An apparatus for labeling three-dimensionally connected components in a three-dimensional image is provided. The apparatus includes a two-dimensional labeling processor which labels each connected component in two-dimensional images giving a proper component code, and a coordinate calculator which calculates coordinates of a representative point representing each connected component. The apparatus further includes a connectivity detection processor which checks connectivity of representative points in adjacent two-dimensional image planes and an editing processor which modifies the component codes already provided by the two-dimensional labeling processor using the connectivity information to obtain three-dimensionally labeled image codes.