“Lantana” opens in that most intriguing of fashions, with the camera panning through thick underbrush to reveal a woman’s dead body. As the film gets underway, we are left to assume the corpse was a vision of what’s to come, and that one of our female characters is destined to wind up dead in the bushes. Who will it be? It piques our interest.

It is not properly a murder mystery, though that does figure in. “Lantana” is primarly a film about the amusing and poignant ways strangers’ lives intersect, and about how we tend not to value what we have until we lose it, or almost lose it.

Leon Zat (Anthony LaPaglia) is a police detective who has heart trouble and is prone to fits of violence. He is having an affair with Jane (Rachael Blake), whom he and his wife Sonja (Kerry Armstrong) know from their ballroom dance class. Jane is separated from Pete (Glenn Robbins) and lives next door to Nik (Vince Colosimo) and Paula (Daniella Farinacci) — the only happily married couple in the film.

Sonja knows her marriage is in trouble, and she’s seeing a psychiatrist named Valerie (Barbara Hershey). Valerie’s 11-year-old daughter was murdered two years ago, and she’s written a book about the experience — a deed her husband John (Geoffrey Rush) does not approve of. Their marriage has been in the rubbish heap since their daughter died, and now Valerie thinks John may be having an affair with her gay patient Patrick (Peter Phelps).

All of these relationships and indirect connections become relevant in light, playful ways, and then more seriously when someone turns up dead. What do men like John and Leon have to live for anymore?

The writer is Andrew Bovell, based on his play “Speaking in Tongues.” That title is more useful than “Lantana” is. “Speaking in Tongues” suggests the story’s theme of communication within relationships, while “Lantana” is a thick, bushy shrub — presumably where that corpse was found. It is more metaphorical now: The seeds of skepticism have grown into a full-blown jungle of mistrust and fear among the characters. Without breaking through that obstacle, none of these people can be happy.

Director Ray Lawrence keeps things on an even keel, coaxing solid performances from all the leads and maintaining a brisk pace. These are, for the most part, believable and honest characters, though I’m not sure they always behave the way they would in real life. “Lantana” does not penetrate the heart the way it ought to, but it certainly make an impression.

B (; R, frequent harsh profanity, some very strong.)