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The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

(For your noisy data you might want to use a stricter criterion than just "larger than all neighbours", e.g. larger by a threshold. Also, for simplicity I used the slow ComputationalGeometry package but you'll probably want something faster.)

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those out:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)

The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

(For your noisy data you might want to use a stricter criterion than just "larger than all neighbours", e.g. larger by a threshold. Also, for simplicity I used the slow ComputationalGeometry package but you'll probably want something faster.)

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those out:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)

The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

(For your noisy data you might want to use a stricter criterion than just "larger than all neighbours", e.g. larger by a threshold. Also, for simplicity I used the slow ComputationalGeometry package but you'll probably want something faster.)

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)

The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

(For your noisy data you might want to use a stricter criterion than just "larger than all neighbours", e.g. larger by a threshold. Also, for simplicity I used the slow ComputationalGeometry package but you'll probably want something faster.)

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those out:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)

The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)

The idea is to construct the Delaunay triangulation and get the points that have higher values than all of their neighbours (according to this triangulation).

Here's a worked example:

Generate the sample data:

f[x_, y_] := Sin[x] Sin[y] points = RandomReal[{-3, 3}, {300, 2}]; zval = f @@@ points; 

Find the local maxima:

<< ComputationalGeometry` tri = DelaunayTriangulation[points]; tests = And @@ Thread[zval[[#1]] > zval[[#2]]] & @@@ tri maxima = Pick[points, tests] (* ==> {{1.3437, 1.68432}, {2.75095, -2.69678}, {-2.97601, 1.98261}, {-1.57433, -1.57115}} *) 

(For your noisy data you might want to use a stricter criterion than just "larger than all neighbours", e.g. larger by a threshold. Also, for simplicity I used the slow ComputationalGeometry package but you'll probably want something faster.)

Visualize them:

ListDensityPlot[ArrayFlatten[{{points, List /@ zval}}], Epilog -> {Red, PointSize[Large], Point[maxima]}] 

Two of them are on the convex hull. You can filter those:

Complement[maxima, points[[ConvexHull[points]]]] (* ==> {{-1.57433, -1.57115}, {1.3437, 1.68432}} *) 

(Note: it would have been better to filter these based on the indexes of points rather than the coordinates to avoid unnecessary floating point comparisons, but I was lazy :)