1. An endoscope apparatus comprising: an image pickup device that picks up an image of an object; and a controller configured to function as a measurement portion that measures the object based on the image of the object obtained by the image pickup device; wherein the measurement portion comprises: a specification portion that specifies three base points on the image; a base ellipse calculation portion that calculates a base ellipse based on the three base points specified by the specification portion and sets a plurality of search points on the base ellipse, a number of the search points and a distance between the search points being proportional to a perimeter length of the base ellipse; a composing point calculation portion that calculates composing points forming an object region of the object, based on an image region that is based on the plurality of search points that are set by the base ellipse calculation portion; a size calculation portion that calculates a size of the object based on the composing points; and an image processing portion that performs binarization processing to binarize the image; wherein the composing point calculation portion performs a differential filter processing for extracting an edge of the object region based on the image after the binarization processing, calculates an approximation line that approximates to the edge, and calculates the composing points on the edge based on the approximation line, wherein the differential filter processing uses a primary differential filter, a secondary differential filter, and a noise reduction filter.