1. A cell-image analyzing apparatus provided with a computer, for analyzing a cell collective that forms a colony using cell image; wherein the cell-image apparatus comprises an image analysis software that makes the computer function as: a boundary element extracting means for extracting boundary elements of subjects such as cells, intracellular organelles or dust upon analyzing the cell image; a possible colony region determining means for determining, as a possible colony region, a region surrounded by boundary elements of subjects as extracted via the boundary element extracting means and having a size greater than a first criterion value; and a colony region determining means for determining, in the possible colony region determined via the possible colony region determining means, a region that contains more than a predetermined number of clustered regions each being surrounded by boundary elements of subject and having a size smaller than a second criterion value, as a colony region.