“The Incomplete Araki” is a knowingly redundant title for an exhibition of Japan’s most prolific, most controversial, and most disobedient photographer. For more than 50 years, Nobuyoshi Araki has pushed the limits of production — he has taken an uncountable number of photographs, gathered into something like 500 books — and pushed the limits, too, of free expression. He was arrested once on obscenity charges, and Japanese and foreign authorities have censored his exhibitions of Tokyo streetscapes, blossoming flowers, and, most notoriously, women trussed up in the baroque rope bondage technique known as kinbaku-bi, or “the beauty of tight binding.”

Even more than his colleague Daidō Moriyama, or the slightly younger Hiroshi Sugimoto, Mr. Araki has emerged as Japan’s most famous living photographer, and the 77-year-old ropemaster has been enjoying a victory lap of sorts lately. A major retrospective of his work took place in 2016 at the Musée Guimet, Paris’s Asian art museum. Last summer, the Tokyo Photographic Art Museum assembled hundreds of his large-scale prints, Polaroids and books; another show is up in Munich. Now he receives his largest exhibition in New York, though at a different sort of institution: the Museum of Sex, better known for its anatomically explicit bouncy castle and Studio-54-manqué cocktail bar than its engagement with visual art.