The Vora Value, ν, measures the recording accuracy of a set of color filters . The definition of ν takes into account the viewing and recording illuminants and the target color space. The original definition is independent of the data set to be recorded, does not take into account recording noise, and is based on the Euclidean distance measure in the target color space.
The definition of ν does not take into account recording noise, real data sets, or perceptual error measures, each of which would influence the error expression. For measures that take these into account, please see the section on Other Measures below. The original form of ν is simple and provides an effective rough estimate of the accuracy of the filter set.
Motivation: The Measure ν and the Q-Factor
While the CQF captures an important requirement of color scanning filters, recording filters are not used by themselves and it is necessary to evaluate filter sets as opposed to single filters. As in the case of a single filter, it is important for the filter set to measure the energy in P V (f). Thus the approach underlying the q-factor is useful. However, while a single filter can record energy only in one “direction” of the target color space (e.g., a single filter can measure one of the CIE tristimulus values) the purpose of a filter set is to measure energy in all the directions of the target color space. Thus, for example, if we wish to record CIEXYZ tristimulus values, the filter set should accurately measure X, Y, and Z values. An evaluation criterion for a set of recording filters should hence evaluate whether it measures all the energy in P V (f) − that is, whether it measures the energy in P V (f) in all directions of the target color space.
Additional insight into the power of the Vora Value is obtained by considering the case where the target space is the horizontal plane in 3-space. A set of three independent vectors, none of which lie in the plane, form a basis of the 3-space. None of the vectors will have a q-factor of one. It is clear that the span of the three vectors includes the target space. For this case, ν = 1, as it should. Thus, we can create a filter set that produces perfect tristimulus values from imperfect filters. The cost of this is that it requires more filters than the dimension of the target color space, i.e., r > s.
The Measure ν and Principal Angles
The measure ν is based on a mean-square error in the target color space assuming independent, identically distributed data. It does not take into account real data sets, perceptual error, or recording noise.
Finlayson and Drew [4, 5] address the issue of real data sets. They propose a similar measure based on the White Point Preserving Vora Error With Maximum Ignorance With Positivity (WPPVEMIP), which assumes that one is maximally ignorant of the distribution of f except for knowing that all values in the vector f are positive and that the color correction procedure preserves white points. They demonstrate that the WPPVEMIP is a more accurate estimate of the real error, and hence that the corresponding measure is more accurate than ν.
Wolski et al.  address the issue of perceptual error by using a linear approximation of CIE Lab error in the neighborhood of the points in the (known) data set. The filter sets designed by this method minimize an error measure that is a better estimate of perceptual error than the mean square error used to define ν.
Sharma and Trussell  address the issue of recording noise and propose a Figure of Merit (FOM) based on the approach of Wolski et al. The FOM is derived from an error that takes into consideration recording noise.
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