Blink-free photos, guaranteed og Ig Nobel 2006 in math
CSIRO physicist Dr Piers Barnes explains to writer and occasional photographer Nic Svenson how many shots she should take to get one where no-one's blinking. This is Nic's story...
"Anyone who's played photographer at family functions knows that, even if everyone stays perfectly still, there's always someone who blinks.
I often have to take group photos and I wondered just how many shots I'd have to take to get one where no-one's blinking. I started counting: people, photos, photos spoilt due to blinks... It was taking forever! I couldn't make up a rule after ten counts. To be what's known as statistically significant, I'd need around two hundred.
I whinged to my colleague, Dr Piers Barnes, and he said: 'You don't need data, we can model it.' Trying not to feel like an idiot for thinking science is based on hard numbers, I set about finding some figures to plug into the formula Piers was working on.
It turns out that the average number of blinks made by someone getting their photo taken is ten per minute. The average blink lasts about 250 milliseconds and, in good indoor light, a camera shutter stays open for about eight milliseconds.
Figuring out the number of photos to take so I can expect to get one where no-one's blinking relies on probabilities (I'd like to guarantee a good shot, but apparently this is impossible as there's always a chance someone will blink). When sorting out probabilities, you have to consider what might influence them.
The number of photos required to be 99% confident of getting a good one
For our purposes, it's fair to say that blinks are independent. If a group of people are looking at a camera, one person's blinks won't influence another's and, unless you've got something in your eye, your blinks don't influence each other either. It's also safe to say that blinks are random; they don't happen every six seconds.
This means we're looking for the probability of a random event - a blink - occurring during a window of time - how long the shutter's open - that's much shorter than the event itself.
Piers says the probability of one person spoiling a photo by blinking equals their expected number of blinks (x), multiplied by the time during which the photo could be spoilt (t) - if the expected time between blinks is longer than the time in which a photo can be spoilt, which it is.
This makes the probability of one person not blinking 1 - xt. For two people it's (1 - xt).(1 - xt) and for a group of people it's (1 - xt)n, n being the number of people.
This means (1 - xt)n is also the probability of a good photo. Therefore, the number of photos should be 1/(1 - xt)n.
Let's test this: each shutter opening results in either a good photo or a spoilt one. If you make a graph of a lot of these successes and you'll find it follows what statisticians call the normal distribution. Even if you know nothing about stats, you've probably heard of the bell curve - well, that's what the normal distribution looks like.
At one end of the curve the trials are 100% successful: the photographer got all good shots. In the middle, the number of good and bad photos is split 50:50. And, at the other end, are all dud trials: the photographer got no good shots.
Piers then figured out how many shots I'd need to be 99% certain of getting a good one. He found that photographing thirty people in bad light would need about thirty shots. Once there's around fifty people, even in good light, you can kiss your hopes of an unspoilt photo goodbye.
Piers also came up with a rule of thumb for calculating the number of photos to take for groups of less than 20: divide the number of people by three if there's good light and two if the light's bad."
source: Velocity in motion and Wiki
"Anyone who's played photographer at family functions knows that, even if everyone stays perfectly still, there's always someone who blinks.
I often have to take group photos and I wondered just how many shots I'd have to take to get one where no-one's blinking. I started counting: people, photos, photos spoilt due to blinks... It was taking forever! I couldn't make up a rule after ten counts. To be what's known as statistically significant, I'd need around two hundred.
I whinged to my colleague, Dr Piers Barnes, and he said: 'You don't need data, we can model it.' Trying not to feel like an idiot for thinking science is based on hard numbers, I set about finding some figures to plug into the formula Piers was working on.
It turns out that the average number of blinks made by someone getting their photo taken is ten per minute. The average blink lasts about 250 milliseconds and, in good indoor light, a camera shutter stays open for about eight milliseconds.
Figuring out the number of photos to take so I can expect to get one where no-one's blinking relies on probabilities (I'd like to guarantee a good shot, but apparently this is impossible as there's always a chance someone will blink). When sorting out probabilities, you have to consider what might influence them.
The number of photos required to be 99% confident of getting a good one
For our purposes, it's fair to say that blinks are independent. If a group of people are looking at a camera, one person's blinks won't influence another's and, unless you've got something in your eye, your blinks don't influence each other either. It's also safe to say that blinks are random; they don't happen every six seconds.
This means we're looking for the probability of a random event - a blink - occurring during a window of time - how long the shutter's open - that's much shorter than the event itself.
Piers says the probability of one person spoiling a photo by blinking equals their expected number of blinks (x), multiplied by the time during which the photo could be spoilt (t) - if the expected time between blinks is longer than the time in which a photo can be spoilt, which it is.
This makes the probability of one person not blinking 1 - xt. For two people it's (1 - xt).(1 - xt) and for a group of people it's (1 - xt)n, n being the number of people.
This means (1 - xt)n is also the probability of a good photo. Therefore, the number of photos should be 1/(1 - xt)n.
Let's test this: each shutter opening results in either a good photo or a spoilt one. If you make a graph of a lot of these successes and you'll find it follows what statisticians call the normal distribution. Even if you know nothing about stats, you've probably heard of the bell curve - well, that's what the normal distribution looks like.
At one end of the curve the trials are 100% successful: the photographer got all good shots. In the middle, the number of good and bad photos is split 50:50. And, at the other end, are all dud trials: the photographer got no good shots.
Piers then figured out how many shots I'd need to be 99% certain of getting a good one. He found that photographing thirty people in bad light would need about thirty shots. Once there's around fifty people, even in good light, you can kiss your hopes of an unspoilt photo goodbye.
Piers also came up with a rule of thumb for calculating the number of photos to take for groups of less than 20: divide the number of people by three if there's good light and two if the light's bad."
source: Velocity in motion and Wiki