1. A cell-image analyzing apparatus for analyzing a cell collective that forms a colony using a cell image, wherein the cell-image analyzing apparatus comprises a computer and image analysis software that controls the computer to function as units comprising: a boundary element extracting unit for extracting boundary elements of subjects such as cells, intracellular organelles, or dust upon analyzing the cell image; a possible colony region determining unit for determining, as a possible colony region, a region surrounded by boundary elements of subjects extracted by the boundary element extracting unit and having a size greater than a first criterion value; and a colony region determining unit for determining a colony region, wherein the colony region determining unit divides the possible colony region determined by the possible colony region determining unit into the colony region and a non-colony region; wherein the colony region determining unit is configured to predict that, upon growing a marked region from an arbitrary origin on the boundary elements of the subjects in the possible colony region by repeating a process of incorporating adjacent points into the marked region until the marked region contains a preset average number of boundary pixels for a single cell, the marked region containing the average number of boundary pixels is a region occupied by a single cell inside the possible colony region.