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 tubular structure runs; a longitudinal cross-sectional image generator configured to generate a plurality of longitudinal cross-sectional images extending along the longitudinal line, the longitudinal cross-sectional images being cross-sectional images of the tubular structure; 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 tubular structure; a structure element detector configured to detect a specific structural element of the tubular structure from each of the plurality of short-axis cross-sectional images; and a correction unit 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.