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I'm working with a tiff image in arcgis projected in UTM 33N and I need to obtain pixel coordinates of a specific point in the image with known metric coords (UTM 33N). How can I get them?

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    You can use lower corner coordinates and cell size to obtain row and column. Or you can do it mechanically by sampling rasters OF ROWMAP and COLMAP. – FelixIP Jan 30 at 17:51
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There would be two ways to get your coordinates.

The first one is to use Identify Button. You can find it under the Toolbar -> Tools. enter image description here

Now Click on the Pixel, where you want to know the coordinates. Now a window opens and you can see the coordinates behind location. But this coordinates are not really exact. enter image description here

The second way is to convers the raster into a point feature class. You can do it through your ArcToolbox -> Conversion Tools -> From Raster -> Raster to Point.

enter image description here

After ths click with identify on the point you want the location from.

I hope this will work for you.

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