After having its debut in 1975, the Australian film “Picnic at Hanging Rock” confounded audiences and critics alike with its story of the disappearance of three schoolgirls and their teacher while on an outing. Some viewers attempted to parse out its gauzy mysteries while others cried frustration with its lack of resolution. 

Despite this initial disparity in reaction, the movie is now considered a classic and, along with the book on which it was based, inspires creative interpretations to this day, such as Netflix’s 2018 miniseries and several theatrical works, including a forthcoming stage musical. 

The IFC Center starting Friday will be screening a new 4K restoration to commemorate the film’s 50th anniversary, offering those who haven’t experienced its strange rhythms and ellipses the chance to see it on the big screen for a first time. Those who have now get the opportunity to dive into its haunting atmosphere in gloriously updated detail. Arriving on the heels of David Lynch’s death, the revival also provides the chance to muse over how the film’s director, Peter Weir, may have influenced some of the American director’s seminal work, including “Twin Peaks.”

Its story is both easy and difficult to pin down: On Valentine’s Day 1900, a group of girls heads to a popular geological site in southeastern Australia with two school chaperones, Miss McCraw and Mlle. de Poitiers. After tea and cake, four girls decide to take a hike; two of them, Miranda and Irma, are in middle to late adolescence and the other two, Marion and Edith, are younger. Along the way, as they traipse higher and deeper among Hanging Rock’s volcanic formations, they begin to fall into a sort of sun-baked trance. 

Edith, frightened, tired, and parched, runs back down as the three continue their ascent. Later in the evening, back at their boarding school, we find out that the trio, along with Miss McCraw, who was seen hiking up, are missing.

From this point, the film becomes a missing-persons case, though scenes involving the police investigation and a search party don’t seem to interest Mr. Weir much. What he does focus on is the disappearance’s effects on the school, its headmistress, Mrs. Appleyard, and on two boys, Michael and Albert, who watched the missing girls as they began their trek and even followed them for a while. They end up finding Irma near where we last saw her: Alive but unconscious, she later explains she has no memory of what happened to her or the others. 

Running parallel to this storyline are scenes involving Sara, a quiet, headstrong orphan at the school who was intensely close to Miranda but wasn’t allowed to go on the field trip. Her guardian has been remiss with payment of the school’s fees, and Mrs. Appleyard decides to send Sara back to an orphanage. What ends up happening to her is tragic yet also enigmatic considering the last time we see the girl alive, she smiles.

Several movies and books come to mind while watching, including Sofia Coppola’s “The Virgin Suicides,” which was based on the novel by Jeffrey Eugenides. Michael’s obsession over the missing girls mirrors how Ms. Coppola’s 1999 picture is framed by the male memories of five tragic sisters. Furthermore, Russell Boyd’s hazy cinematography and creamy colors surely influenced Ms. Coppola’s entire oeuvre. With its ambiguous occurrence in a wild, scenic setting, one also wonders if the original novel written by Joan Lindsey drew inspiration from E. M. Forster’s acclaimed 1924 book, “A Passage to India.” Additionally, Antonioni’s 1960 Italian masterpiece “L’Avventura,” with its unresolved disappearance, seems related.   

The work of David Lynch, though, is what is most evoked with the film’s haunting look at pretty young women, its talk of “secrets,” and its techniques of overlapping imagery and evocative sound design. Even Mr. Weir’s use of the same musical motifs multiple times comes off as proto-Lynchian, with the later director’s reliance on composer Angelo Badalamenti’s melodies complementary. Then there’s the evocation of dreams in “Picnic at Hanging Rock,” such as when we hear one of the girls recite a line of poetry by Edgar Allen Poe: “A dream within a dream.” Nothing could describe the American master’s particular art better.

While it’s unclear whether Mr. Lynch ever spoke of the film’s influence on his output, there is little doubt that Mr. Weir is also a master director. After “Picnic at Hanging Rock,” the now 80-year-old would go on to direct bigger movies in the next decades, great ones like “The Year of Living Dangerously” (with Mel Gibson), “Witness” (with Harrison Ford), “The Truman Show” (with Jim Carrey), and “Master and Commander: The Far Side of the World” (with Russell Crowe), among others. 

Despite those movies’ male-centric narratives, they do share a few elements with the earlier film, such as their explorations of restrictive societies and dangerous environments. Ultimately, though, the picture stands out within Mr. Weir’s filmography and the history of Australian cinema for its cryptic singularity — a beautiful fever dream wrapped in an enigma, casting a spell on viewers with its disquieting allusions and sunstroke revelries.