Robust Hypothesis Testing and Statistical Color Classification (Dissertation)

The purpose of this research is twofold: (i) the development of a mathematical model for statistical color classification; and (ii) the testing of this model under controlled conditions. We consider the following hypothesis testing problem: Let Z = θ + V, where the scalar random variable Z denotes the sampling model, θ ∈ Ω is a location parameter, Ω ⊂ R, and V is additive noise with cumulative distribution function F. We assume F is uncertain, i.e., F ∈ F, where F denotes a given uncertainty class of absolutely continuous distributions with a parametric or semiparametric description. The null hypothesis is H0: θ ∈ Ω, F ∈ F and the alternative hypothesis is H1: θ ∉ Ω, F ∈ F. Through controlled testing we show that this model may be used to statistically classify colors. The color spectrum we use in these experiments is the Munsell color system which combines the three qualities of color sensation: Hue, Chroma and Value. The experiments show: (i) The statistical model can be used to classify colors in the Munsell color system; (ii) more robust results are achieved by using a Chroma-Hue match instead of a Perfect match; (iii) additional robustness can be achieved by classifying a color based on measurements averaged over a neighborhood of pixels versus measurements at a single pixel; and (iv) a larger color spectrum than the Munsell color system is needed to classify a range of man-made and natural objects.