1. A pedestrian motion predicting device comprising: a photographing unit mounted on a vehicle, the photographing unit configured to photograph a periphery of the vehicle and to create image data of the periphery of the vehicle; a controller; and a data storage, wherein the controller receives the image data from the photographing unit, and the controller is configured to detect a pedestrian from the image data; the controller is configured to acquire leg width values of the pedestrian from the image, each of the leg width values being a space between legs of the pedestrian; the data storage configured to store the leg width values of the pedestrian in time series acquired by the controller; the controller is configured to analyze a periodicity of the leg width values based on the leg width values of the pedestrian in time series stored in the data storage; and the controller is configured to detect a break in the periodicity of the leg width values and to predict, based on a leg width change amount, whether the pedestrian will rush out at a speed according to the leg width change amount, the leg width change amount being a difference between a leg width value before the break in periodicity and a leg width value after the break in periodicity.