Re: Identifying clusters of adjacent points on a lattice — Solution

• To: mathgroup at smc.vnet.net
• Subject: [mg81425] Re: Identifying clusters of adjacent points on a lattice — Solution
• From: Gareth Russell <russell at njit.edu>
• Date: Sun, 23 Sep 2007 04:29:00 -0400 (EDT)
• References: <fcvr81\$7r9\$1@smc.vnet.net>

```Hi again,

Daniel Lichtblau pointed me towards WeakComponents[]. I contructed a
function around that to process a binary matrix such that each
connected patch of 1's is replaced by a patch of distinct integers 1,
2, ... n where n is the total number of patches. I takes about 1 second
to process a 100 by 100 matrix with approx 250 patches. The last line
can easily be altered to produce {x,y,i} triples. I post it in here in
case it's useful to anyone.

Gareth

findPatches[m_] :=
Module[{x, y, indexMatrix, rowEdges, colEdges, allIndices, clusterIndices,
soloIndices, xy, groups},
Needs["GraphUtilities`"];
x = Length[m[[1]]];
y = Length[m];

indexMatrix = Table[i*x + j, {i, 0, y - 1}, {j, 0, x - 1}];

rowEdges =
DeleteCases[
Flatten[
Table[
If[{m[[i, j]], m[[i, j + 1]]} == {1, 1},
indexMatrix[[i, j]] -> indexMatrix[[i, j + 1]], 0], {i, 1, y}, {j, 1,
x - 1}]], _Integer];

colEdges =
DeleteCases[
Flatten[
Table[
If[{m[[i, j]], m[[i + 1, j]]} == {1, 1},
indexMatrix[[i, j]] -> indexMatrix[[i + 1, j]], 0], {j, 1, x}, {i, 1,
y - 1}]], _Integer];

allIndices = Flatten[Extract[indexMatrix, Position[m, 1]]];
clusterIndices = WeakComponents[Join[rowEdges, colEdges]];
soloIndices = Complement[allIndices, Flatten[clusterIndices]];

xy = Map[{Floor[#/x] + 1, Mod[#, x] + 1} &,
Join[clusterIndices, Map[{#} &, soloIndices]], {2}];

groups = Range[Length[xy]];

Normal[SparseArray[
Flatten[Table[Map[# -> groups[[i]] &, xy[[i]]], {i, 1, Length[groups]}],
1],{y,x}]]
]

On 2007-09-21 03:18:25 -0400, Gareth Russell <russell at njit.edu> said:

> Hi,
>
> Is there any way to use the built-in clustering routines to find
> clusters of ajacent elements on a 2d lattice? For example, I might
> generate a 'map' with
>
> SeedRandom[1];
> testMap = =E2=80=A8 Last[CellularAutomaton[{1018, {2, {{0, 2, 0}, {2, 1, 2},
> {0, 2, 0}}}, {1, =E2=80=A8     1}}, Table[If[Random[Real] < 0.1, 1, 0], {100},
> {100}], 10]];
>
> I would then like to find and label the separate 'patches' consisting
> of clusters of 1's. Ultimately, I'm looking for a list of {x,y,id}
> triples where the x and y are the coordinates of each 1 and the id is a
> number that identifies the patch to which that element belongs, but the
> trick is to find the clusters. I can't see how any of the included
> options for FindClusters would perform this particular test (each
> cluster must consist of elements connected to at least one other
> element by a distance of 1).
>
> Of perhaps there is another way?
>
> Thanks,
>
> Gareth

--
Gareth Russell
NJIT

```

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