1. A shape measurement apparatus comprising: an illuminator that irradiates light onto a measurement target object disposed on a stage; an image capturing unit that captures an image of the measurement target object; a characteristic amount calculator, that calculates a characteristic amount corresponding to at least one of a color and brightness of a plurality of points of interest on a surface of the measurement target object, based on an image of the measurement target object obtained by the image capturing unit in a state in which light is emitted from the illuminator; a storage unit that stores predetermined data that associates a value of the characteristic amount with information that specifies an orientation of a normal line on the surface based on the characteristic amount value; and a shape calculator that calculates orientations of normal lines at the plurality of points of interest, based on the values of the characteristic amount calculated by the characteristic amount calculator, by referencing the predetermined data stored in the storage unit, and calculates a three-dimensional shape of the surface of the measurement target object based on a result of the calculated orientations, wherein the storage unit stores a plurality of data sets generated, respectively, for a plurality of reference positions arranged in a field of view of the image capturing unit, and the shape calculator selects the data set to be referenced based upon a position of a point of interest.