Variability of spectral tristimulus values

Abstract

As t he spectral trist imulu s va lues of t he Cl E Standard Obscrver System fo r Color i mcLr y are measurable qua nt ities, t heir varia bili ties should be kn own . T h is p aper d escr ibes a procedure for d eriving " wit h in" a nd " between" vari ances a nd covariances in t he sp ectral tristimulus values , based on color-matching data for indi vidu al observers. Th e " wi t hin " va riances are based on t he replicatio ns of color-mixture data b y an obser ver . Thc " hetwecn " varian ces are based on differ ences a mong t he color-mixt ure data of individu al obser vers. A statistical model is gi ven for t he syste m in whi ch the exp eri mental data ar e obtained. Form ulas fo r expected v alu es (means) , varia nces, and co variances ar e de veloped . Vari ances a n d covarian ces belongin g to different sources of un cer tain ties in t he experi menta l data are co nsidered . A procedure is d eveloped for determining the un cer tain t ies i n t he constant s of a linear t ra nsfor ma t ion to a system ana logo us to t he presen t Cl E syste m. T he for mula s for varia nces a nd co varia nces af ter linear transformation ar e give n, for a rigoro us empi rically-based c hoice, a nd a lso for a n arbitrary choice of t ransfor mation co nst a n ts. The complet e s tan dard obser ver ys te m for every 10 ml' co nsisting of means vari an ces a nd co var ia nces deri ved from a n ar bi trary tra nsfor matio n is listed. The b'etween-obs' cr ver varia bilit ies ar e fo und to be abo ut 10 p ercent of t he averag~s of t he color-mixt ure data and t he average ratio o f t he bet ween-obser ver va ri a bili ties to t he within-observer varia bili t ies is foun d t o be a bout 5. 7.