1. A medical method, comprising: providing a hand-carried ultrasonic probe having transmission and reception capabilities; moving said probe by hand over a skin surface of a patient along an at least partially random path; during the moving of said probe, transmitting an outgoing ultrasonic pressure wave from said probe into the patient; also during the moving of said probe, receiving reflected ultrasonic pressure waves from internal tissues of the patient; periodically preprocessing the received reflected ultrasonic pressure waves to derive preliminary structural data pertaining to the internal tissues of the patient, said data consisting essentially of separate sets of data, each of said sets of data corresponding to a respective location of said probe relative to the patient; storing said sets of data; analyzing said preliminary structural data of the stored sets of data to determine three-dimensional shapes of the internal tissues of the patient; and generating a video signal encoding a relatively high-resolution video image of said three-dimensional shapes.