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Updated: January 12th, 2011 10:01 AM CDT

Taming the Multicolor Jungle

Most attempts at color-based recognition in machine vision are founded on a model of single-colored objects
Figure 1
© WAY-2C Color Machine Vision
Figure 1. Three single-color items—one red, one white and one whose color is equal to the mean between red and white (pink). The traditional physical vector model can work quite well for correctly identifying each of these by determining which of these lies closest to the unknown to be classified.
Figure 2
© WAY-2C Color Machine Vision
In Figure 2 we add a fourth item to those in Figure 1, one that has equal amounts of red and white. The resulting bimodal color distribution can no longer be adequately represented by a single vector.
Figure 3
© WAY-2C Color Machine Vision
Figure 3 shows a set of multicolor fabric samples. The need for automated inspection based on differentiation and recognition of such fabrics is common in the manufacture of automotive interior components. Use of the single-color model has little to commend it for these fabrics.
Figure 4
© WAY-2C Color Machine Vision
Figure 4 shows the calculated relationships between test and reference color distributions of Figures 1 and 2. P = pink, R = red, W=white, RW=red and white. IN indicates that test color distribution falls “inside” corresponding reference distribution; OUT indicates that test distribution falls outside reference distribution. In contrast to classification, which uses more than one reference class, verification uses a single reference distribution representing color values for the expected class.
Figure 5
© WAY-2C Color Machine Vision
Figure 5 shows a single anomalous capsule among many normal capsules. Each capsule shows two main colors in various shades depending on lighting.
Figure 6
© WAY-2C Color Machine Vision
In Figure 6 the anomalous item in Figure 5 is recognized and flagged by the system. It shows the results of a verification test on each capsule position based on a reference built from an image containing only normal capsules and their surroundings.
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By Robert K. McConnell, Ph.D., WAY-2C Color Machine Vision

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.

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