1. A medical image processing apparatus for generating a medical image of a target vessel by using three-dimensional volume data representing a portion in a living body, said apparatus comprising: a volume data obtaining unit which obtains predetermined three-dimensional volume data including a tubular tissue of the target vessel; a region specifying unit which specifies a region including a position on the tubular tissue in the three-dimensional volume data at each of a plurality of such positions as said region specifying unit specifies a planar region which orthogonally intersects with the longitudinal direction of the tubular tissue, said region specifying unit establishing an orthogonal cross sectional region orthogonal to the longitudinal direction of the target vessel by marching along the target vessel in a marching direction; an extraction unit which extracts information on the tubular tissue in each of the specified regions; a parallel region specifying unit which specifies a first parallel region and a second parallel region along the target vessel at each of said positions wherein the parallel regions are perpendicular with each other and perpendicular with the orthogonal cross sectional region at each position; a parallel region extraction unit which extracts information on the tubular tissue in each of the specified parallel regions; a marching direction determination unit for determining the marching direction based on the information on the tubular tissue extracted from each of the specified parallel regions; a center specifying unit of said extraction unit for specifying a center position of a cross section of the tubular tissue in each of the plurality of regions specified by said region specifying unit; and a medical image generating unit which generates a medical image representing the tubular tissue, based on the information extracted by said extraction unit.