1. A cell division tracking apparatus comprising: an imaging device including an image sensor, which images cells; and a system controller which controls the apparatus to: image the cells multiple times by the imaging device, and acquire cell images and track division processes of the cells based on a cell image group composed of the cell images; detect a cell region in each of the cell images; detect a mother cell region corresponding to a mother cell immediately before cell division in each of the cell images; set a search range to search for daughter cell regions corresponding to daughter cells resulting from the division of the mother cell based on the mother cell region detected by the mother cell detection unit; and judge whether the cell regions are the daughter cell regions based on a region in which the cell regions overlap the search range regarding the cell images collected at and after a detection of the mother cell region.