NickersonColorDifference {munsellinterpol}

Calculate the Nickerson Color Difference between two Colors

Description

Calculate the Nickerson Color Difference between two colors, given in Munsell HVC; see Nickerson.

Usage

NickersonColorDifference( HVC0, HVC1, symmetric=TRUE ) 

Arguments

HVC0

a numeric Nx3 matrix with HVC values in the rows, or a vector that can be converted to such a matrix, by row. HVC0 can also be a numeric 3-vector with a single HVC, and it is then replicated to match the size of HVC1.
HVC0 can also be a character N-vector with Munsell Notations, which is converted to an Nx3 matrix using HVCfromMunsellName().

HVC1

a numeric Nx3 matrix with HVC values in the rows, or a vector that can be converted to such a matrix, by row. HVC1 can also be a numeric 3-vector with a single HVC, and it is then replicated to match the size of HVC0.
HVC1 can also be a character N-vector with Munsell Notations, which is converted to an Nx3 matrix using HVCfromMunsellName().

symmetric

if FALSE then use the original Nickerson difference formula, and if TRUE then use a symmetrized version; see Details.

Details

If HVC0=H_0,V_0,C_0 and If HVC1=H_1,V_1,C_1 then the original Nickerson formula is:

NCD(HVC0,HVC1) = 0.4 C_0 \Delta H ~+~ 6 \Delta V ~+~ 3 \Delta C

where \Delta H = |H_0 - H_1| (on the circle), \Delta V = |V_0 - V_1| and \Delta C = |C_0 - C_1| . Unfortunately, if HVC0 and HVC1 are swapped, the color difference is different. The first color is considered to be the reference color and the second one is the test color. The difference is not symmetric.
Another problem is that the difference is not continuous when the second color is a neutral gray, for rectangular coordinates on a plane of constant V.

Both of these problems are fixed with a slightly modified formula:

NCD(HVC0,HVC1) = 0.4 \min(C_0,C_1) \Delta H ~+~ 6 \Delta V ~+~ 3 \Delta C

For the first formula set symmetric=FALSE and for the second formula set symmetric=TRUE.

Value

A numeric N-vector with the pairwise differences, i.e. between row i of HVC0 and row i of HVC1.

Author(s)

Jose Gama and Glenn Davis

References

Nickerson, Dorothy. The Specification of Color Tolerances. Textile Research. Vol 6. pp. 505-514. 1936.

Examples

NickersonColorDifference( '7.6P 8.9/2.2', '8P 8.2/3'  )
##  [1] 6.952