Does 3D slicer have any tools with a function similar to AMIRA's "magic wand"?

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Yes, and also hopefully you find there are also much better tools.

I think the closest to the Magic Wand effect is “Flood filling” effect, provided by SegmentEditorExtraEffects extension.

I would also recommend to try “Grow from seeds” effect as explained here: Bone segmentation to create 3D-printable STL. You may also try to use Watershed effect, which takes some more time to compute but provides smooth surfaces.

I would also recommend to check out segmentation tutorials here: https://www.slicer.org/wiki/Documentation/Nightly/Training#Slicer4_Image_Segmentation

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