1. An image processing apparatus for a magnification observation apparatus including an object lens, and an imaging device optically coupled to the object lens, and configured to acquire an image representing an object to be measured as an object image, comprising: a display configured to display the object image, and to display, on the object image, a measuring portion designating image corresponding to a specific portion the object image; a storage configured to store a preset positional relation between the measuring portion designating image and a plurality of detecting regions at which a predetermined characteristic portion including an edge part is detected from the object image, and to store a measuring condition; and a processor configured to perform a manual movement of a position of the measuring portion designating image relatively to the object image in response to a manual input, to detect the edge part as the predetermined characteristic portion at each of the plurality of detecting regions from the object image based on the position of the measuring portion designating image relatively to the specific portion of the object image, and to calculate a geometrical physical quantity based on the measuring condition and the edge part detected as the predetermined characteristic portion and wherein the process part is operated so that, when a distance between the measuring portion designating image and the specific portion of the object image falls within a predetermined range by operation of the operation part, the measuring portion designating image is moved so as to make a position of the measuring portion designating image agree with a position of the specific portion of the object image.