## Copyright (C) 2004 Josep Mones i Teixidor
##
## 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} {@var{S} = } qtdecomp (@var{I})
## @deftypefnx {Function File} {@var{S} = } qtdecomp (@var{I},@var{threshold})
## @deftypefnx {Function File} {@var{S} = } qtdecomp (@var{I},@var{threshold},@var{mindim})
## @deftypefnx {Function File} {@var{S} = } qtdecomp (@var{I},@var{threshold},@var{[mindim maxdim]})
## @deftypefnx {Function File} {@var{S} = } qtdecomp (@var{I},@var{fun})
## @deftypefnx {Function File} {@var{S} = } qtdecomp (@var{I},@var{fun},@var{P1},@var{P2},...)
## Performs quadtree decomposition
##
## qtdecomp decomposes a square image @var{I} into four equal-sized
## blocks. Then it performs some kind of test on each block to decide if
## it should decompose them further. This process is repeated
## iteratively until there's no block left to be decomposed.
##
## Note that blocks are not decomposed if their dimensions are not even.
##
## The output is a sparse matrix whose non-zero elements determine the
## position of the block (the element is at top-left position in the
## block) and size of each block (the value of the element determines
## length of a side of the square-shaped block).
##
## S = qtdecomp(I) decomposes an intensity image @var{I} as described
## above. By default it doesn't split a block if all elements are equal.
##
## S = qtdecomp(I, threshold) decomposes an image as decribed, but only
## splits a block if the maximum value in the block minus the minimum
## value is greater than @var{threshold}, which is a value between 0 and
## 1. If @var{I} is of class uint8, @var{threshold} is multiplied by 255
## before use. Also, if@var{I} is of class uint16, @var{threshold} is 
## multiplied by 65535.
##
## S = qtdecomp(I, threshold, mindim) decomposes an image using the
## @var{threshold} as just described, but doesn't produce blocks smaller
## than mindim.
##
## S = qtdecomp(I, threshold, [mindim maxdim]) decomposes an image as
## described, but produces blocks that can't be bigger than maxdim. It
## decomposes to maxdim even if it isn't needed if only @var{threshold}
## was considered.
##
## S = qtdecomp(I, fun) decomposes an image @var{I} and uses function
## @var{fun} to decide if a block should be splitted or not. @var{fun}
## is called with a m-by-m-by-k  array of m-by-m blocks to be
## considered, and should return a vector of size k, whose elements
## represent each block in the stacked array. @var{fun} sets the
## corresponding value to 1 if the block should be split, and 0
## otherwise.
##
## S = qtdecomp(I, fun, ...) behaves as qtdecomp(I, fun) but passes
## extra parameters to @var{fun}.
##
## @end deftypefn
## @seealso qtgetblk, qtsetblk

## Author:  Josep Mones i Teixidor <jmones@puntbarra.com>

function S = qtdecomp(I, p1, varargin)
  if (nargin<1)
    usage("S=qtdecomp(I)");
  endif
  
  if (!ismatrix(I) || size(I,1)!=size(I,2))
    error("qtdecomp: I should be a square matrix.");
  endif

  ## current size (assumed to be square)
  curr_size=size(I,1);

  ## initial mindim to a sensible value
  mindim=1;
 
  ## sensible default maxdim value
  maxdim=curr_size;

  if (nargin<2)
    ## Initialize decision method variable
    ## We could have implemented threshold as a function and use an
    ## uniform interface (function handle) to decide whether to split or
    ## not blocks. We have decided not to do so because block
    ## rearrangement that is needed as a parameter to functions is
    ## expensive.
    decision_method=0;
  elseif (isreal(p1))
    ## p1 is threshold
    threshold=p1;
    decision_method=1;

    if(strcmp(typeinfo(I), 'uint8 matrix'))
      threshold*=255;
    elseif(strcmp(typeinfo(I), 'uint16 matrix'))
      threshold*=65535;
    endif

    if (nargin>3)
      usage("S=qtdecomp(I,threshold,mindim),        \
	  S=qtdecomp(I,threshold,[mindim maxdim])");
    elseif (nargin==3)
      dims=varargin{1};
      if (isvector(dims)&&length(dims)==2)
	mindim=dims(1);
	maxdim=dims(2);
      elseif (isreal(dims))
	mindim=dims;
      else
	error("qtdecomp: third parameter must be 'mindim' or '[mindim maxdim]'");
      endif
      ## we won't check if mindim or maxdim are powers of 2. It's too
      ## restrictive and don't need it at all.
    endif
    
  elseif strcmp(typeinfo(p1),"function handle") ...
  	  || strcmp(typeinfo(p1),"inline function")
    ## function handles seem to return true to isscalar
    fun=p1;
    decision_method=2;
  else
    error("qtdecomp: second parameter must be a integer (threshold) or a function handle (fun).");
  endif
  
  ## initialize results matrices
  res=[];

  ## bool to flag end
  finished=false;

  ## array of offsets to blocks to evaluate
  offsets=[1,1];

  if (maxdim<mindim)
    error("qtdecomp: mindim must be smaller than maxdim.");
  endif

  ## See if we have to split a minimum regarless other considerations.
  if (maxdim<curr_size)
    initial_splits=ceil(log2(curr_size/maxdim));
    if(initial_splits>0)
      divs=2^initial_splits;
      if (rem(curr_size,divs)!=0)
	error("qtdecomp: Can't decompose I enough times to fulfill maxdim requirement.");
      endif
      ## update curr_size
      curr_size/=divs;
      if(curr_size<mindim)
	error("qtdecomp: maxdim restriction collides with mindim restriction.");
      endif
      els=transpose([0:divs-1]*curr_size+1);
      offsets=[kron(els,ones(divs,1)), kron(ones(divs,1),els)];
    endif
  endif

  while(!finished && rows(offsets)>0)
    ## check other ending conditions:
    ## is size is odd?
    ## is splitted size < than mindim?
    if ((rem(curr_size,2)!=0)||((curr_size/2)<mindim))
      ## can't continue, lets add current evaluation blocks to results
      res=[res; offsets, ones(size(offsets,1),1)*curr_size];
      finished = true;
    else
      if (decision_method<2)
	db=logical(ones(rows(offsets),1));
	for r=1:rows(offsets)
	  o=offsets(r,:);
	  fo=offsets(r,:)+curr_size-1;

	  if(decision_method==0)
	    ## is everything equal?
	    if (all(I(o(1),o(2))==I(o(1):fo(1),o(2):fo(2))))
	      db(r)=0;
	    endif
	  else
	    ## check threshold
	    t=I(o(1):fo(1),o(2):fo(2));
	    t=t(:);
	    if ((max(t)-min(t))<=threshold)
	      db(r)=0;
	    endif
	  endif
	endfor
      elseif(decision_method==2)
	## function handle decision method
	## build blocks
	b=zeros(curr_size,curr_size,rows(offsets));
	rbc=offsets(:,1:2)+curr_size-1;
	for r=1:rows(offsets)
	  b(:,:,r)=I(offsets(r,1):rbc(r,1),offsets(r,2):rbc(r,2));
	endfor

	db=feval(fun, b, varargin{:});
      else
	error("qtdecomp: execution shouldn't reach here. Please report this as a bug.");
      endif

      ## Add blocks that won't divide to results
      nd=offsets(find(!db),:);
      res=[res; nd, ones(size(nd,1),1)*curr_size];
      
      ## Update curr_size for next iteration
      curr_size/=2;
      
      ## Prepare offsets for next iteration
      otemp=offsets(find(db),:);
      hs=ones(rows(otemp),1)*curr_size;
      zs=zeros(size(hs));
      offsets=[otemp;otemp+[hs,zs];otemp+[zs,hs];otemp+[hs,hs]];
    endif
  endwhile

  S=sparse(res(:,1),res(:,2),res(:,3),size(I,1),size(I,2));
endfunction


%!demo
%! full(qtdecomp(eye(8)))
%! %It finds 2 big blocks of 0 and it decomposes further where 0 and 1 are mixed.


%!# Test if odd-sized limits split
%!assert(full(qtdecomp(eye(5))), reshape([5,zeros(1,24)],5,5));
%!assert(full(qtdecomp(eye(6))), repmat(reshape([3,zeros(1,8)],3,3),2,2));

%!# Test 'equal' method
%!test
%! a=ones(2,2);
%! b=[2,0;0,0];
%! assert(full(qtdecomp(eye(4))), [a,b;b,a]);

%!shared A, B2, B4
%! A=[ 1, 4, 2, 5,54,55,61,62;
%!     3, 6, 3, 1,58,53,67,65;
%!     3, 6, 3, 1,58,53,67,65;
%!     3, 6, 3, 1,58,53,67,65;
%!    23,42,42,42,99,99,99,99;    
%!    27,42,42,42,99,99,99,99;    
%!    23,22,26,25,99,99,99,99;    
%!    22,22,24,22,99,99,99,99];
%! B2=[2,0;0,0];
%! B4=zeros(4); B4(1,1)=4;

%!test
%! R=[ones(4,8); [ones(2),B2;ones(2,4)], B4];
%! assert(full(qtdecomp(A)), R);
%! assert(full(qtdecomp(A,0)), R);

%!# Test 'threshold' method
%!test
%! R=[ones(4,8); [ones(2),B2;B2,ones(2)],B4];
%! assert(full(qtdecomp(A,1)), R);

%!test
%! R=[[B4,[B2,B2;B2,B2]]; [[ones(2),B2;B2,B2],B4]];
%! assert(full(qtdecomp(A,10)), R);

%!test
%! R=[[B4,[B2,B2;B2,B2]]; [[B2,B2;B2,B2],B4]];
%! assert(full(qtdecomp(A,10,2)), R);

%!assert(full(qtdecomp(A,100,[2, 4])), [B4,B4;B4,B4]);

%!# Test 'fun' method
%!# Can't define a function inside tests because Octave
%!# complains about nested functions. If you know how to
%!# do it please add function handle tests.

%!# inline version
%!# We use [size(A),1](3) as a trick since size(A,3) fails if A is 2D.

%!# no params
%!test
%! first_eq=inline("(A(1,1,:)!=(54*ones(1,1,[size(A),1](3))))(:)","A");
%! assert(full(qtdecomp(A,first_eq)),[ones(4),B4;ones(4,8)]); 

%!# 1 param
%!test
%! first_eq=inline("(A(1,1,:)!=(c*ones(1,1,[size(A),1](3))))(:)","A","c");
%! assert(full(qtdecomp(A,first_eq,54)),[ones(4),B4;ones(4,8)]); 

%!# 3 params
%!test
%! first_eq=inline("(A(1,1,:)!=((c1+c2+c3)*ones(1,1,[size(A),1](3))))(:)","A","c1","c2","c3");
%! assert(full(qtdecomp(A,first_eq,4,40,10)),[ones(4),B4;ones(4,8)]); 



%
% $Log: qtdecomp.m,v $
% Revision 1.8  2006/01/03 02:09:15  pkienzle
% Reorder tests so that shared variables are displayed unless relevant.
%
% Revision 1.7  2006/01/02 22:05:06  pkienzle
% Reduce number of shared variables in tests
%
% Revision 1.6  2004/09/09 19:36:35  jmones
% all_va_args -> varargin{:}. Now works on 2.1.58
%
% Revision 1.5  2004/09/08 14:07:22  pkienzle
% Fix test for 'inline function'
%
% Revision 1.4  2004/08/11 19:52:41  jmones
% qtsetblk added
%
% Revision 1.3  2004/08/11 00:05:21  jmones
% seealso qtgetblk added to doc
%
% Revision 1.2  2004/08/10 00:19:42  jmones
% Corrected misleading comment.
%
% Revision 1.1  2004/08/09 01:48:54  jmones
% Added qtdecomp: quadtree decomposition
%
%