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I am trying to find a tool in QGIS that does the same function as Region group in ArcGIS.

What I am trying to do is to identify uniquely each patch of a raster that has a certain value (e.g "Value" =1) using neighbouring cells.

From the region group docs:

For each cell in the output, the identity of the connected region to which that cell belongs is recorded. A unique number is assigned to each region.

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To get a similar tool to Region Group, you need to use r.clump in GRASS, which can be accessed from QGIS if you have installed GRASS using OSGeo4W advanced installer.

The tool can be found inQGIS -> Processing Toolbox -> GRASS Commands -> Raster -> r.clump

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As a test, I used small portion of land use map with 7 classes, as you can see below:

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After running the tool, the land use map was reclassified into 35 groups (35 unique pixel values) with different colors to see the groups clearly, as you can see below:

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