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Question:

This is a bit of an abstract question, but bear with me. I am averaging images, to try and deduce what the average image of a specific subject looks like (just out of curiosity, it might produce some interesting results).

In order to know what kind of averaging method is permitted, i am trying to determine as what kind of data images can be classified (nominal, ordinal, interval or ratio). I would think a collection of images from a specific subject (creative commons portraits scraped from flickr for example) can be classified as nominal data, since there is no sense in ordering portraits (which would make it ordinal data, or higher).

In my opinion the images are on the same level as names, but instead of a linguistic representation of something, they are a visual representation of something (thereby functioning on the same level as a name). Which would make it nominal data.

But then again: digital images are in essence an array of numbers (rgb values), which could mean that it's measured at the ratio level (or at least the colors are). So a mean average is possible, but is it sensible?


My other question should clarify what it is i am trying to achieve: Averaging images

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I would like to suggest that your thinking already is well beyond merely classifying images as nominal, categorical, etc., and that such classification is far too limited and outmoded to be a useful framework for you. You may find it more productive to use your objectives as a point of departure: why are you analyzing images? What will the purpose or output of the analysis be? These considerations will help answer whether a mean image is sensible in your particular application. –  whuber Feb 20 '12 at 15:08
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I wholeheartedly agree with @whuber, that this data classification scheme is "far too limited and outmoded to be a useful framework". Here is a preprint of a paper you might find helpful: cs.uic.edu/~wilkinson/Publications/stevens.pdf –  gung Feb 20 '12 at 18:34
    
@gung, thanks for the research paper, very informative! –  user9318 Feb 20 '12 at 21:45
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I wrote a very non-technical piece about this on Associated Content here –  Peter Flom Feb 20 '12 at 22:15
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@PeterFlom, thanks, i'm glad to read that steven's measurement levels aren't the holy grail they used to be when i was a student :) –  user9318 Feb 21 '12 at 10:22

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up vote 2 down vote accepted

Samuel, welcome to the website.

There's been extensive literature on functional data analysis originating from statistics in the last 15 or so years -- see the classic monograph by Ramsey and Silverman (2005, 2nd ed), and you can find a bunch of others. In this literature, one observation = one image, and this literature doesn't have any second thoughts treating measurements as continuous data (which you refer to as ratio data). The ways of properly aligning images and applying other transformations to ensure that the common statistical methods, from averaging to ANOVA or PCA, are meaningful. If you are stuck with looking at images as nominal data, there won't be much you'd be able to do with them.

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Well i could use modal averaging, which can be useful. And how is image data proven to be ratio (or continuous) data in the literature you quoted? I understand that one observation is one image. But there are several requirements that are not met as far as i know: there is no non-arbitrary zero value in the images i am using, or even a way to quantify difference between the images. (remember, i am talking about level of measurement of the content of the images, not in the attributes of the way that content is represented (the pixel and color data)) –  user9318 Feb 20 '12 at 14:33
    
And one further question; why would you classify what i am trying to do as functional data analysis exactly? Does that not refer to the properties of the way the images are represented (i.e. the color values), instead of what i am actually analysing (the images as a whole)? –  user9318 Feb 20 '12 at 14:37

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