1. A cell division tracking apparatus comprising: an imaging unit which images cells; a control unit which controls the imaging unit to image the cells multiple times and acquires a cell images and tracks division processes of the cells based on a cell image group composed of the cell images; a cell detection unit which detects a cell region in each of the cell images; a mother cell detection unit which detects a mother cell region corresponding to a mother cell immediately before cell division in each of the cell images; a search range setting unit which sets 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 a daughter cell judgment unit which judges 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.