ОПТИКА И СПЕКТРОСКОПИЯ, 2007, том 103, № 6, с. 887-890
y^K 535.60
ARTIFICIAL AND BIOLOGICAL COLOR: THE ABCs
© 2007 r. H. J. Caulfield* and J. Fu**
*Alabama A&M University Research Institute, P.O. Box 313 Normal, AL 35762 **Computer Science Department Alabama A & M University Normal, AL 35762 USA
Received December 28, 2006
Abstract—Faced with radiation of immeasurable complexity that bears on important distinctions among objects in the world, nature chose not to measure the spectrum, even at low resolution. Rather Biological Color measures using two or more broad, spectrally overlapping sensitivity curves and uses the resulting data to compute discriminants (colors) that brains attribute to their percepts of those objects. Artificial Color seeks to design sensors and process the resulting data in the same or a very similar way. Here we seek to provide a unified view of prior and current work in this field.
PACS: 42.66.Ne
INTRODUCTION TO BIOLOGICAL COLOR
Most forms of color do not survive in fossils, but physical color, e.g., those in sea shells survive quite well. Three major events in the evolution of life occurred very rapidly in evolutionary time terms: physical color, image forming eyes, and the Cambrian explosion that gave birth to essentially all general life forms still surviving. A very plausible argument can be made that image forming eyes that could make use of color provided a huge advantage to animals so capable. This set off an arms race leading to better vision, more color, and new animals [1]. All of this occurred almost 550 million years ago. It is important to note that once color evolved, it stayed. Most animals with image forming eyes use two or more broad, spectrally-overlapping sensitivity curves in so doing and thus have spectral discrimination capability - Biological Color. And color is still evolving. Primates alone among mammals have trichromatic vision, and some women have four kinds of cone cells and thus experience color differently from any man [2].
INTRODUCTION TO CONVENTIONAL SPECTRAL IMAGING
When engineers seek to use spectral information in imaging system, they usually think in terms of a fixed number of spectral bands (usually nonoverlapping and often contiguous). Here we consider two extremely different cases: multi band satellite cameras and HSI (hy-perspectral imaging) cameras [3]. Many satellite imaging cameras use several broad spectral bands. This is attractive because the more bands we use, the less light is available for each. That is, sensitivity demands fewer bands. The bands are so chosen that they are likely to contribute significantly different information. Because there are multiple bands, irradiance levels can be normalized out leaving only spectral information. HSI
cameras use many (often 100 or more) narrow, discrete, contiguous spectral bands. This has the advantage of gathering much more potentially-valuable spectral information than can be gathered with those few-band cameras, but the price paid is lower sensitivity, higher complexity, higher cost, more difficulty in processing, and so forth.
INTRODUCTION TO ARTIFICIAL COLOR IMAGING
There are two aspects to Artificial Color: the recording using multiple, broad, spectrally-overlapping sensitivity curves in detection and the use of the resulting data to compute discriminants or other properties that can be attributed to the object for some use [4-8]. Commercial color cameras are designed to record and reproduce something close to the color appearance an ordinary trichromatic human male might experience. So the color camera has filter-detector curves that are close to the RGB (Red, Green, Blue) sensitivity curves of human trichromatic cone cells. Thus, because they are deliberately imitating the best studied Biological Color camera (the human eye), ordinary color cameras are Artificial Color cameras. But, before our work, little use of biomimetic processing was used even for these cameras. Rather, people have treated the three detected RGB signals as the end results rather than as data to be used to compute discriminants. Remember, you do not see R, G, and B images. You see some discriminant (color) your brain has computed using R, G, and B. A biomi-metic Artificial Color approach must do some significant computation with the detected quantities.
But the human RGB curves were not evolved to be optimum for any particular purpose. Ultimately, the Artificial Color camera should design and implement sensitivity curves optimized for the task at hand rather than use what is simply readily available.
All of this emphasizes a primary difference between Artificial Color and Biological Color. Biological Color must serve multiple purposes - find food, avoid becoming food, find mates, and so forth and do so under a variety of difficult circumstances. Artificial Color cameras can be specialized for a particular task, e.g., telling valid form counterfeit Euros from images taken with a standard camera using standard lighting. If the choice of sensitivity curves and the processing have trouble telling apples form oranges, it does not matter. It is a consequence of the projection of the complex spectra into two or three numbers that there are infinitely many spectra (called metamers) that give the same numbers. They are indistinguishable in principle with that camera. Specializing the camera and processing for one purpose creates undesirable metamers for other purposes - a simple manifestation of the famous "no-freelunch theorem" [9].
A second major difference between Biological Color and Artificial Color is in applications. Biological Color has a primary purpose (discrimination) and sometimes a secondary one (communication, e.g., blushing, sexual arousal, and so forth). Artificial Color can be used to compute useful properties such as wavelength of a monochromatic illuminant, temperature of an emitter, and so forth as will be shown below.
DESIGNING THE SENSITIVITY CURVES
There are several ways one can design sensitivity curves [10]. We list three here in no particular order.
1. Intuitive design. Sometimes this is easy. Suppose we want to make a camera that measures temperature in some range. Also suppose, for the moment, that the emissivity vary little with wavelength. We know where the peaks of the blackbody curves are, so that suggests a wavelength range. But peaks are places where the emission is changing very little (actually not at all) with wavelength. It is better to choose the range where the magnitude of that change is greatest. We might choose two Gaussian curves peaked at both ends of the selected range and one centered half way between them. The standard deviation might be half the range for all three. All of this is possible, because we know the spectrum to arbitrary accuracy for any temperature.
2. Moving Gaussians. Suppose we specify a wavelength range and N (N = 2, 3, ...) Gaussians of means 1/N of the range. Then all we have to do is experiment with the means of Gaussians. Unfortunately, there is no simple-to-compute figure of merit to be computed and we generally have no suitable data unless hyperspectral images are available. This latter remark is important, as it shows the proper relationship between HSI and Artificial Color. HSI gathers the data needed to design an Artificial Color system that accomplishes the desired results without the continuing need for an HSI camera. The resulting Artificial Color camera is cheaper, more sensitive, more reliable, and so forth and can accom-
plish essentially the same fixed function. The difference is between a general system that can handle any task and a specified system for handling one specific task. The figure-of-merit problem has no easy solution. Designing processing for each possible design, testing the design on a large number of data, and assigning a monotonic figure of merit to the results is incredibly demanding of computational resources. For most purposes, it is better to use an easier-to-evaluate figure of merit. We might design linear discriminants for each choice of means and compare results for each design. We can then use some local optimization technique such as steepest descent or some sort of evolutionary method to choose a good set of means.
3. Free form design. Here we allow the curve shape and location to be described by multiple parameters. This complicates the problem considerably, but yields even better results. Our work on this shows that we sometimes design spectral curves with negative components that are unphysical in terms of spectral filters. We must add a bias to keep the filter positive, sacrificing effectiveness in the process. We can also break the filter into two parts whose results can be subtracted to give the desired results.
DESIGNING THE DISCRIMINANTS
In principle, ant pattern recognition method will work, but we have concentrated on the best method we know of to generalize reliably using discriminants trained on a relatively small number of members of the training set. Generalization is the ability to classify new, un-trained-on instances correctly. In general there are two things that tend to produce good generalization: simplicity of the discriminant (pattern recognition experts speak of the Vapnik-Chervonenkis dimension) and large margin between members of the training set. Margin measures the distance between the samples along the decision boundary (the so-called support vectors) and the decision surface in the hyperspace in which the samples are embedded. Unfortunately, maintaining a good margin requires large Vapnik-Cher-vonenkis dimension, so a compromise is required. The method we use avoids that tradeoff by classifying instances in sequence. At every step, we use a linear discriminant (yielding the minimum possible Vapnik-Chervonenkis dimension). We then set the margin to be whatever we want. Of course, that will usually lead to many misclassifications. We remove all of the misclas-sified
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