1. A line-of-movement generating apparatus comprising: an acquisition unit that acquires images captured by an image capturing device each at a corresponding one of a plurality of time points; a detection unit that detects one or a plurality of moving objects from the images each captured at a corresponding one of the plurality of time points; an extraction unit that extracts a line of movement of each of the detected one or plurality of moving objects; a setting unit that sets a region where a line of movement tends to have a missing portion in an image captured by the image capturing device; a calculation unit that calculates a likelihood indicating a degree of certainty of the extracted line of movement of each of the one or plurality of moving objects, the calculation unit calculating the likelihood according to an expression by which the likelihood decreases as a starting point or an ending point of the line of movement is further from the region; and a confirmation unit that confirms a line of movement of the one or plurality of moving objects on the basis of the calculated likelihood.