benz

Different Views & Log Scaling

Blog Post created by benz on Sep 23, 2016

Originally posted Apr 8, 2013

 

Which view or scale is the right one for your needs?

In a recent post on his “bad astronomy” blog (http://www.slate.com/blogs/bad_astronomy/2013/04/06/curiosity_rover_picture_of_mount_sharp_changed_to_look_like_earth.html) astronomer Phil Plait describes how “Astronomers commonly change the contrast from a linear scale—where something that’s twice as bright is shown that way—to a logarithmic scale, which goes by factors of ten.”  Plait explains that converting to a log scale helps to pick out faint sources in an image. 

That’s a close analog to one of the reasons to use a log scale described in my previous post, and a starting point for discussing different views of measurement data.  Plait’s blog post included a NASA image that had both its contrast and color balance altered to make the scene look more like it would on Earth.  To make the comparison clearer I created the graphic below, combining the original rover image (without contrast or color balance changes) and one with Earth-like color balance.

Mt. Sharp panorama from the Curiosity Mars rover with original color balance and contrast (top) and with altered contrast and Earth-like color balance (bottom). Images courtesy NASA/JPL-Caltech

Mt. Sharp panorama from the Curiosity Mars rover with original color balance and contrast (top) and with altered contrast and Earth-like color balance (bottom). Images courtesy NASA/JPL-Caltech

So, in the vernacular of this blog, which image is the better measurement?  Both are better in their own way and it’s a matter of choosing what you want to see.  The original image represents what you would see if you were standing there and taking a picture without adjusting white balance.  Neat!  I know I’m not the only one who would give a small fortune to be able to go to Mars and look around, but that’s not going to happen and this uncorrected image is about the closest I’ll get.

However if you’re an Earth-trained geologist (the only known type so far) and want to use visual cues to do science on Mars you might prefer the bottom image with its familiar white balance and enhanced light/shadow cues.  The nonlinear scaling mimics how our eyes respond to light and of course the same thing is generally true of hearing.  Many systems and phenomena in nature have a lot of dynamic range, and log or other nonlinear scaling is an effective way to deal with it.

Another way to understand this comparison is as an example of how phenomena that are obscure in one measurement can be much clearer in another.  The better measurement is not always the one that is more accurate or faster, or closer to some ultimate truth.  It’s the measurement that gives you the answer or insight you need most clearly and reliably.  Sometimes that’s a straightforward matter of accuracy or measurement speed, sometimes not.

 

I have in mind a couple of examples from wireless communications and you’ll see them in days to come.  If you’ve got examples of your own I’m interested in them so please leave a comment.

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