Distance and Similarity Measures

Definition:The notion of distance or similarity between two color vectors is of paramount importance for the development of the vector processing techniques such as noise removal filters, edge detectors and image zoomers.

Since each color vector is uniquely determined via its magnitude (length) and direction (orientation), the evaluation of the color vectors can be realized in the magnitude domain, the directional domain, or it can utilize both vectors’ magnitude and direction [1], [2], [3].

The most commonly used measure to quantify the distance between two color vectors χ _i =[x _i1,x _i2,x _i3] and χ _j =[x _j1,x _j2,x _j3], in the magnitude domain, is the generalized weighted Minkowski metric:

where c is the non-negative scaling parameter denoting the measure of the overall discrimination power and the exponent L, with L=1 for the city-block distance, L=2 for the Euclidean distance and L→∞ for the chess-board distance, defines the nature of the distance metric [1], [2], [3]. The parameter...