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Many machine vision applications require identification of items at specific locations in an image. These items frequently are identifiable by humans from their characteristic colors. Yet, except for a few specialized applications such as food sorting, color-based recognition is infrequently used in machine vision applications. It's not that the potential of color-based recognition has gone unnoticed, but rather that implementations often have been much more difficult and/or less successful than anticipated. We believe that the difficulties are attributable to extension of a traditional single-vector model into a realm for which it is ill-suited. A statistical model is much more suitable.
The elusive single-color item
When we think of color-based recognition in the abstract, we usually think of single-colored objects. Such objects do exist, often paper, plastic or painted, but without extraordinary care in lighting and camera selection their images are almost never single-colored. Yet most attempts at color-based recognition in machine vision are founded on a model of single- colored objects.
Many technical discussions of color-based recognition start with the fact that colors, as perceived by humans, generally can be represented by three numbers. These numbers may be the relative responses of three types of receptors in the human eye. They also may be the relative intensity of the red, green, and blue phosphors in a computer display, or the cyan, yellow and magenta of printing inks etc. Engineers are accustomed to working with such number triplets; they're referred to as vectors. Vectors are omnipresent in the representation of three-dimensional physical objects in space. Many mathematical tools have been developed to work with vectors, thus aiding the design and fabrication of objects large and small.
It's easy to see how the difference between two colors can be usefully treated as the difference between two vectors. The size of this difference goes to zero when the colors become identical. More than two centuries ago a famous mathematician, Carl Friedrich Gauss, showed how, by making repeated measurements and then averaging the result, we could estimate the true value of the quantity measured (See footnote 1). He also showed that from the variance, or scatter, of the measurements we could estimate the uncertainty in the true value.
Usually overlooked are two assumptions Gauss found necessary to link the measure of mean and variance to the estimate of a true value and its uncertainty: The quantity of interest must be single-valued, and the most likely value must be the mean value. These assumptions are reasonable if one is measuring, say, the length or mass of a beam, or the angle between two sides of a triangle. They are not necessarily valid when considering the colors of an object.