Illusions: The Mona Lisa and Abraham Lincoln

What do the famous portrait and the former U.S. president have in common?

SPANISH PAINTER EL GRECO often depicted elongated human figures and objects in his work. Some art historians have suggested that he might have been astigmatic—that is, his eyes’ corneas or lenses may have been more curved horizontally than vertically, causing the image on the retina at the back of the eye to be stretched vertically. But surely this idea is absurd. If it were true, then we should all be drawing the world upside down, because the retinal image is upside down! (The lens flips the incoming image, and the brain interprets the image on the retina as being right-side up.) The fallacy arises from the flawed reasoning that we literally “see” a picture on the retina, as if we were scanning it with some inner eye.

No such inner eye exists. We need to think, instead, of innumerable visual mechanisms that extract information from the image in parallel and process it stage by stage, before their activity culminates in perceptual ­experience. As always, we will use some striking illusions to help illuminate the workings of the brain in this processing.

Angry and Calm
Compare the two faces shown in a. If you hold the page about nine to 12 inches away, you will see that the face on the right is frowning and the one on the left has a placid expression.

But if you move the figure, so that it is about six or eight feet away, the ­expressions change. The left one now smiles, and the right one looks calm.

How is this switch possible? It seems almost magical. To help you ­understand it, we need to explain how the images were constructed by Philippe G. Schyns of the University of Glasgow and Aude Oliva of the Massachusetts Institute of Technology.

A normal portrait (photographic or painted) contains variations in what neuroscientists such as ourselves term “spatial frequency.” We will discuss two types of spatial frequency: The first is “high”—with sharp, fine lines or details present in the picture. The second is “low”—conveyed by blurred edges or large objects. (In fact, most images contain a spectrum of frequencies ranging from high to low, in varying ratios and contrasts, but that is not important for the purposes of this column.)

Using computer algorithms, we can process a normal portrait to remove either high or low spatial frequencies. For instance, if we remove high frequencies, we get a blurred image that is said to contain “low spatial frequencies in the Fourier space.” (This mathematical description need not concern us further here.) In other words, this procedure of blurring is called low-pass filtering, because it filters out the high spatial frequencies (sharp edges or fine lines) and lets through only low frequencies. High-pass filtering, the opposite procedure, retains sharp edges and outlines but removes large-scale variations. The result looks a bit like an outline drawing without shading.

These types of computer-processed images are combined together, in an atypical manner, to create the mysterious faces shown in a. The researchers began with normal photographs of three faces: one calm, one angry and one smiling. They filtered each face to obtain both high-pass (containing sharp, fine lines) and low-pass (blurred, so as to capture large-scale luminance variations) images. They then combined the high-pass calm face with the low-pass smiling face to obtain the left image. For the right image, they overlaid the high-pass frowning face with the low-pass calm face.

What happens when the figures are viewed close-up? And why do the expressions change when you move the page away? To answer these questions, we need to tell you two more things about visual processing. First, the image needs to be close for you to see the sharp features. Second, sharp features, when visible, “mask”—or deflect attention away from—the large-scale objects (low spatial frequencies).

So when you bring the picture near, the sharp features become more visible, masking the coarse features. As a result, the face on the right looks like it is frowning and the one on the left, like it is relaxed. You simply do not notice the opposite emotions that the low spatial frequencies convey. Then, when you move the page farther away, your visual system is no longer able to resolve the fine details. So the expression conveyed by these fine features disappears, and the expression conveyed by low frequencies is unmasked and ­perceived.

This article was originally published with the title "Illusions: Cracking the da Vinci Code."

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