A method performed by a computing system comprises receiving shape information for an elongate flexible portion of a medical instrument. The medical instrument includes a reference portion movably coupled to a fixture having a known pose in a surgical reference frame. The fixture includes a constraint structure having a known constraint structure location in the surgical reference frame. The elongate flexible portion is coupled to the reference portion and is sized to pass through the constraint structure. The method further includes receiving reference portion position information in the surgical reference frame; determining an estimated constraint structure location in the surgical reference frame from the reference portion position information and the shape information; determining a correction factor by comparing the estimated constraint structure location to the known constraint structure location; and modifying the shape information based upon the correction factor.