1. A pedestrian detector comprising: an image pick up unit configured to pick up an image of a scene in front of a host vehicle; and a controller including: a characteristic point extractor configured to extract characteristic points from the image which has been picked up by the image pick up unit; a movement information calculator configured to calculate a velocity at which, and a direction in which, each of pixels representing respective characteristic points moves in the image, and to output the velocity and the direction as movement information; a coordinate converter configured to express coordinates of each of pixels in a coordinate system corresponding to an overhead view representing the image of the scene in front of the host vehicle obtained by coordinate conversion; an object attribute determinator configured to determine that the characteristic points represent any one of a two-dimensional object or a three-dimensional object, and in a case where it is determined that the characteristic points represent the three-dimensional object, whether or not the three-dimensional object is a moving object, on the basis of the coordinates of each of the pixels in the overhead view, and on the basis of the movement information of each of the pixels; and a pedestrian determinator configured to determine whether or not the moving object is a pedestrian on a basis of change in the velocity at which the moving object moves in the image in a case where it is determined that the characteristic points represent the moving object.