TSC-100, with a Canon 12:1 servo zoom lens, and it records 410,000 pixels with seven hundred horizontal lines. That’s a lot more than the average camcorder, some have fewer than 300,000 pixels on the image sensor. He had some pretty specialised equipment.”

Howard nodded. “He was a real-estate salesman, he used it to make videos of properties he was selling.”

“Ah, that explains it,” said Bonnie. “We’re lucky he had it, because anything less powerful and we probably wouldn’t see half the details we have. You can make that pixel as large as you want, it’ll still be one unit. You’ll just have a big pixel. What neighbourhood averaging does is to smooth out the image by taking an average of the colour and brightness of individual pixels in a predefined area. There was an improvement in the clarity of the images, but the edges blurred and we actually lost some detail, which was to be expected. Median filtering is a similar computer technique, but it uses a median value instead of an average value. It’s a small difference, but a significant one. I ran through a three-by-three neighbourhood and then a five-by-five, right on up to a nine-by-nine. For the worst areas I’d like to use the technique I mentioned, pixel aggregation. You choose a pixel which has properties you can clearly identify in terms of colour or texture and then you gradually move outwards, adding to it pixels of matching qualities, until you grow a defined region. That produces clusters of matching pixels, which can then be highlighted. I’m afraid it’ll take me quite a while with the equipment I have.”

Howard continued to go through the photographs as he listened to Bonnie’s explanation, most of which went way over his head. One of the pictures showed a row of bald, naked figures. “What are these?” he asked.

“Yes, I’m quite proud of those,” she said. “You could barely see them in the original, and the camera only picked them up once, but they’re there all right. They’re what the snipers are aiming at. Four dummies. The sort used in shop window displays.”

Howard put two photographs on the bench. They showed two sedan cars and a large flatbed truck. “I didn’t see these in the video,” he said.

Bonnie nodded eagerly. “They were only there for a few seconds, when the plane was spinning. The quality isn’t good, but you can see the colour and make. They’re Chrysler Imperials, one blue, one white. The truck I’m not sure about. Could be a Dodge.”

“That’s good, really good,” said Howard. He made a mental note to ask the Sheriff’s Department about tyre tracks at the scene.

The next set of pictures showed a group of three people standing together, a middle-aged man with a paunch, a young man, and a woman. The older man was holding something in his hand. There was a magnifying glass on the bench and Howard used it to examine the object.

“It’s a walkie-talkie, I think,” said Bonnie. “I assume he used it to keep in contact with the snipers.”

“Is there any way of magnifying the photographs any further?” Howard asked.

Bonnie shook her head. Her long braid swung from side to side like a rope. “I’ve taken it as far as I can,” she said. “I can make the images bigger, but I don’t have the software necessary for the sort of filtering that would make them any sharper. You should try one of the Japanese firms. Sony, or Hitachi. They should have the computers geared up for it. Or you could try firms working on artificial intelligence or robotics.”

“Robotics?” queried Howard.

“Robotics companies are big on artificial intelligence, and that’s the sort of expertise you’ll need. The pictures can be cleared up further by the application of algorithms using what are called the Hough Transform and Fourier Transform, and I can tell you which experts would be able to do that. A computer with some form of artificial intelligence could compare adjoining pixels and correct for abnormalities based on an assumption of what it’s looking for.”

Howard frowned. “I don’t follow.”

“Well, if the computer knows it’s looking at a face, it will know that an eye has a certain shape, so has a nose, so has a chin. It has to know whether a dark patch is a moustache, a nostril, or the pupil of an eye. It has to know that human bodies are made up of curves, but that mechanical objects are usually flat surfaces. If it’s looking at a licence plate, for instance, it must know to look for numbers and letters and not abstract shapes. I’m sorry, Agent Howard, I’m not explaining this very well.”

“Cole,” he said, “please call me Cole. And you’re doing just fine. Actually, I know someone who has access to the sort of technology you’re talking about.”

“Really?” she said. “Who would that be?”

“Clayton Electronics.”

Bonnie raised her eyebrows. “They’re good. Of course, their head office is in Phoenix, I’d forgotten. Why didn’t you go to them first?”

Howard stacked the photographs together and slid them back into the file. “We wanted to keep it within the FBI as much as possible. You’ve seen the video, you know what the implications are.”

Bonnie lowered her eyes and her cheeks reddened like a guilty schoolgirl. Howard wanted to ask her what was wrong but felt that she’d shy away from such a direct approach. He waited for her to tell him what was troubling her.

“I had an idea,” she said, still avoiding his eyes. “Well, not my idea, really. It was my husband’s.”

“Your husband?”

She nodded and raised her head. “He’s a mathematician. A PhD. He specialises in computer graphics.”

Howard was bemused, but he listened attentively. Bonnie Kim was clearly very intelligent and anything she had to offer on the case could only be of help.

“I was explaining about the video, about the three men with rifles and the towers, and he said it would make an interesting computer model. You could program the coordinates of the men and the targets, and get a 3-D structure representing their positions.”

Howard understood why she’d been embarrassed. She’d told her husband about the video, and was now worried she’d breached security. He wanted to tell her that it was okay, but he didn’t want to interrupt her. Her eyes were shining with enthusiasm. “You work out the heights of the towers, you calculate the angles and distances to the target, and then you superimpose that model on all the different venues where the target is due to appear.”

Howard tapped the file with his fingers. “He could do that?”

“He could do the preliminary work, sure. I haven’t shown him the video, but if I did he could put together the model, he said. He’d need to know the exact time of day the video was shot, so that he could use the shadows to determine heights and so on, and he might have to go out to the site to make some measurements, but yes, he could do it.”

“What about the venues? How would he get those into his computer?”

“You’d need street plans and the heights of the various buildings. He could customise a program for you, but it would take a lot of work to input the information. Once it’s in, though, the program would produce a 3-D model of the area, and it could then superimpose the snipers and target on it. It would tell you if the snipers were preparing for that venue or not. And if the models do fit, it’ll tell you exactly where the snipers will be. It’s a brilliant idea.”

Howard smiled. “It is. Your husband’s a very clever man. We do have one problem, though. At the moment we don’t know who the target is.”

Bonnie’s mouth opened, showing perfect white teeth. “Oh. I just assumed. .”

“That it was the President?”

She nodded. “You think it’s someone else?”

“Bonnie, we just don’t know. But your husband’s idea is a good one. We know the President’s itinerary well in advance; if he can set the program up for us, I can bring in extra manpower to do the inputting.”

“So I can tell him to go ahead?”

“Sure.”

Bonnie positively beamed. “He’ll be so pleased. He thinks it’ll be like a detective story. He suggested I ask you to come to dinner with us, tonight. I’ll cook, and he can go over the details with you.”

It was an offer Howard couldn’t refuse.

Andy and Bonnie Kim’s house was a spacious single-storey ranch house in a quiet suburban road to the north of Washington. The grass was neatly cropped, the paths were edged with orderly flower beds and the Stars and Stripes fluttered from a white flagpole. Two cars were parked outside when Howard arrived: a Buick Roadmaster

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