How to match voronoi area to it's point

לק"י

Hi!

I'm trying to find a command or a code that can match the voronoi areas I get out from voronoin command to the points they enclose. I use oast of KSSV's code, so if it seems fermiliar, it's from him.

thanks!

that's the code:

[v,c] = voronoin([xroi yroi]) ;
vorareaacd45num10thin1st = zeros(length(c),1) ;
for i = 1:length(c)
    v1 = v(c{i},1) ; 
    v2 = v(c{i},2) ;
    vorarea(i) = polyarea(v1,v2) ;
end

[Amit Ifrach]

לק"י

Hi Image Analyst, thanks for the answer!

I'll explain the main goal and then maybe i'll be able to explain what I need a little bit better.

I'm imaging a cell down to it's single molecule level. I want to use voronoi diagram on the cell's 'image' (it's xy csv of the points of the molecules). the problem is that the image contains alot of background noise that I need to ignore and to take only the voronois areas in the cell.

The (wrong) startegy I wanted to use was to inpolygon on points within the cell, delete everything else outside of it and afther that to do a voronoi. the problem is that allways I'll get big areas at the edge of the cell and cutting out points won't help. I want to use inpolygon to 'take out' the areas within the drawn polygon instead.

The problem is, that my code generate voronoi areas without a way to recognize which areas they are, or which point the surround. I need a way to ascribe area to dot it surrounds so I can 'take out' these points using inpolygon.

is there any way to do so? I thought to do it manually with for loop, but I don't know how the voronoin command assigns the areas to the c vector (which x and y point does it use).

thanks!

Amit.

[Bjorn Gustavsson]

The way I recall the Voronoi-boundaries are built from the line-segments prependicular to the midpoints of the Delaunay-triangulation-edges (normals halfway on the nearest-neighbour-lines, so the dual of the Delaunay-triangulation). If you could share a typical image it might be easier to modify your aproach?

Answer 1

[Bjorn Gustavsson]

The way I interpret your question each point [xroi,yroi] will be inside one Voronoi-cell (though my QD-tests leave a couple of edge-points outside the Voronoi-cells?). It should be possible to find out which by using inpolygon:

for i1 = length(c):-1:1
  v1 = v(c{i1},1);
  v2 = v(c{i1},2);
  idx = find(inpolygon(xroi,yroi,v1,v2));
  if ~isempty(idx)
    idxXYinCellj(i1) = idx(1);
  end
  if numel(idx) > 1
    disp(['Cell ',num2str(i1),' contains ',num2str(numel(idx)),' points?'])
  end
end

HTH