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distancexform.m
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distancexform.m
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%DISTANCEXFORM Distance transform
%
% D = DISTANCEXFORM(IM, OPTIONS) is the distance transform of the binary
% image IM. The elements of D have a value equal to the shortest distance
% from that element to a non-zero pixel in the input image IM.
%
% D = DISTANCEXFORM(OCCGRID, GOAL, OPTIONS) is the distance transform of
% the occupancy grid OCCGRID with respect to the specified goal point GOAL
% = [X,Y]. The cells of the grid have values of 0 for free space and 1 for
% obstacle. The resulting matrix D has cells whose value is the shortest
% distance to the goal from that cell, or NaN if the cell corresponds to an
% obstacle (set to 1 in OCCGRID).
%
% Options:
% 'euclidean' Use Euclidean (L2) distance metric (default)
% 'cityblock' Use cityblock or Manhattan (L1) distance metric
%
% 'animate' Show the iterations of the computation
% 'delay',D Delay of D seconds between animation frames (default 0.2s)
% 'movie',M Save animation to a movie file or folder
%
% 'noipt' Don't use Image Processing Toolbox, even if available
% 'novlfeat' Don't use VLFeat, even if available
% 'nofast' Don't use IPT, VLFeat or imorph, even if available.
%
% 'delay'
%
% Notes::
% - For the first case Image Processing Toolbox (IPT) or VLFeat will be used if
% available, searched for in that order. They use a 2-pass rather than
% iterative algorithm and are much faster.
% - Options can be used to disable use of IPT or VLFeat.
% - If IPT or VLFeat are not available, or disabled, then imorph is used.
% - If IPT, VLFeat or imorph are not available a slower M-function is used.
% - If the 'animate' option is given then the MATLAB implementation is used.
% - Using imorph requires iteration and is slow.
% - For the second case the Machine Vision Toolbox function imorph is required.
% - imorph is a mex file and must be compiled.
% - The goal is given as [X,Y] not MATLAB [row,col] format.
%
% See also IMORPH, DXform, Animate.
% Copyright (C) 1993-2017, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
%
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% RTB 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 Lesser General Public License for more details.
%
% You should have received a copy of the GNU Leser General Public License
% along with RTB. If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com
function dx = distancexform(occgrid, varargin)
opt.delay = 0.2;
opt.ipt = true;
opt.vlfeat = true;
opt.fast = true;
opt.metric = {'euclidean', 'cityblock'};
opt.animate = false;
opt.movie = [];
[opt,args] = tb_optparse(opt, varargin);
if opt.movie
opt.animate = true;
end
if opt.animate
opt.fast = false;
opt.ipt = false;
opt.vlfeat = false;
clf
end
count = [];
switch opt.metric
case 'cityblock'
ipt_metric = opt.metric; % if we use bwdistgeodesic
m = [ inf 1 inf
1 0 1
inf 1 inf ];
case 'euclidean'
ipt_metric = 'quasi-euclidean'; % if we use bwdistgeodesic
r2 = sqrt(2);
m = [ r2 1 r2
1 0 1
r2 1 r2 ];
end
if ~isempty(args) && isvec(args{1}, 2)
%% path planning interpretation
% distancexform(world, goal, metric, show)
goal = args{1};
occgrid = double(occgrid);
% check the goal point is sane
assert(occgrid(goal(2), goal(1)) == 0, 'RTB:distancexform:badarg', 'goal inside obstacle')
if exist('imorph', 'file') && opt.fast
if opt.verbose
fprintf('using MVTB:imorph\n');
end
% setup to use imorph
% - set obstacles to NaN
% - set free space to Inf
% - set goal to 0
occgrid(occgrid>0) = NaN;
occgrid(occgrid==0) = Inf;
occgrid(goal(2), goal(1)) = 0;
count = 0;
ninf = Inf; % number of infinities in the map
while 1
occgrid = imorph(occgrid, m, 'plusmin');
count = count+1;
if opt.animate
cmap = [1 0 0; gray(count)];
colormap(cmap)
image(occgrid+1, 'CDataMapping', 'direct');
set(gca, 'Ydir', 'normal');
xlabel('x');
ylabel('y');
pause(opt.delay);
end
ninfnow = sum( isinf(occgrid(:)) ); % current number of Infs
if ninfnow == ninf
% stop if the number of Infs left in the map had stopped reducing
% it may never get to zero if there are unreachable cells in the map
break;
end
ninf = ninfnow;
end
dx = occgrid;
elseif exist('bwdistgeodesic', 'file') && opt.ipt
if opt.verbose
fprintf('using IPT:bwdistgeodesic\n');
end
% solve using IPT
dx = double( bwdistgeodesic(occgrid==0, goal(1), goal(2), ipt_metric) );
else
if opt.verbose
fprintf('using MATLAB code, faster if you install MVTB\n');
end
% setup to use M-function
occgrid(occgrid>0) = NaN;
nans = isnan(occgrid);
occgrid(occgrid==0) = Inf;
occgrid(goal(2), goal(1)) = 0;
count = 0;
ninf = Inf; % number of infinities in the map
anim = Animate(opt.movie);
while 1
occgrid = dxstep(occgrid, m);
occgrid(nans) = NaN;
count = count+1;
if opt.animate
cmap = [1 0 0; gray(count)];
colormap(cmap)
image(occgrid+1, 'CDataMapping', 'direct');
set(gca, 'Ydir', 'normal');
xlabel('x');
ylabel('y');
if opt.animate
anim.add();
else
pause(opt.delay);
end
end
ninfnow = sum( isinf(occgrid(:)) ); % current number of Infs
if ninfnow == ninf
% stop if the number of Infs left in the map had stopped reducing
% it may never get to zero if there are unreachable cells in the map
break;
end
ninf = ninfnow;
end
anim.close();
dx = occgrid;
end
if opt.animate && ~isempty(count)
fprintf('%d iterations, %d unreachable cells\n', count, ninf);
end
else
%% image processing interpretation
% distancexform(world, [metric])
if exist('imorph', 'file') && opt.fast
if opt.verbose
fprintf('using MVTB:imorph\n');
end
% setup to use imorph
% - set free space to Inf
% - set goal to 0
occgrid = double(occgrid);
occgrid(occgrid==0) = Inf;
occgrid(isfinite(occgrid)) = 0;
count = 0;
anim = Animate(opt.movie);
while 1
occgrid = imorph(occgrid, m, 'plusmin');
count = count+1;
if opt.show
cmap = [1 0 0; gray(count)];
colormap(cmap)
image(occgrid+1, 'CDataMapping', 'direct');
set(gca, 'Ydir', 'normal');
xlabel('x');
ylabel('y');
if opt.animate
anim.add();
else
pause(opt.delay);
end
end
ninfnow = sum( isinf(occgrid(:)) ); % current number of Infs
if ninfnow == 0
% stop if no Infs left in the image
break;
end
end
anim.close();
dx = occgrid;
elseif exist('bwdist') && opt.ipt
if opt.verbose
fprintf('using IPT:bwdist\n');
end
% use IPT
dx = bwdist(occgrid, ipt_metric);
elseif exist('vl_imdisttf') && opt.vlfeat
if opt.verbose
fprintf('using VLFEAT:vl_imsdisttf\n');
end
im = double(occgrid);
im(im==0) = inf;
im(im==1) = 0;
d2 = vl_imdisttf(im);
dx = sqrt(d2);
else
if opt.verbose
fprintf('using MATLAB code, faster if you install MVTB\n');
end
occgrid = double(occgrid);
occgrid(occgrid==0) = Inf;
occgrid(isfinite(occgrid)) = 0;
count = 0;
while 1
occgrid = dxstep(occgrid, m);
count = count+1;
if opt.show
cmap = [1 0 0; gray(count)];
colormap(cmap)
image(occgrid+1, 'CDataMapping', 'direct');
set(gca, 'Ydir', 'normal');
xlabel('x');
ylabel('y');
pause(opt.show);
end
ninfnow = sum( isinf(occgrid(:)) ); % current number of Infs
if ninfnow == 0
% stop if no Infs left in the image
break;
end
end
dx = occgrid;
end
end
end
% MATLAB implementation of computational kernel
function out = dxstep(G, m)
[h,w] = size(G); % get size of occ grid
% pad with inf
G = [ones(1,w)*Inf; G; ones(1,w)*Inf];
G = [ones(h+2,1)*Inf G ones(h+2,1)*Inf];
w = w+2; h = h+2;
for r=2:h-1
for c=2:w-1
W = G(r-1:r+1,c-1:c+1); % get 3x3 window
out(r-1,c-1) = min(min(W+m)); % add distances and find the minimum
end
end
end