Just how common these procedures have become is hard to track but the number of surgeons performing image-enhancing work such as nose jobs and eye lifts has increased sharply. The Korean Society of Aesthetic and Plastic Surgery, a professional group, says its membership has risen 85% to 960 since 2000. Another group, the Korean Society of Plastic and Reconstructive Surgeons, lists 1,300 members. (California, with a population of 34 million, has 864 plastic surgeons, according to the state medical board.)