1. An image processing device for processing a captured image of a target object under observation, the image processing device comprising: an imaging device for capturing a plurality of images of the target object, the target object being conveyed on a conveying path; a sensor for sending a detection signal when the target object reaches an imaging range of the imaging device; and an image processing device comprising: a detection signal input unit for receiving a detection signal from the sensor; a command output unit for outputting an imaging command to the imaging device; an operation input unit for receiving operation data from an external source; an image output unit for outputting an image to a display device; and a delay amount setting unit for setting an amount of delay for controlling output timing of the imaging command from the command output unit, the amount of delay being time interval between the detection signal input unit receiving the detection signal and the command output unit outputting the imaging command in an observation process of the target object, wherein the delay amount setting unit is configured for acquiring a target position in a first captured image of a first target object based on the operation data; instructing the command output unit after a predetermined time interval to output the imaging command to the imaging device after the detection signal input unit receives the detection signal; detecting a position of the first target object in a second captured image of the first target object acquired after instructing the command output unit to output the imaging command to the imaging device; deriving, for a subsequent observation process, the amount of delay required to capture an image of a target object conveyed near the acquired target position based on relationship between the acquired target position in the first captured image and the detected position of the first target object in the second captured image; and setting the derived amount of delay as the time interval between the detection signal input unit receiving the detection signal and the command output unit outputting the imaging command in the subsequent observation process, wherein the amount of delay is derived from an amount of correction and a moving speed of the first target object, and the amount of correction is calculated by an inner product of a first vector indicative of a moving direction and moving distance of the first target object to the targeted position and a second vector indicative of moving direction and moving distance of the first target object conveyed on the conveying path in the imaging range.