1. A moving-object counter apparatus comprising: a controller configured to act as: a first captured-image acquisition unit that acquires a plurality of images captured at respective times different from each other by a first imaging apparatus capturing images of a predetermined region; a moving-object moving-path specifying unit that specifies, on the basis of the plurality of images acquired by the first captured-image acquisition unit, one or more moving paths along which one or more respective moving objects have moved in the predetermined region; a virtual-line setting unit that sets a virtual line on the basis of the one or more moving paths specified by the moving-object moving-path specifying unit, the virtual line being imagined on the images acquired by the first captured-image acquisition unit, and serving as a reference for counting of one or more moving objects that have passed through a predetermined position in the predetermined region; and a first moving-object counter unit that counts, by counting one or more moving paths that cross the set virtual line among the one or more moving paths specified by the moving-object moving-path specifying unit, the one or more moving objects that have passed through the predetermined position, wherein the moving-object moving-path specifying unit detects, in each of the plurality of images acquired by the first captured-image acquisition unit, a moving-object region that is a region in which a moving object is positioned among the one or more moving objects, and the virtual-line setting unit sets, on the basis of attribute values of the plurality of detected moving-object regions, coordinates through which the virtual line passes on the images, wherein the coordinates through which the virtual line passes on the images are coordinates of a moving-object region having the smallest attribute value or the smallest amount of change in the attribute value among the plurality of detected moving-object regions.