Several color indexing methods that use color histograms were also evaluated to provide comparison for the color sets method. Four image retrieval techniques were used in the queries: (1) euclidean histogram distance, (2) histogram intersection, (3) quadratic histogram distance and (4) color sets.
The euclidean distance between two color histograms h and g is given by
In this distance formula there is only comparison between the identical bins in the respective histograms. Two different bins may represent perceptually similar colors but are not compared cross-wise. All bins contribute equally to the distance.
The color histogram intersection was proposed for color image retrieval in [SB91]. The intersection of histograms h and g is given by:
Colors not present in the user's query image do not contribute to the intersection. This formulation differs from that proposed by Swain and Ballard [SB91] in order to make it a true distance metric. The intersection formula in [SB91] is not symmetric in h and g and therefore is not a distance metric.
The color histogram quadratic distance is used by the QBIC system [FFN 
93]. The quadratic distance between histograms h and g is given by:
The quadratic distance formula uses the cross-correlation 
between histogram bins based on the perceptual similarity of the colors 
and 
. One appropriate value for the cross-correlation is given by 
where 
is the distance between color and normalized with respect to the maximum distance. In this case the histogram quadratic distance formula reduces to the form on the right [HSE 95].