1. A measurement apparatus comprising: a three-dimensional point cloud model memory unit for storing a three-dimensional point cloud model including a point cloud each showing a three-dimensional position; an image displaying unit for displaying an image captured by a camera on a displaying device and prompting a user to specify a position within the image; a measurement image point obtaining unit for inputting the position within the image specified by the user as a measurement image point from an inputting device; a vector calculating unit for calculating a vector showing direction from a center of the camera to the measurement image point inputted by the measurement image point obtaining unit; a neighborhood extracting unit for extracting one neighboring point of the measurement image point from the point cloud of the three-dimensional point cloud model; a neighboring plane calculating unit for calculating a particular plane including the one neighboring point extracted by the neighborhood extracting unit; and a feature position calculating unit for calculating an intersecting point of the particular plane calculated by the neighboring plane calculating unit and the vector calculated by the vector calculating unit as a three-dimensional position of the measurement image point.