Color is not a metric space implications for pattern recognition, machine learning, and computer vision

Using a metric feature space for pattern recognition, data mining, and machine learning greatly simplifies the mathematics because distances are preserved under rotation and translation in feature space. A metric space also provides a “ruler”, or absolute measure of how different two feature vectors are. In the computer vision community color can easily be miss-treated as a metric distance. This paper serves as an introduction to why using a non-metric space is a challenge, and provides details of why color is not a valid Euclidean distance metric.