Thursday, September 14, 2017

Does a Mantis Shrimp have a Real Color Space?

The small mantis shrimp (a stomatopod crustacean) has a mean right hook--able to accelerate its “punch” to a speed of 50 mph in a few milliseconds, smashing prey and glass fish tanks. It also has an amazing visual system, with 12 or more different receptor cells covering 300 to 720 nm.

Mantis shrimp from the front.[]

A fairly recent article by H H Thoen et al. in Science [1] describes two hypotheses for the color vision of a particular mantis shrimp (one of more than 500 known species). The first hypothesis is that the color vision is “like ours” in making opponent-pair comparisons between receptor types that allow good discrimination of wavelength.  The other hypothesis is that the mantis shrimp processes each kind of receptor input (spectral band) separately, a method that would give poor wavelength discrimination but might have other advantages.  It turns out that, despite having many more photoreceptor types than we do, the mantis shrimp has poorer wavelength discrimination. Therefore, Thoen et al conclude that the mantis shrimp has no color space at all, but recognizes reflectances by comparing inputs to each kind of receptor separately.  The idea is that color discrimination (e.g., by humans) is facilitated by a ratio (comparison) between spectral bands at the same point in the visual field, whereas the mantis shrimp performs ratios of inputs at different spatial locations to each spectral band separately, and thereby performs reflectance recognition at 12 spectral bins. The authors claim that the mantis-shrimp spectral sensitivity curves are narrow enough so that within-band ratios derived from them exhibit illuminant invariance (color constancy) and allow the mantis shrimp to accurately recognize a reflectance in 12 bins. But the spectral sensitivity curves of the mantis shrimp, shown in Fig. 1A of the same article, tend to have bandwidths of about 100 nm, similar to our own receptor sensitivities. The poor wavelength discrimination of the mantis shrimp seems to be experimental fact, and that would imply a reduced inter-band comparison.  However, that does not mean color constancy by within-band ratios must be enhanced in this animal. 

Another of these authors’ ideas seems to have more traction. If the bands act separately, the neural processing may be accelerated to match the mantis shrimp’s top-speed lifestyle.  The quickly passing world could be processed by a kind of “push-broom sensor” architecture, whereby the 12 kinds of receptors are arranged in one spatial direction, replicates of the arrangement occupy the perpendicular spatial direction, and motion in the first spatial direction accumulates spatial details in a time-encoded form.  Such a design is common for the push-broom sensors that we use in our remote sensing apparatus based on the same principle.

Yet another idea from Thoen et al. is also worth mention: These authors seem to believe that a true color space requires inter-band comparisons, and that such comparisons impose a processing overhead that may not be acceptable to a simple if strongly aggressive creature such as the mantis shrimp.  This rationale bears comparison with the idea, briefly explored by Mark Fairchild ([2], [3]), that even humans don’t need a color space at all, and that what we call color can be expressed with a small number of one-dimensional scales. By this reasoning, color space is a construct of theory, and not intrinsic to visual information. 

Such discussion will inevitably lead to a philosophical and definitional problem.  What, after all, comprises a color space, versus “not-a-space”? Mark Fairchild required a space to have a metric, but I think that requirement could be waived, as could Thoen’s band-comparison requirement.  To me a space is just a representation that allows important features to be salient.  It’s hard to visualize a structure in a 12-dimensional space (such as that of the mantis shrimp investigated by Thoen, et al.), if that space is represented in conventional rectangular coordinates.  But there’s an alternative picture, in which the 12 coordinate axes are lined up parallel with each other and evenly spaced in a plane. Each spectrum is a 12-component object in the space, and shows up as a point on each of the parallel one-dimensional axes.  The original 12D point is represented as an open polygon, with vertices being the component values along the consecutive axes, and line segments connecting the consecutive vertices. Such a structure allows you to see 12-dimensional structures in two dimensions. For example, all the points on a line in the 12-dimensional rectangular space generate a set of 11 intersection points that characterize the line.  The use of parallel coordinates to represent high-dimensional data was invented by Alfred Inselberg more than 30 years ago [4].  Maybe our champion mantis shrimp is using such a representation to track prey, detect mates, and fool anthropocentric color researchers. 

Representative sample of parallel coordinates [By Yug - Own work, CC BY-SA 4.0,]


[1]. H H Thoen, M J How, T-H Chiou, and J Marshall. A different form of color vision in mantis shrimp. Science Vol. 343, 24 Jan 2014, 411- 413.

[2] M D Fairchild. Is there really such a thing as color space? Foundations of uni-dimensional appearance spaces. ISCC/IS&T/SID Special Topics Meeting Revisiting Color Spaces, San Jose CA (2011), 21-22.

[3] M D Fairchild and R L Heckaman. Deriving appearance scales. IS&T Color and Imaging Conference 20 (2012), 281-287.

[4] A Inselberg. The plane with parallel coordinates. Visual Computer 1 (4): 69-91 (1985).

Michael H. Brill