Crowd Science

Module 7, lesson 6 · 50 minutes

Counting crowds from images

How to estimate a crowd’s size by zones, density and area; how Still and Altenburg counted two crowds in Washington in January 2017; and where the error really comes from.

You’ll be able to

  • estimate a crowd by dividing it into zones and multiplying each zone’s area by its density;
  • explain the method behind the 2017 inauguration and Women’s March estimates, and their numbers and caveats;
  • name the main sources of error and judge which matter most.

Introduction

In January 2017 a new US president was inaugurated in Washington, and within days the Women’s March filled much of the same city. How many people were at each became, briefly, a political argument. On 22 January the New York Times published estimates made with two crowd scientists from Manchester Metropolitan University, Marcel Altenburg and Keith Still: about 160,000 people in the inauguration areas in the hour before the speech, and at least 470,000 at the Women’s March at about 2 p.m.

Those numbers were not head counts. They came from a method you can learn in an afternoon and apply to any photograph with a known scale: divide the crowd into zones, estimate each zone’s density, multiply by its area, and add up. The method is simple. Doing it well is not, and the interactive in this lesson is designed to show you why.

Zones × density × area

A crowd is rarely uniform, so a single density times the total area will be wrong. Instead, split the occupied ground into zones that each look roughly uniform, and estimate each separately:

N ≈ Σ Aᵢ · ρᵢ (sum over zones of area × density)

Aᵢ
area of zone i, m²
ρᵢ
estimated density in zone i, p/m²
N
estimated number of people

Still describes the method as built on his RAMP analysis (lesson 2), with areas measured from aerial imagery in Google Earth Pro, and two ways of filling in each zone: “a count or a density check”. A count means counting heads; a density check means judging each zone’s density and multiplying by its area.

Two methods, one photograph

The two approaches can check each other. Applied to a photograph of the US Capitol from Abraham Lincoln’s era, they gave “between 7,050 (areas x packing density) and 7,350 (head count)”: a difference of about 4%, and a reminder that even a careful head count of a single photograph has uncertainty.

Washington, January 2017

For the inauguration, Still writes that images came “live from 7 different video feeds… at the 45 minutes before the Oath of Office”. Both counts used the RAMP technique “coupled with the car park data and metro ridership information”. The densest areas were isolated at “an average density of 2.5 people per square meter”, and the results were described as conservative estimates, not complete counts.

The two Washington estimatesAs published in the New York Times, 22 January 2017, with Altenburg and Still.
CrowdWhenEstimate
Presidential inaugurationThe hour before the speechabout 160,000
Women’s MarchAbout 2 p.m. (window 1:30–2:15 p.m.)at least 470,000

Two observations from Still stand out. First, the empty ground: “2/3rds of the area in the 2017 inaguration [sic] event are empty”. An estimate that treated the whole Mall as occupied would have been three times too high. Second, his Times Higher Education article put the inauguration crowd at about one-third of Barack Obama’s 2009 crowd and the Women’s March at three times the inauguration; it also noted that a safe density is normally “two people per square metre”, and that a reported “1 million” in Times Square is “usually a tenth of that number”.

As a check on the scale (our arithmetic), 160,000 people at an average of 2.5 p/m² would occupy 64,000 m², a little over six hectares of densely filled ground. At 2 p/m², the same ground would hold 128,000. Small differences in the density assumed move the answer by tens of thousands.

The often-quoted figure of 1.8 million for the 2009 inauguration is not a Still and Altenburg estimate, and this course does not attribute it to them. Their comparison was a ratio: about a third.

Where the error comes from

Every term in N ≈ Σ Aᵢρᵢ can go wrong.

  • Density by eye. Crowds “rarely pack in regular formation”, and low camera angles make them look denser (lesson 5 shows why).
  • Zone boundaries. Where a dense core thins into a fringe, the line you draw decides how much sparse ground is counted at the dense rate.
  • Empty areas. Fountains, trees, stages, roads and simple gaps inside an apparently full area. Two-thirds of the inauguration area was empty.
  • Time. A photograph is a moment; crowds come and go. That is why the 2017 estimates were tied to specific times.
  • Movement. A marching column is blurred in video, and the people in it are somewhere else a minute later.

Automation helps with some of these. After 2006 the Jamarat Bridge used automated camera counting, which counts people crossing a line rather than estimating a standing crowd. The interactive below lets you find out which errors matter most, by making them yourself.

  1. Start with level 1. Draw one zone over the crowd, pick a density from the reference squares, and reveal the truth. How close were you?
  2. Move to level 2 and click “Hide the truth” if it is showing. Draw your zones, then use up to five 5 m sample squares (change the tool) to check your density guesses. Reveal and read the table: which row holds most of your error?
  3. Keeping your densities, redraw only the zone edges to hug the crowd more tightly and leave out the fountain, trees and stage. Watch the error change.
  4. Try level 3, where a marching column on the road is blurred by movement. What do you do with it?
  5. Press “New scene” and try to get within 10% using no more than three zones and five samples.

Most of the error usually comes from the zone boundaries and the empty ground inside them, not from the dense core. A good density guess applied to a badly drawn zone is a bad estimate. That is why Still’s observation that two-thirds of the inauguration area was empty mattered so much.

How Still and Altenburg did it: RAMP analysis; areas measured in Google Earth Pro; zones at an average of 2.5 p/m² in the densest areas; images from seven video feeds in the 45 minutes before the oath; car park and metro ridership data as a cross-check; conservative estimates, not complete counts. The scene here is generated, fictional and seeded: every dot is a person, so the truth is exact. Where your zones overlap, the later one replaces the earlier. You can also add zones and samples by typing coordinates.

A square of 10,000 m² is photographed from above during a rally. You estimate the crowd at 2.5 p/m² across the square and get 25,000. A colleague points out that a third of the square is a fenced lawn, a fountain and an empty road, and that the edges of the crowd are at about 0.5 p/m² over another 2,000 m². Re-estimate.

Occupied area = 10,000 − 3,333 ≈ 6,667 m². Of that, 2,000 m² is fringe at 0.5 p/m² (1,000 people) and 4,667 m² is core at 2.5 p/m² (about 11,700). Total ≈ 12,700, about half the first estimate. Nearly all the correction came from the empty ground and the boundary, not from the core density.
  • “Counting a crowd means counting heads.” For large crowds the practical method is zones × density × area, checked against sample counts and other data.
  • “The densest part is where the error is.” Usually the larger errors are in where the zones end and in the empty ground they include.
  • “A crowd estimate is a total attendance.” It is a count at a moment. Attendance over an event is larger and needs other data, such as transport counts.
  • “Still and Altenburg estimated 1.8 million for 2009.” That figure is not theirs.