1. A medical image processor comprising: an extraction unit configured to extract a longitudinal line from three-dimensional volume data for a medical image, the longitudinal line representing how a blood vessel runs; a longitudinal cross-sectional image generator configured to generate a plurality of longitudinal cross-sectional images which radially intersect one another on a line parallel with the longitudinal line, the longitudinal cross-sectional images being cross-sectional images of the blood vessel; a short-axis cross-sectional image generator configured to generate a plurality of short-axis cross-sectional images intersecting the longitudinal line, the short-axis cross- sectional images being cross-sectional images of the blood vessel; a structure element detector configured to detect a specific structural element of the blood vessel from each of the plurality of short-axis cross-sectional images and the plurality of longitudinal cross-sectional images, the specific structural element being a lumen and a calcification area of the blood vessel; and a correction unit, including a processor, configured to correct the specific structural element detected from each of the plurality of short-axis cross-sectional images on a basis of the plurality of longitudinal cross-sectional images so that a positional relationship becomes consistent between the specific structural element detected from each of the plurality of longitudinal cross-sectional images and the specific structural element detected from each of the plurality of short-axis cross-sectional images, wherein the correction unit extracts a plurality of contour points of the lumen of the blood vessel, and measures a distance between one of the contour points as a target contour point and a straight line joining two contour points located respectively before and after the target contour point, if the distance is larger than a certain distance, the correction unit determines that the target contour point is a front end point of a branch of the vessel, and the correction unit performs correction in which the lumen of the blood vessel is moved inside the blood vessel so that the lumen of the blood vessel is smoothed.