Friday, December 21, 2007

What color is your PET?

Contributed by Michael H. Brill, Datacolor
Appears in ISCC News, No. 430 (Nov-Dec 2007)

Last September I was an “accompanying person” at a conference on molecular imaging. It might seem close to my area of expertise, but it is not. Accordingly, my color-scientist thinking led to a strange take on concepts in that field. Ostranenie (from the Russian остранение) is the literary device of forcing an audience to see something in an unfamiliar way, to enhance perception of the familiar. An example is to refer to driving a car as sitting on top of repeated gasoline explosions, or to refer to the human brain as electrified meat. For lots of ostranenie, read any book by Kurt Vonnegut---or be an accompanying person.

At the conference, I heard about positron-emission tomography1 (PET). The PET scan is a diagnostic tool whose cuddly name hides the fact, salient at the conference, that the imaging events are positron-electron (matter-antimatter) annihilations that are made to happen inside your body. Now, an electron is a sizeable particle whose complete annihilation (and also that of an injected positron with the same mass) produces a lot of energy. “Is it safe?” I asked, with none of the menace of Szell in Marathon Man. “It’s been known to be safe for three decades,” was the reply, replete with the condescension I’ve come to associate fondly with the medical profession.

Seeking confirmation from my own meager knowledge, I tried to cast this problem in a framework familiar to color science: Find the wavelength associated with the energy of a positron-electron annhilation. Does it convey warmth by the mechanism of a heat lamp, sunburn you, incur the dose-calibrated ionization damage of a dental X-ray, or more generally rock your world? (In the title to this column, I loosely call “PET color” the PET-induced-photon spectrum.)

Everyone I asked at the conference knew that a positron-electron annihilation liberates two photons, each with 511 KeV of energy, in opposite directions (to conserve momentum). But nobody had turned that number into wavelength, so I did a back-of-the-envelope calculation:

PET photon energy 511 KeV converts to energy E = 8.186 x 10-14 Joules (J), via 1.602 x 10-19 J/eV,. Planck's constant is h = 6.626 x 10-34 J-sec, and c = 2.998 x 108 m/sec. Hence the PET photon wavelength is h c/E = 0.002427 nm. At this wavelength, a photon from PET has far more energy than one from a dental X-ray (~0.06 nm) or chest X-Ray (~ 0.03 nm), and in fact is near the shortest wavelength attributed to X-Rays (0.001 nm).

Given that PET positrons produce hard X-rays in our fragile bodies, how can this be safe? Presumably, the total dosage of radiation in a PET scan is low, even though the energy per photon is high. Let’s check the plausibility of this assumption. One application of PET is to see brain metabolism through uptake of a radioactive glucose analogue that emits (you guessed it) positrons. The pseudocolors that are used to encode the metabolism level in the PET image1 are, of course, correlated with radiation emitted from the affected brain cells when the positrons annihilate with local electrons. One would think the radiation dosage to those brilliantly metabolizing brain cells would be quite high, even for relatively low average dosages in the whole brain.

Ultimately, the dose depends on how many photons are needed for a PET scan. Although tomography implies a volume scan and hence a lot of photons needed to light up the right pixels, a PET scan has a spatial resolution of 5-6 mm (much coarser than most other diagnostic images). Relative to diagnostic X-rays, PET scans need fewer photons per pixel to combat shot noise. But a lot of photons are wasted, because the image is captured only in a short cylinder around the affected area. And surprisingly, the photons do less damage to the local tissue than ionization due to the original positron.

As I found out, the computation of radiation dose is serious business in radiochemistry. Empirical studies (mostly on mice) make model fits to vulnerability as a function of such variables as organ type, metabolic rate, uptake rate, and geometry. The complication quickly exceeded the envelope I was writing on.

Back to color science, then. Can we tweak those PET pseudocolors so they’re more informative to doctors? Don’t even try: doctors are used to the present colors. Okay, back to literary devices then, such as ostranenie. That seems safe enough.


Wednesday, October 10, 2007

Colors and contextual effects

Osvaldo da Pos, University of Padua, Italy
Appears in ISCC News, No. 429 (Sept-Oct 2007)

There are two basic convictions about colors: (1) they carry information about the objects they belong to; and (2) their appearance depends on the context of the light, the spatial disposition of nearby objects, and their temporal changes. The two features sometimes strongly conflict. Constancy, whereby the color of an object tends to appear unchanged although environmental factors vary, vies with dependence on context. It is not rare for contextual effects to be considered illusory, although their occurrence obeys established rules.

The figures here exemplify how a visual illusion can be analyzed. Why does the central square, always the same, appear different when the surroundings are varied?

Striking changes occur when the lateral squares start in contact with the central one, and then a small misalignment or gap between them produces a completely different appearance. When there is no gap or misalignment, a cross is seen, composed of one strip transparent over the other: Two superimposed colors are seen in the grey square at the same time and in the same direction of sight, one in front and the other behind and through the first.
The two colors seen in the central grey square depend on the colors of the two adjacent squares. Already Helmholtz [1] tried to explain why those specific two colors were seen: it depended on the knowledge of the laws governing additive color mixtures, which, in the case of complementary colors, give an achromatic result. Therefore the colors of the adjacent squares are perceived in the central grey because their fusion precisely gives rise to that particular grey. Hering gave a radically different explanation involving no cognitive activity, but only physiological interactions. The two adjacent colors induce their complements in the grey area, so both the colors are visible in that grey square, although in different parts. Nevertheless those two weak colors can spread inside the square and completely characterize it, as only the sides can limit their spreading. Accordingly the central square appears transparent because in it both the colors of the back strip and of the front one are simultaneously perceivable (this would ultimately be the basic definition of transparency/translucency).

Although cognitive science still follows Helmholtz, the current understanding of the colored transparency (or translucency) effect does not resort to higher level "knowledge," but rather to physiological processes (based on cone excitation ratios [2], physical principles (based on Kubelka-Munk rules [3]; or on spectral filtration [4]), psycho-physical models (based on color convergence [5], [6]), phenomenological models (based on color similarity [7], [8], X junctions [9],[10]).

Even today we do not share a unique explanation of why the central grey square appears so different in different situations, so most people still speak of perceived translucency as an illusion, implicitly assuming that when a good explanation is achieved no illusion will exist anymore. A reasonable objection would be that, even when we reach a convincing explanation, still we would remain amused in seeing that the same grey square appears so different in different contextual conditions; the illusory aspect would remain intact, despite the scientific explanation.

[1] Helmholtz H. von, 1866 Handbuch der Physiologischen Optik, Leipzig: Voss
[2] Ripamonti C., Westland S., da Pos O. 2004 Conditions for perceptual transparency. Journal of Electronic Imaging. 13, pp. 29-35
[3] Brill M. H. 1976 Physical foundation of the perception of achromatic translucency. MIT Research Laboratory of Electronics Progress Reports No. 117 January, pp. 315-320
[4] Beck J. 1978 Additive and subtractive color mixture in color transparency, Perception & Psychophysics, 23, 256 - 267.
[5] Metelli F. 1974, The Perception of Transparency, Scientific American, 230, (16), pp. 90-96
[6] Chen, V. J., & D’Zmura, M. 1998 Test of a convergence model for color transparency perception. Perception, 27, 595-608.
[7] Hering E., Über die Theorie des simultanen Contrastes von Helmholtz. Vierte Mitteilung. Die subjective "Trennung der Lichtes in zwei complementare Portionen" In: Wissenschafliche Abhandlungen; hrsg. von der Sachsischen Akademie der Wissenschaften zu Leipzig, Leipzig : G. Thieme, n. [57], pp. 1- 11)
[8] Da Pos O. 1989-1991 Trasparenze. Transparency. Icone: Milano
[9] Watanabe T., Cavanagh P. 1993 Transparent surfaces defined by implicit X- junctions. Vision Research 33, 2339-2346
[10] Masin S.C. 2006 Test of models of achromatic transparency. Perception 35(12), 1611-1624.