Counting fully bound holes in a bitmap image?

I have a monochrome bitmap image, and I wish to find fully bound holes in the image. Only holes that are fully bound by black pixels should be included:

0000000000   
0001111100   
0010000010   
0001000110   
0000111100   
0000000000   
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has one hole

but

0100000010
0100000110
0011111100
0000000000

would have 0

This is somewhat similar to CCL (Connected Component Labelling). If you invert the bitmap then you are just looking for 4-connected blobs which do not touch the edge of the image frame.