GetRandomEllipseImage.m

% GetRandomEllipseImage(K)
% generate a logical image with K overlapping ellipses
% 

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function bw=GetRandomEllipseImage(K)

IMSIZE=1000;
mu1=[500,500];

bw=logical(zeros(IMSIZE));

pts={};
ptsEdge={};
bValidEllipse=0;

while ~bValidEllipse
    for kk=1:K
        [pts{kk} ptsEdge{kk}] = GetRandomEllipsePts(mu1,IMSIZE);
    end
    
    % place each ellipse
    for kk=2:K
        ptsCombined=vertcat(pts{1:kk-1});
        idxK = 1+round((length(pts{kk})-1)*rand());
        idxCombined = 1+round((length(ptsCombined)-1)*rand());
        offset = ptsCombined(idxCombined,:)-pts{kk}(idxK,:);
        pts{kk} = pts{kk} + repmat(offset,[size(pts{kk},1) 1]);
        ptsEdge{kk} = ptsEdge{kk}+repmat(offset,[size(ptsEdge{kk},1) 1]);
    end
    idxPts={};
    for kk=1:K
        idxPts{kk}=sub2ind([1000,1000],pts{kk}(:,2),pts{kk}(:,1));
    end
    
    idxPtsOverlap=GetOverlap(idxPts);
    % make sure no ellipse is fully contained in another
    nNonOverlap=idxPtsOverlap(2.^[0:K-1]);
    nNonOverlap=cellfun(@length,nNonOverlap);
    if all(nNonOverlap~=0)
        bValidEllipse=1;
    end
end

ptsCombined=round(vertcat(pts{:})); 
idxCombined=sub2ind(size(bw),ptsCombined(:,2),ptsCombined(:,1));
bw(idxCombined)=1;


function [pts, ptsEdge] = GetRandomEllipsePts(mu,IMSIZE)

RADII_0=10;
RADII_1=20; 

r1 = RADII_0+RADII_1*rand();
r2 = RADII_0+RADII_1*rand();

theta = 2*pi*rand();

cv = [r1^2 0;0 r2^2];

[pts]=genEllipse(mu,cv);
ptsEdge = genEllipse(mu,cv,1,0);

pts=pts-repmat(mu,[size(pts,1) 1]);
ptsEdge = ptsEdge-repmat(mu,[size(ptsEdge,1) 1]);
rotate = [cos(theta) -sin(theta);sin(theta) cos(theta)];

pts=pts*rotate;
ptsEdge=ptsEdge*rotate;

pts=pts+repmat(mu,[size(pts,1) 1]);
ptsEdge=ptsEdge+repmat(mu,[size(ptsEdge,1) 1]);

bw=false(IMSIZE);
idx=sub2ind(size(bw),round(ptsEdge(:,2)),round(ptsEdge(:,1)));

bw(idx)=1;

bw = imfill(bw,'holes');
[r c]=find(bw);
pts=[c r];

function idxPtsOverlap=GetOverlap(idxPts)

K=length(idxPts);
idxPtsOverlap={};
% idxPtsOverlap goes from 1..2^K-1
% the index is a binary vector specifying the overlap regions,
% e.g. 1,2,4,8, etc are points only in ellipses 1,2,3,4 etc.
% 3 is in 1 and 2, 5 is in 4 and 1, etc.
% no overlap between superset and subset pixels
for n=1:(2^K)-1
    rgBinary=dec2bin(n);
    idx1 = find(rgBinary);
    if length(idx1)==1
        idxPtsOverlap{n}=idxPts{idx1};
        continue
    end
    nIntersect=idxPts{idx1(1)};
    for i=2:length(idx1)
        nIntersect=intersect(nIntersect,idxPts{idx1(i)});
    end
    idxPtsOverlap{n}=nIntersect;
end

for i=1:length(idxPtsOverlap)
    for j=1:length(idxPtsOverlap);
        if i==j
            continue
        end
        rgBinaryI = dec2bin(i);
        rgBinaryJ = dec2bin(j);
        
        if length(find(rgBinaryI))<length(find(rgBinaryJ))
            idxPtsOverlap{i}=setdiff(idxPtsOverlap{i},idxPtsOverlap{j});
        end
    end
end