Washington, D.C., February 2009 -- A crowd of historic proportions turned out to watch the inauguration of Barack Obama on January 20. And for the first time ever for a Mall event, an overhead photograph was released so that you and I can estimate the size of the crowd, just as the "experts" would.

Here I apply simple digital photo processing to that image and a little arithmetic to show one way they would have arrived at a serious estimate of about a million, the number cited by the Washington Post and New York Times. Then I discuss why this estimate is probably too high. (Pure fantasy is the figure of 1.8 million put out by the D.C. mayor's office, subsequently rounded up to two million in retelling by celebrities and some journalists.)

It's essential to be looking directly down on the gathering to arrive at an accurate estimate. Photographs taken at oblique angles result in foreshortening that makes a crowd look denser than it is.

For example, in this image notice the open area opposite the Smithsonian Castle between the two large populated elliptically-shaped areas. It's impossible to tell that it is nearly as wide as one of those groups, a fact that can be seen clearly in the overhead view.

I mark each part of the crowd with a color depending on how dense it appears to the eye. Here I've used three colors: red for the highest density, green for middle density and blue for the lowest.

Then I determine how many pixels have been assigned to each color. The mechanics of this process and relating the pixel count to square feet on the ground to arrive at an estimate of the crowd size are covered in the details page. One thing is immediately apparent in this image: most of the crowd area (79 percent, in fact) is colored red, the hightest density. This means that the final estimate depends heavily on the value we choose for that density.

Initially, I used 2.5 square feet per person. This is the value used by the experts cited as authoritative by the Post and Times. If I assign half that density -- that is, 5 square feet per person -- to the green areas, and one quarter, or 10 square feet per person, to the blue areas, I compute about 802,000. For the Capitol grounds area, I followed the practice used by the experts and simply assigned the value of 240,000, the number of tickets issued, even though many ticketholders were delayed in getting into that restricted area. The sum of these two numbers is about 1.04 million, which is not far from the experts' estimate of about a million.

A crowd density of 2.5 square feet per person is a tightly packed condition where you would barely be able to raise your arms. This area, as the newspapers (fittingly) described it, is about the same as the area of an unfolded newspaper. Photographs posted on the Web taken by people at the scene do show crowding of this density -- in areas where people were pressing against a barricade. In pictures taken from further back within, people's heads appear to be three feet or more apart.

Inspection of the original satellite photograph (top figure in this page) shows that even in the high-density areas -- the areas that I marked red -- the green grass of the Mall and the light gravel of the walkways show through faintly. In other words, there is open space visible. Since the resolution of the satellite camera is said to be about 17 inches, for a pixel to be the color of the ground, there would have to be an open area of 17 inches on a side, or about two square feet.

Therefore, a more realistic estimate of the density of the areas marked red is four square feet per person, the value the Park Service used for crowds before it stopped issuing size estimates. If we apply that number to the inauguration crowd we get about 508,000 instead of 802,000. Combined with the assigned count of 240,000 from the Capitol grounds, our total for the Mall crowd would be 748,000.

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Charles Packer mailbox@cpacker.org