October 10, 1995

CALIFORNIA COMPANY USES CALCULUS TO PIN THE CRIME ON THE CRIMINAL

By ROBERT LANGRETH
The Wall Street Journal

The two men were on trial for murder. Convictions might have been easy: A gas-station security camera had filmed the whole tussle, culminating in fatal gunshots. But the videotape was so blurry that no one could really tell who attacked whom. The two argued self-defense, and the Los Angeles County jury hung.

So local detectives turned to Cognitech Inc., a tiny company armed with a powerful new technique for enhancing fuzzy images. Cognitech's improved video clearly showed the suspects pinning the victim face down against the ground and firing into his skull. Both defendants eventually pleaded guilty.

In the past two years, analyzing crime and accident videotapes has blossomed into a full-time business for Cognitech, based in Santa Monica, Calif. It is among a handful of companies applying sophisticated mathematics to clearing up crime and accident videotapes.

Before these companies existed, police trying to enhance poor videos had to buy commercial "photoshop" software, which generally processes one frame at a time and is limited to simple operations such as improving contrast. Or they could send their videotape off to the Federal Bureau of Investigation's crime lab in Virginia, which often takes months to analyze videos. Thus companies like Cognitech "are filling a void," says Dave Brougham, deputy district attorney of Los Angeles County.

Cognitech's technique may give it a leg up on the competition. Based on a branch of calculus known as nonlinear differential equations, the technique "smooths out" static and other distortions in an image, while retaining the sharp edges that define key features of faces or objects. In contrast, previous techniques for cleaning up video tended to leave featureless blobs.

Cognitech founder Leonid Rudin makes an unlikely expert witness. A Jewish political refugee from the former Soviet Union, he came to the U.S. in the late 1970s to study computer science at California Institute of Technology. Among other things, he studied nonlinear differential equations used by physicists and engineers to mathematically describe sonic booms and other types of shock waves traveling through fluids. As opposed to simpler, "linear" equations, these shock-wave equations are particularly good at describing things with sharp edges or boundaries.

It occurred to Mr. Rudin that the shock-wave equations might also be useful for enhancing images. In his doctoral thesis, he proposed a method of improving images by assuming that the actual edges of objects or faces obscured beneath a blurry picture could be described by shock-wave equations. By finding solutions to these equations, one would remove distortions and other noise, without also wiping out important features.

Essentially, the differential equations assume both a logical outline for the sharp boundaries within each frame and the nature of distortions caused by poor focus, atmospheric refraction, electronic noise and other factors that blur an image. The computer then solves the equations over and over again with each successive solution refining the assumed boundary curves.

The technique is roughly analogous to taking a satellite photo of the earth and trying to draw in topographic lines representing major geologic features. In this case, the "topographic lines" are the edges of objects, as represented by major changes in color or brightness. As the computer does this over a period of seconds or minutes, "the image, slowly, slowly gets better defined," Mr. Rudin says.

His thesis attracted the attention of mathematician Stanley Osher at the University of California at Los Angeles, and the two formed Cognitech to explore uses of the technique. Initially, the company's work focused on military applications. But Mr. Rudin had always been fascinated with forensic science, and a now-famous beating caught on videotape gave him a chance to indulge his interests.

At the height of the 1992 Los Angeles riots, cameras in TV-news helicopters videotaped a white truck driver, Reginald Denny, being pulled out of his truck and severely beaten by several black men. Defense lawyers for one of the main attackers contended the videotape was too poor to link it to their client. But Cognitech's analysis disclosed a dark patch on the attacker's left arm in exactly the same location as a tattoo on the defendant's arm. The defendant was convicted.

Since then, business has been brisk. Cognitech's 12-person staff handles eight to 10 cases a week, at a price of several thousand dollars per case, from a small office in Santa Monica. One room is jammed with video gear for converting tapes from detectives and other clients to digital format. The actual enhancement work is done on computer workstations at employees' desktops.

On a typical day, Mr. Rudin prowls the office looking over employees' shoulders as they analyze videotapes, asking questions and making suggestions. For particularly stubborn videotapes, the indefatigable Mr. Rudin often stays late into the night adapting computer programs to do that type of image better.

Cognitech isn't alone in the expanding video-enhancement field. Another small company, Trec Inc. in Huntsville, Ala., sells software for enhancing videotapes to the FBI and other law enforcement agencies. And Aerospace Corp., a nonprofit military-research agency, recently started a small unit to analyze crime videotapes. It now handles a couple of dozen cases per year.

Neither the FBI nor Trec will comment on their enhancement techniques. Aerospace, for its part, says a variety of standard mathematical methods for improving images serve it just fine. "Standard image enhancement is a whopping field," agrees Massachusetts Institute of Technology electrical engineer Alan Willsky. He adds that "the jury's still out on the overall impact" of Cognitech's method.

In any case, all sides expect their caseloads to increase, as more businesses buy sophisticated video-security systems. Cognitech, for example, has expanded its work to investigations of industrial accidents and even military jet crashes.

The ultimate goal, officials at both Cognitech and Aerospace say, is to develop fast, user-friendly software for sharpening videos. "Our dream is to have real-time video processing," Mr. Rudin says. "A detective would put a poor tape in one end of a machine, and at the other end the enhanced video would come out."