Papanicolaou stain unmixing for RGB image using weighted nucleus sparsity and total variation regularization

The Papanicolaou stain, consisting of five dyes, provides extensive color information essential for cervical cancer cytological screening. The visual observation of these colors is subjective and difficult to characterize. Direct RGB quantification is unreliable because RGB intensities vary with staining and imaging conditions. Stain unmixing offers a promising alternative by quantifying dye amounts. In previous work, multispectral imaging was utilized to estimate the dye amounts of Papanicolaou stain. However, its application to RGB images presents a challenge since the number of dyes exceeds the three RGB channels. This paper proposes a novel training-free Papanicolaou stain unmixing method for RGB images. This model enforces (i) nonnegativity, (ii) weighted nucleus sparsity for hematoxylin, and (iii) total variation smoothness, resulting in a convex optimization problem. Our method achieved excellent performance in stain quantification when validated against the results of multispectral imaging. We further used it to distinguish cells in lobular endocervical glandular hyperplasia (LEGH), a precancerous gastric-type adenocarcinoma lesion, from normal endocervical cells. Stain abundance features clearly separated the two groups, and a classifier based on stain abundance achieved 98.0% accuracy. By converting subjective color impressions into numerical markers, this technique highlights the strong promise of RGB-based stain unmixing for quantitative diagnosis.