Correction: Some versions of this article incorrectly said that 6 million people a day view the Mona Lisa. The Leonardo da Vinci painting, at the Louvre in Paris, is viewed by about 6 million people a year. This version has been updated.

Four-and-a-half months after she was charged with trying to tear a Gauguin painting from a wall in the National Gallery of Art — and just three weeks after she was released from St. Elizabeths Hospital — a Northern Virginia woman was arrested in a similar assault on a work by Matisse at the museum.

In both cases, the works were unscathed. But the ease with which Susan J. Burns, 53, allegedly approached and manipulated the paintings spotlights one of the museum community’s greatest dilemmas: How can arts institutions protect cultural masterpieces without hurting the intimate viewing experience?

In the high-tech, post-Sept. 11 age, art museums conduct bag searches and use 24-hour security cameras, motion detectors and Art Guards — palm-size alarms that sit on the backs of paintings and emit a high-pitched screeching sound if the artwork is lifted off its hook.

“But there’s little that can ultimately prevent someone from vandalizing a painting if they really want to,” said Bill Anderson, co-founder of Art Guard, which services the National Gallery of Art and other museums nationwide. “The sad paradox is that to really protect it, you need plexiglass. But if you put it under glass and behind ropes, you might as well just show it in a catalogue.”

The FBI’s Art Crime Team and the Association for Research Into Crimes Against Art track stolen art but don’t collect data on vandalized art.

Such vandalism occurs around the world. Defacement is often a form of religious or political protest, said Robert Wittman, the retired founder of the Art Crime Team and vice chairman of the security committee of the American Association of Museums. The destruction of cultural property falls into this category, as when the Taliban blew up two colossal Buddhas of Bamiyan in Afghanistan.

History’s most infamous attacks on artworks were carried out by Hans-Joachim Bohlmann, the “serial art vandal.” For several decades, beginning in the 1970s, Bohlmann defaced more than 50 paintings at public exhibitions, often with sulfuric acid, including works by Rembrandt, Rubens and Dürer, inflicting about $180.3 million in damage. (He ultimately received a diagnosis of mental illness.)

Most art vandalism — like most art theft — is mundane. “It’s not like people going in on wires like ‘Mission Impossible,’ ” said Wittman, who wrote a book, “Priceless,” about his swashbuckling undercover career recovering stolen art. “Sometimes it’s people with spray paint, lipstick, hammers, literally pencils. But the main thing to prevent defacing art is to put art behind plexiglass and velvet rope.”

But security can be a balancing act for museums that want to retain the spirit of accessibility, said Peter Mroczkiewicz, deputy director of the office of protection services at the Smithsonian Institution. “When you go to the Louvre and see the Mona Lisa behind the plexiglass, it’s really tough for a true art lover who wants to be able to see the brush strokes,” he said.

“As a professional, I would like to see everything under plexiglass,” he noted wryly. “But we understand that’s not always the way to go.”

The Mona Lisa, one of the world’s most iconic artworks, is behind bulletproof glass at the Paris museum. It was stolen on Aug. 21, 1911, and was missing for two years before a Louvre employee was caught trying to sell it to an Italian museum. It also has been attacked at least four times — with acid, with a rock, with red paint and even with a teacup, which was purchased at the museum and hurled by a Russian woman angry that she had been denied French citizenship.

Art insurance companies such as AXA Art Insurance are pushing museums to employ more protections against vandalism — recommending specialized training for guards and the latest in motion detectors.

“When I heard [the National Gallery suspect] attacked a second time, I was like, ‘Oh my gosh,’ ” said Robert Pittinger, AXA’s director of underwriting. “We always have to be concerned about preserving art for future generations. In this case, we were lucky it wasn’t damaged.”

Mike Kirchner, director of security for Harvard Art Museums, says the first line of defense is alert guards and museum employees.

“Everyone has to start a relationship with a smile, a nod, a good morning with people coming into the museum,” he said. “You can scan the crowd, you can try to look for people who don’t want to make eye contact. Everyone should always be on alert.”

The National Gallery declined to comment on Friday’s attack because the incident is under investigation. According to D.C. Superior Court records, Burns, who has schizophrenia, is under observation at St. Elizabeths. Nonetheless, some guards at the museum said Sunday that they had photocopied her mug shot and put it in their coat pockets.