1. A lane marker recognition apparatus for recognizing a lane marker on a road frontward or rearward of a vehicle in repeated cycles, the apparatus comprising: a characteristic object detection unit configured to detect a characteristic object on a road; a lane marker extraction unit configured to extract data on a lane marker from data on the detected characteristic object; a centerline calculation unit configured to calculate a centerline position and a centerline shape on the road from the extracted data; a width calculation unit configured to calculate a lane width of the road from the extracted data; and a parameter follow-up unit configured to perform a follow-up process of parameters defining the centerline position, the centerline shape, and the lane width based on the calculated centerline positions, calculated centerline shape, and calculated lane width, wherein when the lane marker extraction unit extracts the data on the lane marker at a present cycle, the lane marker extraction unit uses a result from the follow-up process performed at a past cycle by the parameter follow-up unit.