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## Estimating size of Mall crowd

Click on picture for full-size image.

I start with this crop of the widely-posted satellite image.

I create a negated gray-scale version and paint the crowd with
the maximum intensity (i.e. 255) of
either red, green, or blue, depending on the crowd density.

I map all gray pixels to zero.
Then I use an image processing tool to determine the mean of
each channel,
averaged over the whole image.
The number of pixels having a given color is recovered by
solving for x in the relation

mean * image_size = 255 * x
The results are

red: 21845 pixels,
green: 2863,
blue: 2969

Relative to the crowd density in the red areas (density = 1.0),
I have assigned the green areas to be .5 and the blue to be .25.
The effective number of pixels at density 1.0 is therefore

21845*1.0 + 2863*.5 + 2969*.25 = 24018.

This is equivalent to a square 155 pixels on a side.

Using a map, the distance between 3rd Street and 14th Street
is found to be 4772 feet. In the image, the distance is
522 pixels. From these numbers the 155*155 square of pixels
translates to a square 1417 feet on a side, or 2,007,228 square
feet. If we use 2.5 square feet per person as the maximum density,
We compute 802,891 for the number of people in the red, green,
and blue areas combined.

Charles Packer
mailbox@cpacker.org
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