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In the talk after the movie, the three legends delved into the story behind one of the film's landmark scenes: the "You talkin' to me?" line De Niro's character Travis Bickle gives to himself in the mirror.
"A key improvisation in the movie was Bob in the mirror," Scorsese told the crowd, referring to De Niro's delivery of the line.
De Niro made up the entire sequence of Bickle talking to himself on the spot.
As Schrader pointed out, he wrote a vague description of what would go on in the scene.
"The script said he looks in the mirror and plays like a cowboy, pulls out his gun, talks to himself," Schrader said. "So Bob called me and said, 'What does he say?' and I said, 'Well, act like you're a kid and you got that little holster and cap gun and you're standing there.' He took it from there."
At that point in the movie, Bickle has purchased a small arsenal of handguns and plays out what he's going to do to clean up New York City.
Walking to the mirror, he mimics an altercation by saying, "You talkin' to me? ... Well, I'm the only one here." And then he pulls out the gun he has in his sleeve.
The moment has been repeated countless times since the movie opened in 1976.
The quote was recently ranked number eight in The Hollywood Reporter's list of 100 favorite movie quotes of all time.
Before Thursday night's screening, De Niro had some fun with the line.
Introducing the film with his fellow founder of the festival, Jane Rosenthal, De Niro said, "Forty f---ing years, one of you have said it to me... so let's get it out of our system now."
He then had the crowd at New York City's Beacon Theater repeat, "You talkin' to me?" at once.