I went to the Corcoran galley of Art this past weekend to see the exhibit of artist Chuck Close. An amazing array of mosaic or block portraits made with paint, paper pulp, thumb prints,...Stand far away and the portrait is obvious, but the closer you look (no pun intended) the portraits turn into a jumble of abstract marks, symbols, colors, and textures. After the visit I did a little research and found this article from Science about this effect. In a 1999 article by psychologist Denis Pelli, "Close Encounters - An Artist Shows How Size Affects Shape," shows the following graph and its caption from an experiment. They had viewers stand close to a Close portrait and more away, noting when a facial feature (the nose) eventually emerged.

The nose test. The critical face width of Close's portraits plotted against the number of marks across the face. The regression lines, one for each of five observers (accounting for half of the variance), are plots of the results for judging nose emergence on each of the 33 gridded portraits from the Chuck Close retrospective (except the Keith/Six Drawings Series) (2). X and O are raw data for two observers. Size independence predicts a vertical line. All five lines have log-log slopes close to 1 (mean 1.0, SD ± 0.2), showing that the perceived shape does depend on size.

I would think a better plot would have face width as the explanatory variable and marks across the face to be the response. Independence would then be testing for a slope of zero (a more standard way for statisticians to represent it). Here is the original graph flipped to see the scatter.

Of course the lines drawn here are not the regression lines of the marks regressed on the face width. In fact, it appears that a new regression of marks on face width would have slopes much closer to zero! Is it significantly different from zero? I'd have to digitize the data off the graph to check for sure, but was the original graph chosen to emphasize the conclusion that size and shape are dependent?

## 2 comments:

I'm not sure I see your point. The plot is the maximum size at which the face appears to have a nose, properly measured in degrees.

The independent variable is how fine a grid is used for the pixels.

I would expect that faces could get much larger and still be recognizable if the pixels are finer.

The model I would have is that there is a low-pass filter, and that spatial frequencies higher than a certain amount would not interfere with the image. So the maximum face size in degrees should be a linear function of the number of pixels, with the pixels/degree cutoff being where the low-pass filter starts rolling off.

Their plot seems compatible with this theory, though I'd rather have seen a plot of min pixels/degree as a function of pixels/face, rather than max degrees/face as a function of pixels/face.

It's not the model that I'm taking issue with, only the way it is tested. Testing for an infinite slope, even if you want to reject it, is problematical. Sampling variability is likely to be very large. Testing independence with a slope of zero less prone to these problems.

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