1. A medical image processing apparatus comprising: an acquisitor that acquires a perspective image including a treatment target; a first landmark detector that detects a position of a landmark, which is characteristic part with respect to an image surrounding the treatment target, in the perspective image; and an estimator that, estimates a position of the treatment target based on the position of the landmark detected by the first landmark detector and relationship information indicating a relationship in position between the landmark and the treatment target, wherein the relationship information is obtained by acquiring positions of a plurality of landmarks in each of a plurality of images imaged in different respiratory phases having a picture angle that is the same as the perspective image and learning relationship between the positions of the plurality of the landmarks and positions of the plurality of treatment targets on at least one common respiratory phase, the relationship information includes a parameter of a function for deriving the position of the treatment target from the position of the landmark.