An astonishing feat of cinema presented with the utmost modesty, “Corn Island” observes a hardy old peasant and his obedient granddaughter as they carry out one of the world’s most daunting farming traditions. With just these two central characters, virtually no dialogue and the simplest of settings — a small, almond-shaped sliver of arable land floating midway between the shores of Georgia and Abkhazia — director George Ovashvili crafts a haunting portrait of a place where present-day political conflict and centuries-old survival collide. While far too slow for mainstream viewers, this worthy Karlovy Vary fest winner rewards patient auds with an unparalleled bigscreen experience.

Told in the austere art-film tradition of Kaneto Shindo’s “The Naked Island,” which conveys the punishing experience of trying to raise crops in such an impractical location, Ovashvili’s second feature (after 2009’s “The Other Bank”) makes few if any commercial concessions — and proves all the stronger for it. The story, which spans a single harvest season, begins with the old man (Ylias Salman) testing the quality of the soil on so-called Corn Island and ends a year later with another farmer’s arrival.

Here, depicted with unsentimental dignity, is the heroism of hard work as practiced by characters so marginal as to have gone unrecorded until now. They are nameless, known primarily to us by their faces: His is a weathered mask, difficult to read, hers that of a young sylph on the brink of womanhood, more open and expressive. Every so often, soldiers pass by in small motorboats, and always they stare as if transfixed by her beauty. But most of the time, the girl (played by newcomer Mariam Buturishvili) and her grandfather are alone, left to cultivate this strange no man’s land in peace.

Peace, it turns out, is relatively hard to come by. The island lies in the Inguri River, which forms a natural border between Georgia and the republic of Abkhazia, where secessionists broke away and reclaimed this segment of the country for themselves, brutally driving out the Georgians in the process. What should be an idyllic existence is often punctuated by the sound of gunfire — and not just from the soldiers, either. Local hunters also pose a threat.

And yet, these two unlikely farmers — him too old, her too young — go about their task with unwavering determination. The island itself is barren, so they must bring everything they require from the nearby shore. This is as far away as Ovashvili dares to venture, preserving the mystery of how and where the pair normally live. Like the colonists of an alien planet, they plant their flag on unfamiliar soil and proceed to build a makeshift cabin from scratch, carrying the timber for walls and straw for roof over by boat.

We observe as the old man tills the soil and the girl scatters the corn seeds. On her virgin visit, she arrives carrying a rag doll, but this she quickly sets aside as grown-up responsibilities take precedence. The characters speak so little, our minds fill with questions: Where are her parents? Do other options not exist in her life? More than 20 minutes go by before the first line of dialogue, and another 30 elapse before the next exchange, leaving only enigmas. Still, she seems to understand what is expected of her, tending the wicker fishing trap, curing and drying the fresh catch.

Such actions, so ordinary to the characters, are nothing short of mesmerizing for outsiders. Shooting on 35mm, d.p. Elemer Ragalyi elegantly observes these two utterly convincing actors’ behavior, changing up angles and movements so the relatively enclosed quarters never get stale. And then something happens to upset the quotidian routine: A wounded Georgian soldier (Irakli Samushia) washes ashore, taking refuge among the corn stalks, which now tower above their heads. His arrival forces the old man — who had been Switzerland in the standoff between the Georgian and Azkhazian forces till now — to jeopardize his neutrality, endangering himself to protect and shelter a man he’s still unsure whether he can trust with his granddaughter.

If all this sounds rather simplistic, the logistics of shooting were anything but, rivaling even the most complicated big-studio production. After years of searching for an island that might work, Ovashvili decided to build one from scratch — actually two, one for overhead shots that show this unconventional plot of land in context, and another within an artificial lake, where he had total freedom to maneuver the camera. Then, rather than filming in sequence over the course of an entire growing season, the crew planted, uprooted and replanted corn stalks of appropriate heights for each scene. All told, in terms of sheer arduousness, the characters had it relatively easy compared with those working behind the scenes to orchestrate each meticulously calibrated beat of this powerful parable.