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Up to now, most of the color edge detection methods are monochromatic-based techniques, which produce, in general, better than when traditional gray-value techniques are applied. In this overview, we focus mainly on vector-valued techniques because it is easy to understand how to apply common edge detection schemes to every color component. Opposed to this, vector-valued techniques are new and different. The second part of the article addresses the topic of edge classification. While edges are often classified into step edges and ramp edges, we address the topic of physical edge classification based on their origin into shadow edges, reflectance edges, orientation edges, occlusion edges, and specular edges. In the rest of this article we discuss various vector-valued techniques for detecting discontinuities in color images. Then operators are presented based on vector order statistics, followed by presentation by examples of a couple of results of color edge detection. We then discuss different approaches to a physical classification of edges by their origin.