Brightness and Darkness

Dedicated to the memory of our beloved Tutti

2008-04-19T14:58:00.000-07:00

I guess the greatest sadness comes when you lose the greatest love. I've been putting this off for quite some time now, but I've finally bit the bullet. This post is dedicated to a great little cat, who we miss so much. Here are a few snapshots of his brief life.

He was weee big when we got him...

And he did love his mummy, the pillow, so...

When he grew, he grew fond of the washing machine...

But he thought little of String Theory

He made his pop very happy when he got interested in computers...

Not so much when he tried to wake him though...

RIP, our little friend...

Color Perception in Six Dimensions

2007-10-16T09:12:00.000-07:00

The classic theory of human color perception, known as opponent-color theory, postulates that three axes, brightness-darkness, redness-greenness and blueness-yellowness, form the dimensions of color space. In other words, color space is three-dimensional (3-D). Central to this theory is the assumption that pairs of opponent colors subtract. In my previous post, I indicated that our research group had found evidence that brightness and darkness fail to subtract, and consequently, that brightness and darkness form perceptual dimensions. I did not, however, discuss how we reached this conclusion. I also hinted that this notion of 'extra dimensions' could be extended to the domain of redness-greenness and blueness-yellowness; that is, to the entire human color space.

To understand how, one needs to look more closely at the actual experiments we conducted, known as color matching experiments. In one such experiment, for example, subjects adjusted the luminance (light intensity) of the ring on the left side in the figure below such that the ring appeared to have the same gray shade as the ring on the right side of the figure. For expository purposes, I have matched the two gray rings as best I could. As you will likely perceive, a residual difference between the two rings remains.

Recall from my first post that the white background and the black disk on the left side simultaneously induce darkness and brightness, respectively, into the left ring by a principle of contrast. According to opponent-color theory, the brightness and darkness components should partially cancel. This implies that, all else being equal, subjects should be able to adjust the luminance of the left ring such that its gray shade perfectly matches the gray shade associated with the right ring.

To quantify residual perceived differences in gray shades, we had subjects rate the 'possibility of making a perfect match' and the 'similarity between gray shades' in our experiments. Consistent with the demonstration above, the data show that it is nearly always impossible to make a perfect match. Indeed, we go much further to show that the degree of mismatch between gray shades can be mathematically modeled by assuming that brightness and darkness are processed independently in the brain; that is, we show that brightness and darkness form perceptual dimensions.

We are now in a position to extend the concepts of impossible color matching and extra dimensions to the chromatic domain (i.e. redness-greenness, blueness-yellowness). This extension builds on the work of Vebjørn Ekroll and colleagues at the University of Kiel in Germany. Ekroll and colleagues provide circumstantial evidence that subjects have great difficulty making color matches under exactly the conditions predicted by a theory in which redness and greenness (blueness and yellowness) form perceptual dimensions. Indeed, Ekroll's work provided the inspiration for our experiments on brightness and darkness.

To see these extra chromatic dimensions, consider the following display. Note that the effect is subtle, particularly with the low resolution image that must be displayed here, but can be augmented by turning the room lights off and focusing carefully on the display in the manner described below.
In the top row, I have drawn a line of seven red-blue (purple) disks. In the middle row, the same disks are embedded in a color gradient varying from red-blue to yellow-green. Due to the perceptual contrast effect, however, the disks do not all appear the same color. In the bottom row, I have attempted to make color matches to the corresponding disks in the middle row by sequentially comparing each disk pair. You can compare the colors of the corresponding disks (column-wise) in the middle and bottom rows for yourself by looking sequentially at each disk in the pair.

You will probably agree that, while the rightmost disks appear quite similar, the leftmost disks don't look very much alike. Now stare at the white space between the middle and bottom rows, and without moving your eyes, compare the colors of the leftmost disks in those rows. Now stare at the space between the top and middle rows and compare the leftmost disks there. Notice anything weird? It seems like the color of the leftmost disk in the middle row can be either red-blue or yellow-green, depending in whether you are comparing it to the top or bottom row. I call this effect attentional coloring.

The paradoxical nature of partial color matching and attentional coloring can both be traced to a failure of redness and greenness (blueness and yellowness) to subtract. Following the work of Eli Brenner and colleagues at Amsterdam University, we can quantify the perceived color of each disk as a combination of the physical color of the disk plus a contrast component which is complementary in color to the region immediately surrounding the disk. On the one hand, the leftmost disks in the middle row are colored by a combination of the real (physical) red-blue and the illusory yellow-green induced from the red-blue surround. On the other hand, the rightmost disks are colored by the real red-blue and the illusory red-blue induced by the yellow-green surround. In the latter case, the real and illusory components add, in the former case they remain separated. Attentional coloring works, I propose, by 'extracting' from the ambiguous (red-blue AND yellow-green) disk the color that correctly matches that of the comparison disk (red-blue OR yellow-green).

As with brightness and darkness, we thus conclude that each 'opponent' color actually forms a dimension of color space. In all, we have six dimensions: brightness, darkness, redness, greenness, blueness, yellowness. It is in this sense, then, that I mean color perception 'lives' in a 6-D space. Interestingly, this idea finds support in an obscure paper published in 1963 by Crane and Piantanida. The findings of that paper have recently been challenged on the grounds that seeing illusory redness and illusory greenness simultaneously amounts to seeing real brown. I would just like to point out here that real and illusory colors cannot generally be matched. Thus, color matching is not a good way to test the subtraction assumption of opponent-color theory.

What good is all this? Well, it implies that color space is much larger than most scientists had previously imagined. I suspect that an active area of research over the next few years will be the concern of how this huge color space may account for the nearly-infinite variety of colors we see, from earthy to metallic to pastel to neon to luminous and beyond.

Brightness and Darkness as Perceptual Dimensions

2007-09-21T12:18:00.000-07:00

I am going to begin a series of posts based on an article that my colleagues Marcel P. Lucassen, Frans W. Cornelissen and I have just published in PloS Computational Biology. The paper is entitled Brightness and Darkness as Perceptual Dimensions.

We commonly think of the shades of gray we see (say, on a computer screen) as lying somewhere between the blackest black and the whitest white. Indeed, this line of thinking is so pervasive that we have codified it in common language: We say things like, "the issue is gray, not black and white". In what follows, I am going to use the words "black" and "dark", or "white" and "bright", interchangeably.

We know that bright and dark are only meaningful when considered in relation to something. In the figure below, for example, some disks appear "brighter" than the background whereas others appear "darker". This is an illusion, as all the disks are physically identical!

The brain constructs the "brightness" and "darkness" by a principle of contrast against the background. With a darker background (right side), the disks appear progressively more bright. The converse is true with the brighter background (left side). The above example seems to reinforce the notion that bright and dark form the endpoints of a continuum containing all gray shades (we can literally see the continuum in the figure).

It turns out that saying that bright and dark 'bookend' the gray continuum is the same thing as saying that both brightness and darkness cannot be seen simultaneously in the same surface region. On the contrary, we find evidence that both brightness and darkness CAN be seen simultaneously. This 'failure of cancellation' implies that brightness and darkness form (independent) dimensions of visual perception. By the corollary above, it also means that dark and bright cannot constitute the endpoints of a continuum containing all the gray shades we see.

In our paper, we mathematically model gray shades as points on a graph, with one axis of the graph representing brightness and the other darkness. That is, we posit that gray shades 'live' in a two-dimensional (2-D) space, formed by brightness and darkness dimensions, rather than the conventional 1-D space. We use this insight to explain a number of otherwise puzzling observations, including why some gray shades appear metallic. The ring on the left side of the display below, for example, appears more 'metallic' than the 'earthy' gray of the ring on the right side.

This theory also explains the recent puzzling finding of Piers Howe and Margaret Livingstone, whereby the illusory darkness induced in the Hermann Grid Illusion cannot be canceled by real brightness: As brightness and darkness constitute perceptual dimensions, they cannot, in principle, cancel one another. Stayed tuned for the next installment in the series, where I will discuss how the theory described above can be extended to redness-greenness and yellowness-blueness. The implication is that human color perception lives in a 6-D space, rather than the conventional 3-D space!

B and D Anime

2007-08-29T14:02:00.000-07:00

If you Google the phrase Brightness and Darkness, you will come up with a whole bunch of references to scientific studies of visual perception, and you will also come up against the lyrics of this weird anime song.

Welcome to Brightness and Darkness

2007-08-29T13:42:00.000-07:00

Welcome to Brightness and Darkness. Here is a picture of my cat. He doesn't know it yet, but he is about to go on a big trip from Europe to the United States. Bon voyage, my furry feline friend, bon voyage...