1. A target-image detecting device configured to detect a target image as a part of photographed images and as an image of a target object from the photographed images, the target-image detecting device comprising: a memory that stores information; an obtaining unit that sequentially obtains a plurality of the photographed images that form a moving image; a detector that detects a target image included in the photographed images obtained by the obtaining unit, generates a detection result, and accumulates the generated detection result in the memory as detection history; and a deciding unit that: refers to the detection history of the memory, decides whether a detection result of a target image of the same target object is included in a latest predetermined number of detection results, outputs the detection result when the detection result is included, and does not output the detection result when the detection result is not included, wherein the detector accumulates identification information for identifying the detected target image in the memory by relating the identification information to the detection result, wherein, when a target image of which a target object detected this time is the same as that of the target image detected in the past, the detector accumulates, in the memory, identification information that is the same as identification information of the target image detected in the past by relating the identification information to a detection result of the target image detected this time, and wherein the deciding unit makes the decision by using the identification information of the target image.