Color deconvolution. Optimizing handling of 3D unitary optical density vectors with polar coordinates

Color deconvolution relies on determination of unitary optical density vectors (OD(3D)) derived from pure constituent stains initially defined as intensity vectors in RGB space. OD(3D) can be defined in polar coordinates (phi, theta, radius); always being equal to one, radius can be ignored. Easier handling of unitary optical density 2D vectors (OD(2D)) is shown.

OD(2D) pure stains used in anatomical pathology were assessed as centroid values (phi, theta) with a measure of variance: inertia based on arc lengths between centroid value and sampled points. These variables were plotted on a stereographic projection plane. In order to assess pure stains OD(2D), different methods of sampling RGB pixels were tested and compared: (2) direct sampling of nuclei from preparations using (a) composite H&E and (b) hematoxylin only and (2) for any pure stain RGB image, different associated 8-bit masks (saturation, brightness and RGB average) were used for sampling and compared. Behaviors of phi, theta and inertia were obtained by moving threshold in 8-bit mask histograms. Phi and theta stability were tested against variable light intensity during image acquisition and by using 2 different image acquisition systems.

The more saturated RGB pixels are, the more stable phi, theta and inertia values are obtained. Different commercial hematoxylins have distinct OD(2D) characteristics. UltraView DAB stain shows high inertia and is angularly closer to usual counterstains than ultraView Red stain, which also has a lower inertia. Superior accuracy is expected from the latter stain. Phi and theta OD(2D) values are sensitive to light intensity variation, to the used imaging system and to the used objectives. An ImageJ plugin was designed to plot and interactively modify OD(2D) values with instant update of color deconvolution allowing heuristic segmentation.

Utilization of polar OD(2D) eases statistical characterization of OD(3D) vectors: conditions of optimal sampling were demonstrated and various factors influencing OD(2D) stability were explored. Stereographic projection plane allows intuitive visualization of OD(3D) vectors as well as heuristic vectorial modification. All findings are not restricted to anatomical pathology but can be applied to bright field microscopy and subtractive color applications in general.