Border kill  
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Menu:   Processing > Morphology… > Connectivity->Fill holes  
Script:   border  
Use this command to remove objects that touch the borders in multiphase images
. The function works by assigning the zero value to those foreground pixels located within the selected distance from the image border or selection outline.

If you choose this command, the following options will become available:

Displays the input image frame number. If you want to process another image, type or select the corresponding value.  

Displays the number of the frame in which the output image will be created. Depending on the Preferences. ImageWarp will set it either to the first available value or to the Input frame number. Type or select another value if you want the output image to be created in a different frame.  
Select this check box to watch the Preview of the output image.  
Lets you select the minimal distance from the border allowed for the objects. If at least one pixel of the object is located closer to the boundary, the object will be erased.