Error propagation due to color space transforms

It is known that the transformation of RGB color space to the normalized color space is invariant to changes in the scene geometry. The transformation to the hue color space is additionally invariant to highlights. However, due to sensor noise, the transforms become unstable at many RGB values. This effect is usually overcome by ad hoc thresholding, for example if the RGB coordinates are located near the achromatic axis then the corresponding hue value is rejected. To arrive at a principled way to deal with the unstabilities that result from these color space transforms, the contribution of this report is as follows. Uncertainties in the measured RGB values are caused by photon noise, which arises from the statistical nature of photon production. Using a theoretical camera model, we determine the number of photons required to cause a color value transition. Based on the associated uncertainty according to the Poisson distribution, we then derive theoretical models that propagate this uncertainty to the uncertainty in the transformed color coordinates. We propose a histogram construction method based on Parzen estimators that incorporates this theoretical reliability. As a result, we overcome the need for thresholding of the transformed color values.