N/sub 16/ space is related to the 16-neighborhood, which can be considered as an extension of the conventional 4-neighborhood and 8-neighborhood. Two new concepts for N/sub 16/ space are introduced in this paper: (1) M-connectivity, which can eliminate the ambiguity caused by multiple path connections in a 16-neighborhood; and (2) the M-path boundary which is necessary for forming a closed boundary in N/sub 16/ space. Both of these help to improve the use of the 16-neighborhood in digital image processing and the easy extension of the work made with the 4-neighborhood and the 8-neighborhood to larger neighborhoods.