"I insist on astonishment," said Graciela Iturbide (b. 1942). To make photographs more astonishing than those of Graciela Iturbide would be a challenge, indeed. Not more shocking. That is a different impulse and this Mexican photographer does not stoop to conquer; instead, she visually embraces her unusual subjects, especially those operating outside the norm. Of course, the norm in Mexico is always in question and there are abundant opportunities there to take pictures of the outrageous and bizarre. Such works are common to the point of cliché. Iturbide is the exception as she composes her pictures with compassion.

"Danza De La Cabrita / The Goat’s Dance" at the J. Paul Getty Museum in Los Angeles is the artist’s first survey in this country. Organized by Getty curator of photographs Judith Keller, the show highlights Iturbide’s acclaimed 1979 photographs of the woman of Juchitán, a Zapotec Indian village in a remote area of Oaxaca that is largely matriarchal. While the men work in fields or labor, the women control the marketing of goods and therefore the economy. Iturbide, who spent six years taking the photographs, was invited there by the Mexican artist Francisco Toledo, a leading activist in recognizing and preserving the culture of the pre-Hispanic peoples around Oaxaca.

Iturbide photographed the Juchitán women, who tend towards enormous girth, wearing the traditional outfits of the Tehuantepec region, embroidered smocks, layered, ruffled skirts in many colors while adorned with gold necklaces and earrings. This is the outfit of such symbolic power, signifying the integrity of indigenous culture, that it was appropriated by Frida Kahlo and worn by her in the bustling streets of Mexico City. The Juchitán women appear proud, amused, unapologetic about drinking beer out of the bottle and eating generous portions. They are a study in strength. Iturbide’s best known picture is that of a woman who is wearing a crown of living iguanas on her head. She had sewn their mouths shut and carried them to market to sell them for the iguana stew that is considered a delicacy in that area. She stares at the viewer, and photographer, defiantly as though daring anyone to confront her about her strange headdress.

As bold as the pictures of women are Iturbide’s photographs of the transvestites. These pictures of young men swishing about in their finest array in the village’s humblest locations offer a special poignancy.

The Getty has published Juchitán, a catalogue of these pictures with an insightful essay by Keller. The exhibition of 140 pictures, however, is an overview of Iturbide’s career and it reveals themes that have emerged over the past 30 years. Many were drawn from the museum’s holdings but also from the collection of Daniel and Susan Steinhauser, who have promised many of them as gifts to the museum.

Iturbide, now 65, was raised in a prosperous Mexico City family, married at 19 and had three children. She also began studying filmmaking at the Centro Universitario de Estudios Cinemagraficos in Mexico City. After her six-year-old daughter died suddenly in 1970, she switched to study still photography. Her teacher and mentor was photographer Manual Álvarez Bravo, creator of numerous iconic images of Mexico. With his guidance and support, she was able to channel the grief over the loss of her child into creative efforts as a photographer. She later divorced and pursued photography as a career. Álvarez Bravo encouraged her to photograph the country’s culture outside of Mexico City, especially the Indian communities that he had celebrated in his own work.

Soon, Iturbide annealed formal elegance with an eye for subjects of questionable appeal. Her photographs have a steely edge yet she also evinces compassion for subjects. She asks permission to take her pictures rather than simply snapping away.

For example, in 1986, she came to Los Angeles to take photographs for a book, A Day in the Life of America. Her photographs of the cholas of East L.A., with their ratted hair, white t-shirts and baggy trousers, capture a pride and spirit similar to that of the women of Juchitán. In one photograph, they pose under a mural of Pancho Villa and other Mexican heroes, none of whom they recognized. Since the great revolutionaries were painted wearing sombreros, they thought they were mariachis. That certainly says something about a day in the life of a Mexican American. She also photographed La Frontera, the fenced border at Tijuana, chronicling the visual obsession with the Virgin of Guadalupe.

The series that inspired the title for the show concerns the annual Mixteca ritual of slaughtering of goats on private haciendas in northern Oaxaca. Iturbide’s pictures contrast serene, determined women doing their grisly jobs of butchering and flaying. A single goat is saved and crowned in a symbolic connection to the Christian story of salvation.

She recently photographed varieties of cactus and other plants that were saved to be arranged in a Oaxaca botanical garden, another civic improvement conceived by Toledo. The plants were imported from the wilderness in special containers. They were held in place by cords and burlaps packing to protect them. Iturbide’s photographs of El Jardín, the garden, seem emblematic of her larger mission. The cacti are inviting yet covered in rows of thorns. Iturbide clearly is attracted to the dangerous side of beauty.

"Danza de la Cabrita / The Goat’s Dance: Photographs by Graciela Iturbide," Dec. 18, 2007-Apr. 18, 2008, at the J. Paul Getty Museum, 1200 Getty Center Drive, Los Angeles, Ca. 90049

HUNTER DROHOJOWSKA-PHILP is author of Full Bloom: The Art and Life of Georgia O’Keeffe, published by W.W. Norton.