1. A pedestrian-crossing marking detecting device comprising: an image data obtaining section that has a first imaging system and obtains image data on a road surface captured by the first imaging system; a period calculating section that calculates a period of painted portions on the image data when the painted portions of a pedestrian-crossing marking are included in a calculation range of the image data, based on coordinates of the calculation range, geometric parameters of the first imaging system and predefined values of the pedestrian-crossing marking; a frequency analyzing section that analyzes a frequency of an image intensity in the calculation range and calculates a frequency power distribution, based on the basis function in which the integral multiple of the period of the painted portions is assumed as one period; an area detecting section that extracts a coordinate point at which a power level in the frequency power distribution is larger than a predetermined threshold from the calculation range, and detects an area in which the coordinate point is present as a pedestrian-crossing marking area; and a position outputting section that outputs coordinate data on the pedestrian-crossing marking area in the image data.