diff Problems/private/reggrid.m @ 10:207a6ae9a76f version1.0

(none)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/reggrid.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,136 @@
+function [varargout] = reggrid(sz,num,mode)
+%REGGRID Regular sampling grid.
+%  [I1,I2,...,Ip] = REGGRID([N1 N2 ... Np], NUM) returns the indices
+%  of a regular uniform sampling grid over a p-dimensional matrix with
+%  dimensions N1xN2x...xNp. NUM is the minimal number of required samples,
+%  and it is ensured that the actual number of samples, given by
+%  length(I1)xlength(I2)x...xlength(Ip), is at least as large as NUM.
+%
+%  [I1,I2,...,Ip] = REGGRID([N1 N2 ... Np], NUM,'MODE') specifies the
+%  method for distributing the samples along each dimension. Valid modes
+%  include 'eqdist' (the default mode) and 'eqnum'. 'eqdist' indicates an
+%  equal distance between the samples in each dimension, while 'eqnum'
+%  indicates an equal number of samples in each dimension.
+%
+%  Notes about MODE:
+%
+%    1. The 'eqnum' mode will generally fail when the p-th root of NUM
+%    (i.e. NUM^(1/p)) is larger than min([N1 N2 ... Np]). Thus 'eqdist' is
+%    the more useful choice for sampling an arbitrary number of samples
+%    from the matrix (up to the total number of matrix entries).
+%  
+%    2. In both modes, the equality (of the distance between samples, or
+%    the number of samples in each dimension) is only approximate. This is
+%    because REGGRID attempts to maintain the appropriate equality while at
+%    the same time find a sampling pattern where the total number of
+%    samples is as close as possible to NUM. In general, the larger {Ni}
+%    and NUM are, the tighter the equality.
+%
+%  Example: Sample a set of blocks uniformly from a 2D image.
+%
+%    n = 512; blocknum = 20000; blocksize = [8 8];
+%    im = rand(n,n);
+%    [i1,i2] = reggrid(size(im)-blocksize+1, blocknum);
+%    blocks = sampgrid(im, blocksize, i1, i2);
+%
+%  See also SAMPGRID.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  November 2007
+
+dim = length(sz);
+
+if (nargin<3)
+  mode = 'eqdist';
+end
+
+if (any(sz<1))
+  error(['Invalid matrix size : [' num2str(sz) ']']);
+end
+
+if (num > prod(sz))
+  warning(['Invalid number of samples, returning maximum number of samples.']);
+elseif (num <= 0)
+  if (num < 0)
+    warning('Invalid number of samples, assuming 0 samples.');
+  end
+  for i = 1:length(sz)
+    varargout{i} = [];
+  end
+  return;
+end
+
+
+if (strcmp(mode,'eqdist'))
+  
+  % approximate distance between samples: total volume divided by number of
+  % samples gives the average volume per sample. then, taking the p-th root
+  % gives the average distance between samples
+  d = (prod(sz)/num)^(1/dim);
+  
+  % compute the initial guess for number of samples in each dimension.
+  % then, while total number of samples is too large, decrese the number of
+  % samples by one in the dimension where the samples are the most crowded.
+  % finally, do the opposite process until just passing num, so the final
+  % number of samples is the closest to num from above.
+  
+  n = min(max(round(sz/d),1),sz);   % set n so that it saturates at 1 and sz
+  
+  active_dims = find(n>1);    % dimensions where the sample num can be reduced
+  while(prod(n)>num && ~isempty(active_dims))
+    [y,id] = min((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))-1;
+    if (n(active_dims(id)) < 2)
+      active_dims = find(n>1);
+    end
+  end
+
+  active_dims = find(n<sz);    % dimensions where the sample num can be increased
+  while(prod(n)<num && ~isempty(active_dims))
+    [y,id] = max((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))+1;
+    if (n(active_dims(id)) >= sz(active_dims(id)))
+      active_dims = find(n<sz);
+    end
+  end
+
+  for i = 1:dim
+    varargout{i} = round((1:n(i))/n(i)*sz(i));
+    varargout{i} = varargout{i} - floor((varargout{i}(1)-1)/2);
+  end
+  
+elseif (strcmp(mode,'eqnum'))
+  
+  % same idea as above
+  n = min(max( ones(size(sz)) * round(num^(1/dim)) ,1),sz);
+
+  active_dims = find(n>1);
+  while(prod(n)>num && ~isempty(active_dims))
+    [y,id] = min((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))-1;
+    if (n(active_dims(id)) < 2)
+      active_dims = find(n>1);
+    end
+  end
+  
+  active_dims = find(n<sz);
+  while(prod(n)<num && ~isempty(active_dims))
+    [y,id] = max((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))+1;
+    if (n(active_dims(id)) >= sz(active_dims(id)))
+      active_dims = find(n<sz);
+    end
+  end
+  
+  for i = 1:dim
+    varargout{i} = round((1:n(i))/n(i)*sz(i));
+    varargout{i} = varargout{i} - floor((varargout{i}(1)-1)/2);
+  end
+else
+  error('Invalid sampling mode');
+end
+