... ... @@ -12,7 +12,7 @@ They use the law of Bouguer-Lambert-Beer \cite{Beer1852,Perrin1948} for a linear Ruifrok and Johnston only sketch an (analytical) outline of the procedure and do no discuss the practical implementation, or how to reconstruct' images with the estimated dye amounts.\\ \noindent A ImageJ plugin (based on original code made available by A.C.\ Ruifrok) was released in 2004 by Gabriel Landini \cite{Landini2004,Landini2020}. Things such as pure dye identification and image reconstructing have been implemented in this (Java) plugin. \noindent A ImageJ plugin (based on original code made available by A.C.\ Ruifrok) was released in 2004 by Gabriel Landini \cite{Landini2004,Landini2020} and (very) recently updated \cite{Landini2020,Landini2020a}. Things such as pure dye identification and image reconstructing have been implemented in this (Java) plugin. ... ... @@ -178,9 +178,12 @@ For the analysis, it is best when this invented third colour is perpendicular' \begin{equation} \col{k}_3 = \col{\hat{k}}_1 \times \col{\hat{k}}_2 = \begin{bmatrix} k_{G_1}k_{B_2} - k_{B_1}k_{G_2}\\ % Kb*kg - Kg*kb k_{B_1}k_{R_2} - k_{R_1}k_{B_2} \\ % Kr*kb - Kb*kr, k_{R_1}k_{G_2} - k_{G_1}k_{R_2} \end{bmatrix} %Kg*kr - Kr*kg k_{R_1}k_{G_2} - k_{G_1}k_{R_2} \end{bmatrix} \label{anglecross}%Kg*kr - Kr*kg \end{equation} Note that this column still needs to be normalized to $\col{\hat{k}}_3$. Also note that you can find the angle between two columns $n$ and $m$ by taking the inverse cosine of the inner dot product of the two columns (when the columns are normalised): \begin{equation} \varphi_{nm} =\acos\left(\colt{\hat{k}}_n \cdot \col{\hat{k}}_m\right) \label{angledot} \end{equation} Note that this column still needs to be normalized to $\col{\hat{k}}_3$. \subsection{Summary: colour deconvolution in RGB} ... ...