http://imagej.273.s1.nabble.com/Delaunay-Voronoi-intersected-with-boundary-tp5016272p5016285.html
Following up - has anyone encountered this concept of filtering Voronoi neighbors by the criterion that the Voronoi-edge and it’s dual Delaunay-edge strictly intersect?
[sadly, I often “invent” things that I have seen previously, and then “forgotten” - they say that memory is the second thing to go as you age]
> On Apr 29, 2016, at 15:28 , Kenneth Sloan <
[hidden email]> wrote:
>
> That’s a difficult case. My first thought is to use only Voronoi edges with at least one vertex inside the boundary. I think that’s actually what you initially proposed. If the entire boundary between Voronoi edges is outside the boundary, those two particles are not really neighbors.
>
> As someone else noted (sorry - I don’t have the posting handy), Voronoi may not be giving exactly what you want here. It depends on the interpretation of the particles and the Voronoi domains. I might, for example, look at the line segment connecting two of your particles, and exclude those which do not strictly intersect the Voronoi edge separating the corresponding domains. This is just a crude heuristic, but I think it addresses the question of what you really mean by saying that isolated particles are “neighbors”.
>
> for example, in your image, look at the right hand column of particles. Counting up from the bottom, the 2nd and 3rd particles are Voronoi neighbors, but I think it’s defensible to call them “NOT neighbors” for the purpose of your analysis.
>
> Similarly, looking at the left hand column of particles, near the top, the 1st and 2rd particles on the left don’t really qualify as “neighbors”. There are a couple of other examples I think.
>
> I like this heuristic. For each Voronoi edge, generate the dual Delaunay edge. If the two edges intersect properly, call the particles neighbors and use the length of the Delaunay edge in further computation. If not, not.
>
> —
> Kenneth Sloan
>
[hidden email]
> Vision is the art of seeing what is invisible to others.
>
>
>
>
>> On Apr 29, 2016, at 11:13 , schiriki <
[hidden email]> wrote:
>>
>> Hello Kenneth,
>>
>> thank you for your help. I attached an image to better explain the problem.
>> Since in my datasets all or almost all particles will be near the domain
>> border, the problem arises a lot.
>> The picture shows the particles, the domain boundary (close to a rectangle)
>> and the Voronio as computed by imageJ. If I want to use Delaunay to
>> determine distances, also e.g. the particles marked with red or those marked
>> with blue will be considered neighbors, eventhough their Voronoi domains do
>> not share an edge inside the domain.
>>
>> <
http://imagej.1557.x6.nabble.com/file/n5016282/example.jpg>
>>
>> For a single image I could maybe mirror the particles along the border to
>> enforce real Voronoi separation, but I have a lot of data, so doing it by
>> hand is not an option.
>>
>> Thank you,
>> Angelika
>>
>>
>>
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http://imagej.1557.x6.nabble.com/Delaunay-Voronoi-intersected-with-boundary-tp5016272p5016282.html>> Sent from the ImageJ mailing list archive at Nabble.com.
>>
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