While he has legions of ardent supporters, he's not short of detractors riling against his supposedly shoddy musicianship and unconventional behaviour on stage. After the success of Shine, a scathing review by a New York Times music critic dismissed his recording of the Rachmaninoff Piano Concerto No 3 – his signature piece – as "pallid, erratic and incoherent" while the Sydney Morning Herald's Peter McCallum claimed his popularity was based partly on what he called "the appeal of the freak show".

But, as Helfgott himself would blithely say, no one has yet built a statue to honour a music critic. What is not in doubt is that audiences all over the world love him. He is, by default, Australia's most famous classical music personality. Standing ovations, according to his wife, Gillian, are commonplace, as are the emails he receives from fans who have also been touched by mental illness. (Helfgott has schizoaffective disorder and Shine is essentially a tale of his mental breakdown, recovery and redemption.) Could it be that critics and audiences are listening for – and hearing – different things? While reviewers naturally want to make sure the precious notes of the great composers are in expert hands, and that punters are getting value for money, audiences, thinks Gillian, are paying for something different, they want to be inspired.

She is speaking from the idyllic home the couple share in Bellingen, New South Wales, where Helfgott is standing on the balcony talking to the birds. "Are you having a nice day?" he is asking the water fowl on the lawn below. Due to his condition his wife is doing the interviews promoting his visit to Melbourne where he will play the work that made him famous, the mighty Rach Three.

In Shine, Sir John Gielgud, who plays Helfgott's professor, exhorts the young student to conquer Rachmaninoff's masterpiece – the K2 of piano repertoire – before it conquers him, which it does; he wins a piano competition but ends up in a psychiatric ward. Is not continually playing the piece a bit like jamming a finger into an old wound? "David didn't actually break down when he was playing it, that was a bit of dramatic licence," says Gillian. "Actually, he has never broken down playing a piece of music in 68 years."

The titanic work is known for being relentlessly demanding, physically and psychologically, with vast walls of notes to scale; huge chords and dense textures requiring immense technical virtuosity. That, however, is said to be one of Helfgott's strengths. (A recent, favourable review by a Perth critic paid tribute to his "near faultless" performance of Liszt's Hungarian Rhapsodies).  "David's technique is as brilliant as it was," says Gillian. "His virtuosity is still there. And the Rach 3 is his huge passion in his life. He loves it more than any other piece."

This will be the first time he has played it in Melbourne with just two pianos rather than a full-piece orchestra, accompanied by acclaimed local pianist Rhodri Clarke. (Helfgott first performed it with another pianist at the Sydney Opera House last year.)

Audiences can look forward to his trademark style, which will see him running on stage in a Russian shirt, waving enthusiastically.  At the piano, he is known for muttering and singing along to himself in a manner that purists consider to be a travesty of art, but adored by fans who see it as  a mark of breaking down barriers and  making music accessible to everyone.  In that way he is a Joe Soap's pianist; perfect is in his imperfection, a living example that the musical value of a soloist's work cannot be detached from all other human considerations.

For Gillian, his wife of 30 years, it's his passion which is so infectious. "There are millions of brilliant pianists but that extra passion is something within the soul. No one can teach you that."

Helfgott at 68, she says, is at the peak of happiness. Just like the character Geoffrey Rush so accurately portrayed, he still keeps up a verbal torrent and likes to hug everyone, but is mentally and physically stronger than ever.  Not that he could ever live independently; he is too vulnerable and trusting for that. These days he's involved with mental health charities and recently took part in a research programme looking at the effects of classical music on children with autism. Music fills his life,  along with swimming.

When he appears in Melbourne, he will be without glasses for the first time, thanks to surgery to remove cataracts. After he came home from the operation, says Gillian, he spent ages on the balcony before coming to bed. When he finally joined her, he was glowing. "Darling!" he  said to her excitedly. "I can see the stars!"

David Helfgott performs at the Melbourne Recital Centre on June 21.