Working With Biases

Color Calibration Target on the Curiosity Rover. Image credit: NASA/Cornell/JPL

Camera Calibration

One of the identities I ascribe to myself is “scientist.” In particular, I like to think of myself as a data scientist. I like to play with data from various instruments and understand what those data are telling me about a physical property of the material from which those data were acquired. I especially like image data. Spacecraft image data. I love to be one of the first people to ever see an object from another Solar System body. It’s thrilling.

As a data scientist, one of the things that I have spent a lot of time doing is understanding how to calibrate instruments. How to calibrate cameras, in particular.

What is camera calibration? Let’s talk about only the brightness values and colors of the images produced by the camera. Calibration is understanding how the brightnesses and colors the camera produces are related to the real brightnesses and colors of the real world.

At the most basic, calibration is the understanding of the camera’s biases. The very simplest camera system has two distinct biases. For this very simplest camera, the light coming out of the camera, O (for output) is a linear function of the light coming into the camera, I (for input):

O = m*I + b.

You might recognize this as the algebraic equation for a line:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In various mathematics and engineering fields, b is also called the “bias” and m is still just called the “slope.”

To understand the light coming in to the camera, we must correct for this bias and slope that the camera itself introduces to the data. This is the essence of radiometric camera calibration (yes, it’s far, far more complicated in reality).

Every camera has its own linear (or non-linear, for most cameras) calibration equation. You cannot mix calibration equations. Even if two cameras were built by the same company at about the same time, their characteristics are different so the calibration must also be different.

Bias Correction

Now, this site is dedicated to helping understand Pro-Social Behaviors and how they can be contagious, so what does camera calibration have to do with anything else on this site?

Just as we work very diligently to correct the biases that our camera introduces to the data we collect from it, we can work diligently to correct the biases that our experiences introduce.

If I tell you that I parked my car downtown one evening and came back to find it keyed, you might immediately start thinking about the person who did it. 

Let’s take a moment to form a picture of the person who keyed my car. What do they look like? What’s their gender? What’s their age? How were they dressed? What kind of hair do they have? How do they sound? Build all of that picture in your mind and hold it there for a while. Add details as they come to mind. 

Now, ask yourself, do you know anybody who looks, sounds, behaves, etc., like the picture in your mind AND who you KNOW has keyed someone’s car; someone you know personally.

No? Then you know for certain that your picture is based on biases, most given to you through media, through friends, through society as a whole. You know for certain that this is the case because you don’t actually know anyone who has keyed a car, so you can’t be picturing a specific person. The person in your imagination is like a picture made up of a bunch of magazine cutouts, one eye taken from this magazine, a different one from that other magazine, the mouth from a third magazine, and et cetera.

But, what if the answer is, yes, you do know someone who has keyed a car? That must mean that you’re not biased, right? Sorry, no. It means your biases are informed, but it doesn’t mean you’re not biased. Unless you’ve lived in my town and know a lot of people who key cars that are parked downtown, your bias still exists. Your bias is informed, yes, but it may still be completely incorrect for my area.

It’s not a question of whether or not you are biased. It’s a question of whether or not you’re willing to do the self-calibration required to counter that bias.

You wouldn’t use the calibration from the Galileo SSI camera that orbited Jupiter to correct images from the HiRISE camera at Mars, would you?

Similarly, it doesn’t make a lot of sense to use your biases to make assumptions (and more importantly to make decisions and to take actions) about something that goes on outside of your actual experience. If you do, you get at best an incomplete picture, and at worst, you accuse an entire group of people of something they couldn’t possibly have done.

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