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Constancy

To make the color naming and pointing algorithms work in practice, with real images, we can no longer avoid the issue of color constancy. The approach I have adopted to deal with this problem is of a rather pragmatic nature, and I make no claims about its generality or applicability to other problems. Nevertheless, the results are interesting, and the approach seems to be fairly robust with respect to different lighting conditions, and to some extent even with respect to different sensing devices. It is presumably related to the ``white balance'' algorithms implemented in home video cameras and the like, but that is difficult to verify because of the secrecy surrounding commercial applications.

The first thing that needs to be done, if it hasn't been done already, is to gamma correct the image, to make intensities perceptually linear:

where represents the normalized intensity in , represents the gamma correction factor, typically somewhere in the range , and represents the gamma corrected intensity. Video cameras (especially home camcorders) often incorporate gamma correction, but scanners may not, or may allow it to be specified under software control. This step is required since the CIE XYZ standard assumes perceptually linear intensity responses, and also for display on computer (or TV) monitors. I used a gamma correction factor of , if necessary.

Next we need to compensate for differences in lighting, both with respect to intensity and with respect to spectral characteristics. Although the spectrum of the light source can never be completely recovered from the image (see Section ), we can use Von Kries adaptation (Section ) with good results, as long as the spectrum of the light source is not too wildly skewed or irregular. In real camera (and scanner) images it turns out that not only is white not white (i.e. the RGB values are not equal and unity, viz. ), but black is often not black either (i.e. the RGB values are not equal and zero, viz. ). To compound the problem, lighting may vary considerably across a single image (Figure ).

The ``constancy'' algorithm I have developed searches (a subsampled version of) the image for likely representatives of white and black, and then uses those do to a modified Von Kries adaptation:

where is the ``adapted'' pixel value (an RGB vector), is the original pixel value, is the black representative, and is the white representative (both RGB vectors). Finding the black and white representatives works as follows (regarding an image as a set of pixels for convenience):

where is the set of image pixels, represented as normalized RGB vectors in , is the subset of containing potential gray axis pixels, and and are the chosen black and white representatives, respectively. The criterion used to select potential gray axis pixels is another RMS measure, enforcing a summed square error between pixel components of less than . I have obtained good results with . The black and white representatives, then, are the potential gray axis pixels with the lowest and highest brightness, respectively, as determined by a simple sum-of-components measure. A visual way to think of this process is that it stretches the image's actual gray axis and realigns it with the theoretical gray axis for perfectly homogeneous and flat-spectrum lighting, i.e. the line segment . The procedure is illustrated in Figure .

One can image that this procedure might fail on certain images. It is not meant to be foolproof under any circumstances, but to work well enough for our purpose on a large class of ``ordinary'' images.

The performance of the algorithm is of course influenced by the choice of the parameter , and perhaps by the method chosen to compute the brightness of pixels (or blobs). I have not investigated this in any detail, but settled on values that seem to work well for the range of images I have used to test the naming functions on.