Akira Kurosawa made great samurai films. Kenji Mizoguchi filmed the lives of courtesans and geishas with the feel of classical Japanese painting. Yasujiro Ozu made films about middle-class families in Tokyo. Of these three masters of Japan's cinematic golden age, which lasted from the 1930s till the 1960s, Ozu is considered to be the most typically Japanese. So much so that Japanese producers refused at first to release his films abroad. Foreigners wouldn't understand. They might laugh at Japanese in business suits sipping green tea on tatami mat floors. They wouldn't get the subtlety of Japanese family relations. Ozu's style would surely strike action-loving westerners as boring and slow.

Even though Ozu has long been recognised outside Japan as one of the greatest film-makers in history (Wim Wenders even made a film about his work in 1985, entitled Tokyo-Ga), many Japanese still think Ozu is too "Japanese" to be properly understood abroad. Part of the reason may be that Japanese life itself has changed so much since Ozu made such masterpieces as Late Spring (1949) or Tokyo Story (1953). To young Japanese brought up on lurid comic books and animated science fiction, Ozu's world looks as alien as it might to uninformed westerners.

Given the fame of his later movies, it is easy to forget that Ozu's cinematic roots are not traditionally Japanese at all, but firmly planted in Hollywood screwball comedy. The best-known Ozu film of the silent era, I Was Born, But . . . (1932), still shows more traces of Chaplin or Keaton than of anything typically Japanese. But once he found his groove, Ozu rarely veered from his fascination with ordinary Japanese urban family life. His prewar films were often set among the shopkeepers and artisans of plebeian Tokyo. The focus of his later movies was more on the wealthier bourgeoisie. These were recognised genres, by the way, which still survive on television, as they do in the west. Shomingeki ("dramas about little folks") are the Japanese equivalent of Coronation Street or EastEnders, while homu dorama ("home dramas"), soap operas about middle-class family life, are a Japanese version of Neighbours.

Ozu's genius was to lift an essentially middlebrow genre to the level of high art, without losing the broad, natural audience for family dramas. He managed to please both the Japanese masses and intellectual cinephiles. The American expert on Ozu, Donald Richie, remembers taking the Indian director Satyajit Ray to see Tokyo Story and observing how the great man was heaving with emotion at the end.

Plot was never the main point for Ozu. He once said: "Pictures with obvious plots bore me now." He was interested in character. As in the best soaps, you get to know the people through their little quirks and daily habits, their manners of speech, their routines. This takes time – in TV soap operas sometimes years. Ozu never hurries through a film. They feel like daily life, because they simulate the rhythm of life as it is lived by most people. And most people, after all, don't live in action movies.

Most lives are an accumulation of banal events, which are never banal to the people concerned: marriage, separation of children from their parents, divorce, death. Ozu shuffled these themes, like a deck of cards, in different films. And his stock characters – the lonely widower, the marriageable daughter, the company boss and so on – crop up in different movies, often bearing the same names: Hirayama, Kawai, Sugiyama. The bar, where his men relax after a hard day in the office, begins to look familiar after you have seen it reappear in several Ozu pictures. As does the office, or the railway station, or the barber shop, or the pinball parlour.

Food and drink play a vital part in Ozu's film world. Especially in Japan, before the age of laptops and TV dinners, eating and drinking were the main occasions for communal life. Ozu himself not only ate and drank with relish (sex was less of a concern in his films and, it appears, in his own life), but dramatised it with relish too. One usually comes out of an Ozu movie wanting to head for the nearest Japanese restaurant. There is at least one well-known Japanese book about food and Ozu films.

Perhaps it was the sheer ordinariness of Ozu's people, rather than their "Japaneseness", that Japanese producers feared would put foreign audiences off. Surely, foreigners preferred to see more exotic creatures, rushing about with drawn swords, wearing colourful kimonos. In fact, Ozu's characters, unlike people in mediocre soaps, are never just ordinary. They are wonderfully, touchingly alive and, for people all over the world, utterly recognisable. In run-of-the-mill home dramas banality simply looks banal. Ozu celebrated the ordinary, the quotidian, the quiet routines of settled human life, not by prettifying or idealising them, but by revealing beauty where we don't normally look for it.

The American director Paul Schrader once wrote a book entitled The Transcendental Style: Ozu, Bresson, Dreyer. He compared Ozu's stillness to the minimalist styles of the European directors Robert Bresson and Carl Dreyer, and found a similar spiritual quality in all three. Another European comparison with Ozu's films might be the still lifes and genre paintings of the 17th-century Dutch masters. Nothing much happens in a Vermeer painting, and yet, in the depiction of everyday life, everything happens.

There is much humour in Ozu's films, but they are most profoundly marked by an atmosphere of bitter-sweet melancholy. The widower in Late Spring left alone in his house, after his daughter has finally got married, sad but resigned to his fate; or the parents in Tokyo Story, whose children are too self-absorbed to spend much time with them, even though the mother is dying – life, inevitably, is full of loss and disappointments, but there is beauty even in sadness. Japanese have an aesthetic expression for this: mono no aware, the tears we shed over the transience of things. It is hard to translate precisely into English, and is frequently cited as a kind of definition of Japanese culture, but it is something all of us can feel.

Ozu's signature technique, too, has often been described as typically Japanese. His camera remains still. There are, except in some very early films, no sweeping pans, no great panoramic shots, or fast tracking shots, or tight close-ups. Ozu dispensed with many conventions of cinema grammar. His takes are often long. You will see a person stand up, walk out of the room, and come back again, all without a cut. He breaks the rules of cross-cutting too, and shows people in conversation speaking straight to the camera, instead of shooting across their shoulders.

There is absolutely no mistaking the typical Ozu style: a stylised, pared-down, constant gaze from the middle distance, with the camera at the height of people sitting on the floor. His camera never looks down on people, or pushes itself into their faces. This meant that the cameraman often had to work in a crouched position, or even lying on his stomach. One might describe Ozu's cinematic gaze as a form of polite, ironic detachment – much like, I imagine, his attitude to real life. He lived with his mother, never married and yet, like Henry James, had an uncanny insight into relationships he shied away from himself.

The paradox of Ozu's films is that they are stylised, yet totally convincing. Realism – and this is true of all traditional Japanese drama – was never his aim, and yet the people feel real. Ozu was famous for making his actors perform the same motion – lifting a tea cup to their lips, say – over and over again until he got the perfect composition. This sometimes exasperated his actors, but there is never anything wooden about their performances. We believe in them and get caught up in their emotions, as though we know them.

Although Ozu's films are timeless, his style invited criticism from a younger generation. Both in content and style, Ozu was regarded by the next wave of film-makers, such as Nagisa Oshima or Shohei Imamura, as hopelessly conservative. He was certainly never political. The so-called "tendency film", favoured by some leftist directors in the 1950s, attacking the class system or capitalism or the American military presence, was of no interest to him. Ozu never sought to improve the world; he simply expressed life in Japan as he saw it.

Not that he didn't see social problems, or the difficulties of a traditional Asian society adapting to western-style modernity. In fact, all his films show that he was very conscious of change. Tokyo Story is a film about the destruction of Japanese family life by modern ways. He was certainly no prude either. In Early Spring (1956), Ozu treated marital infidelity with an honesty and lack of moralism that would have been unthinkable in Hollywood at the time. But these problems, too, he recorded with wry humour, a little sadness and a sharp eye for the subtleties of human behaviour.

Ozu was not a reactionary who yearned to go back to an earlier age. If he was conservative, it was rather in his pessimism about the possibility of rebellion, of the capacity of individuals to change the course of their lives, let alone society. He shows people struggling to break out of their peculiar circumstances, thwarting traditional ways, longing to be free of old conventions. But they invariably end up resigning themselves to their fate, and in such acceptance, Ozu appears to be saying, there is wisdom, and even the possibility of a certain kind of happiness.

This attitude infuriated the cinematic rebels of the 1960s, who deliberately broke away from the Ozu style with violent drama, sexual aggression and political radicalism. The constant camera motion in early films by Oshima or Imamura was partly a Japanese response to the French new wave, but also a quite conscious challenge to Ozu. They recognised him as a cinematic genius, to be sure, but Ozu was also, to them, the reactionary father figure from whom they had to be liberated.

What few people realised, until not so long ago, was how modern Ozu really was. His minimalism, the breaking down of narrative into stylised units, the lack of frills and ornamentation, even the disenchanted, disillusioned quality of his vision, were typical of modernism. True, these same qualities can also be attributed to Japanese traditions: Zen, and all that. But it took a modern Japanese master to see how a traditional aesthetic meshed with modernity. This is why his films still look modern, while more self-conscious attempts to break with past now simply look outdated.