1. An endoscope apparatus, comprising: an image pickup device in which a plurality of pixel sensors are arranged in a matrix shape, and which starts sequential exposure by at least one of pixel rows with respect to the plurality of pixel sensors to generate image data of a frame image, and outputs image data for each of the pixel rows in an order of starting exposure, wherein said pixel rows are made up of some of the plurality of pixel sensors; a detection device that determines if an image region exists in the frame image, the detection device determining a portion of the frame image to be the image region if said portion of the frame image includes a part of an object region that is edged along a direction parallel to the pixel rows in the frame image, wherein the image region is captured in the frame image by the image pickup device operating in a rolling shutter method, and wherein a first pixel row in the frame image in which an object that is moving at high speed appears and a second pixel row in the frame image in which the object that is moving at high speed does not appear arises since light reflected from the object that is moving at high speed appears only in a short time period, and wherein a boundary portion between the first and second pixel rows in the frame image in the direction parallel to the pixel rows is the edge of object region; and an exposure control device that, if the detection device determines the image region exists, changes an exposure time of each of the pixel rows by the image pickup device simultaneously for all of the pixel rows by the image pickup device if the detection device determines the image region exists, and does not change an entire exposure time of each of the pixel rows by the image pickup device simultaneously for all of the pixel rows by the image pickup device if the detection device does not determine the image region exists.