1. A cell-image analyzing apparatus comprising: a cell imaging system comprising (i) an imaging optical system for forming an optical image of cells that exist in a vessel, and (ii) an image sensor for capturing images of the cells that exist in the vessel by converting the optical image of the cells formed by the imaging optical system into electronic cell image data; a cell-contour emphasizing system which optically emphasizes contour portions of the cells that exist in the vessel, the vessel being arranged at a shot position of the cell imaging system, such that the contour portions of the cells appear emphasized in the optical image of the cells which is formed by the imaging optical system before the optical image of the cells is converted into the electronic cell image data; and a cell-image analyzer which analyzes a predetermined characteristic quantity of the cells using the electronic cell image data generated by the cell imaging system, upon delimiting cell regions; wherein the cell imaging system captures the images of the cells that exist in the vessel, with the contour portions of the cells having been emphasized by the cell-contour emphasizing system, and then the cell-image analyzer automatically analyzes the predetermined characteristic quantity of the cells upon delimiting the cell regions using the electronic cell image data in which the contour portions of the cells that exist in the vessel have been automatically emphasized by the cell-contour emphasizing system and captured by the cell imaging system; and wherein the cell-contour emphasizing system comprises a cell-contour emphasizing position focusing system including an autofocusing mechanism for automatically adjusting a focus of the imaging optical system to a position where the contour portions of the cells that exist in the vessel are emphasized in the optical image of the cells.