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I would like to find local maximum with the moving window 3x3 of a raster image but I don't know how to do this.

Could you please suggest me the way to do this?

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As mentioned by @Michael Miles-Stimson, the first step is to compute a new raster with the value of the minimum in your neighbourhood. This can be done using Focal Statistics tools.

The second step consists in finding the values of the original raster that are equal to your maximum values. This can be done using the Con tool

Con("raster"=="focal_stat_max", 1)

Note that the "non maximum" will be set to NoData in this case, but you can enter another value if you want (e.g. 0)

Con("raster"=="focal_stat_max", 1, 0)

Finally, you convert this as point using raster to point (optional)

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