How to convert 2D triangulation to binary image?
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Does anyone know of an easy way to convert a 2D triangulation to a binary image, which represents the inside?
Let my clarify my question with a picture: http://i41.tinypic.com/2gvvvnl.jpg The goal is to go from left to right...
My triangulation is given its Points and the ConnectivityList (i.e., it was created with the matlab function "triangulation").
It is important that no holes get filled and all features are preserved.
BEST ANSWER SO FAR:
% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
triasMask = ~ismember(1:DT.size(1), holeTrias);
T = triangulation(DT.ConnectivityList(triasMask,:), DT.Points);
% Define query points
X = 0:0.05:1;
Y = 0:0.05:1;
[xMat,yMat] = meshgrid(X,Y);
IN = false(size(xMat));
for t = 1:size(T,1)
vertsXY = T.Points(T.ConnectivityList(t,:),:);
IN = IN | inpolygon(xMat,yMat, vertsXY(:,1), vertsXY(:,2));
end
% Show the result
figure
patch('faces',T.ConnectivityList,'vertices',T.Points,'FaceColor','g')
hold on
plot(xMat(IN),yMat(IN),'b.',xMat(~IN),yMat(~IN),'r.')
采纳的回答
Hi Geert,
Here's something that does what you want. It's not optimised for speed as it simply iterates naively through triangles, but it's at least correct.
% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
triasMask = ~ismember(1:DT.size(1), holeTrias);
T = triangulation(DT.ConnectivityList(triasMask,:), DT.Points);
% Define query points
X = 0:0.05:1;
Y = 0:0.05:1;
[xMat,yMat] = meshgrid(X,Y);
% Query each point
IN = false(size(xMat));
for i = 1:numel(IN)
for t = 1:size(T,1)
vertsXY = T.Points(T.ConnectivityList(t,:),:);
if inpolygon(xMat(i),yMat(i), vertsXY(:,1), vertsXY(:,2))
IN(i) = true;
break;
end
end
end
% Show the result
figure
patch('faces',T.ConnectivityList,'vertices',T.Points,'FaceColor','g')
hold on
plot(xMat(IN),yMat(IN),'b.',xMat(~IN),yMat(~IN),'r.')
How does that work for you?
5 个评论
Sven
2013-8-21
One little speedup can be gained by not considering points outside the convex hull:
% Query each point
IN = false(size(xMat));
k = convhull(T.Points);
for i = find(inpolygon(xMat,yMat, T.Points(k,1), T.Points(k,2)))'
for t = 1:size(T,1)
vertsXY = T.Points(T.ConnectivityList(t,:),:);
if inpolygon(xMat(i),yMat(i), vertsXY(:,1), vertsXY(:,2))
IN(i) = true;
break;
end
end
end
Matt Kindig
2013-8-21
Another speedup can probably be realized by using the FEX contribution inpoly ( http://www.mathworks.com/matlabcentral/fileexchange/10391-fast-points-in-polygon-test). In my experience, it is MUCH faster than the built-in inpolygon(), in addition to being more versatile.
Sven
2013-8-21
Oh, yep, that's true Matt. That submission is indeed faster than the built-in inpolygon (which has a few extra things inside such as allowing for NaN coordinates to define breaks in polygons... I think Mathworks should probably mex-ify it anyway).
Geert
2013-8-22
with R2018b and later this simplifies to
%% Make some data
pts = rand(50,2);
DT = delaunayTriangulation(pts);
% Find a central triangle to remove
[~,holeTrias] = min(sum(abs(DT.incenter - 0.5),2));
holeTrias = [holeTrias DT.neighbors(holeTrias)];
triasMask = ~ismember(1:DT.size(1), holeTrias);
T = triangulation(DT.ConnectivityList(triasMask,:), DT.Points);
% Define query points
X = 0:0.02:1;
Y = 0:0.02:1;
%% use polyshape
tic
[xMat,yMat] = meshgrid(X,Y);
bp = boundaryshape(T);
IN = reshape(isinterior(bp, xMat(:), yMat(:)), size(xMat));
toc
%%
colormap(gray(2))
imagesc(X, Y, IN)
hold on;
patch('faces', T.ConnectivityList, 'vertices', T.Points, ...
'FaceColor', 'r', 'FaceAlpha', .2)
hold off;
axis equal;
axis tight;
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