first element, we can get the rest of the elements)
% (odd rows only have odd no of elements, even rows have only even no
% of elements)
%
%1 (1,1),2
%2 (1,2) (2,1),3,x:y,y:x
%3 (3,1),(2,2),(1,3),4
%4 (1,4),(2,3),(3,2),(4,1),5
%5 (4,2),(3,3),(2,4),6
%6 (3,4),(4,3),7
%7 (4,4),8
%
%
%1 (1,1),2
%2 (1,2) (2,1),3,x:y,y:x
%3 (3,1),(2,2),(1,3),4
%4 (1,4),(2,3),(3,2),(4,1),5
%5 (5,1),(4,2),(3,3),(2,4),(1,5),6
%
%6 (3,4),(4,3),7
%7 (4,4),8
%
function rval=zigzag(mtrx)
if (nargin < 1)
error('usage: zigzag_opt(square-matrix)')
else
S=issquare(mtrx);
if(S <= 0)
error('usage: zigzag_opt(square-matrix)')
end
end
x=1;
y=1;
itrx=1;
rval=zeros(1,S*S);
rval(itrx)=[mtrx(x,y)];
iseven=true;
for itr=2:2*S-1
%[x,y]
%itr
iseven=~iseven;
%predicting the first element
%is the trick!
if(iseven)
if(itr > S)
x=x+1;
y=y;
else
x=x;
y=y+1;
end
else
%odd row
if(itr <= S)
y=y;
x=x+1;
else
y=y+1;
x=x;
end
end
%[x,y]
%compute nelem for_ this row.
if(itr <S+1)
nelem=itr;
else
nelem=2*S-itr;
end
rval(itrx+1)=mtrx(x,y);
%compute target sum
tgt_sum=itr;
%generate the elements
if(iseven)
%even rows ascend in X,
%and have only even no of elements
for itr2=2:nelem
x=x+1;
y=y-1;
%[x,y]
rval(itrx+itr2)=mtrx(x,y);
end
else
%odd rows ascend in Y,
for itr2=2:nelem
y=y+1;
x=x-1;
%[x,y]
rval(itrx+itr2)=mtrx(x,y);
end
end
itrx=itrx+itr2;
end
end
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