The work addresses a long-standing tension in digital pathology. Microscopic examination of stained tissue sections remains the cornerstone of disease diagnosis, from characterizing inflammation to staging malignancies, but the stains and fluorescent labels that make features visible alter the specimen’s native chemical and physical state, and laser-scanning techniques such as confocal microscopy impose measurable phototoxicity. Label-free quantitative polarimetric imaging offers a way around this: by characterizing how polarized light is transformed as it passes through tissue, it can quantify properties such as diattenuation, birefringence and depolarization without touching the sample. Biological tissues are inherently anisotropic media — structural proteins like collagen, myelin and actin filaments have ordered molecular architectures that give them intrinsic optical anisotropy — which makes them naturally amenable to polarimetric contrast. Polarimetric microscopy has already shown clinical relevance in oncological histology, where Mueller matrix imaging has been used to visualize collagen birefringence in normal skin, melanoma, basal cell carcinoma and squamous cell carcinoma, and in gynecological pathology, where it captures the disruption of anisotropically organized collagen fibers during malignant transformation of cervical tissue.

The physical engine of the new framework is the Mueller matrix, a four-by-four matrix that fully encodes how a specimen transforms the polarization state of light. In the team’s home-built microscope, based on an Olympus IX73 system with polarization-fit objectives ranging from 10x to 60x, a solid-state LED source at four wavelengths illuminates the sample through a Polarization State Generator, and a Polarization State Analyzer and CMOS camera record the transmitted light. Both generator and analyzer use rotating retarders modulated in a division-of-time scheme, and the full matrix is reconstructed pixel-by-pixel using a vectorized, single-step pseudo-inverse calculation. The system was calibrated against commercial reference polarimeters at multiple wavelengths, achieving experimental condition numbers below four — a mathematical guarantee that measurement noise is not excessively amplified during the inversion.

The study’s methodological centerpiece is the differential Mueller matrix decomposition, a more recent alternative to classical product-based schemes such as the Lu–Chipman decomposition. Product methods assume the specimen’s polarization response arises from a discrete sequence of physically distinct interactions, which works well for bulk samples but is conceptually awkward for the thin sections used in pathology, where anisotropic and scattering events are distributed and intertwined. The differential approach instead takes the matrix logarithm of the measured Mueller matrix, yielding a mathematically unique solution that avoids the non-commutative factor-ordering problem. From this differential matrix, the framework extracts six elementary optical parameters — linear and circular dichroism, linear and circular birefringence, isotropic absorption, and linear and circular depolarization rates — along with correction terms that recover non-depolarizing information lost to time-irreversible mechanisms such as fluorescence, keeping the recovered dichroic and birefringent properties physically self-consistent.

Two downstream digital steps turn these parameters into something a pathologist can actually use. The first tackles the trade-off between magnification and field of view: the objectives needed to resolve microscopic polarimetric features see only a tiny patch of tissue, yet pathological diagnosis is inherently multi-scale, surveying overall architecture before zooming into tumor margins and invasion fronts. The team’s stitching strategy performs geometric registration entirely in the intensity domain — using SIFT feature matching combined with RANSAC on the total-intensity element of the Mueller matrix, enhanced by histogram equalization — and then applies the resulting transformations identically to all sixteen matrix elements of every tile, anchoring each tile to the known raster grid of the motorized stage. The second step is pseudo-color mapping, which assigns physically distinct polarimetric parameters to the red, green and blue channels after per-channel min-max normalization, so that hue and its spatial variation carry information about the local polarization response rather than mere optical density.

The framework was evaluated on histological sections from a well-established preclinical melanoma model: B16-F10 melanoma cells implanted subcutaneously into the flanks of 18 male C57BL/6 mice, divided into a saline-treated control group and a treatment group receiving a combination of the AS1411 aptamer (AGRO), delivered by intratumoral injection three times per week, and the GK-1 peptide, administered intravenously once weekly. After three weeks of monitoring, tumors were excised, fixed, paraffin-embedded, sectioned at 4 micrometers and H&E-stained, yielding 51 sections — 25 from controls and 26 from treated animals — with the animal work approved by UNAM’s institutional ethics committees. Eight specimens, comprising four matched untreated–treated pairs, were used for the quantitative evaluation.

The stitching performance was strong. Photometric discrepancy across tile seams, evaluated directly on the raw Mueller matrix elements, remained small throughout, with the largest mean discrepancy reaching only 5.25 percent, and the cross-scale mean absolute error against independently acquired lower-magnification reference images was at most 2.5 percent for normalized matrix elements. This means the panoramic reconstructions preserved both spatial continuity and the quantitative polarimetric information measured in single fields of view. For the thin pathological sections studied, the differential decomposition produced tissue representations comparable to those of the established Lu–Chipman decomposition, both qualitatively and across quantitative image-quality metrics such as GLCM contrast, Shannon entropy and average gradient — though no single pseudo-color strategy maximized all three metrics, with the depolarization scheme achieving the highest image entropy (5.8888 for untreated and 5.5280 for treated specimens) while the Lu–Chipman scheme achieved the highest GLCM contrast for treated tissue.

The most striking biological observation concerned depolarization. In the untreated specimens, the diagonal Mueller matrix elements related to depolarization were on average smaller than in treated tissue, indicating stronger depolarization before treatment — a response the authors associate with increased structural heterogeneity in tumor tissue, including cellular disorganization, nuclear pleomorphism and spatial variations in scattering properties. The depolarization-based pseudo-color scheme showed a pronounced spatial gradient across the tumor, transitioning from slate-blue background through deep navy to a bright whitish tumor core, and regions that appeared homogeneous in H&E staining exhibited marked chromatic and textural variation under the polarimetric mappings, suggesting the technique senses microstructural heterogeneity that conventional contrast does not capture. In treated specimens, where H&E showed substantial tumor regression and only faint uniform staining, most mappings appeared visually homogeneous, yet the depolarization scheme retained sparse residual contrast in regions that appeared weakly pinkish-purple in H&E. Quantitatively, when polarimetric feature masks were compared with H&E-derived tumor masks using the Dice Similarity Coefficient, the depolarization scheme scored highest at 0.5971, with the Lu–Chipman scheme second at 0.5725 and the remaining schemes ranging from 0.5063 to 0.5424.

The authors are careful to frame these results as preliminary and exploratory rather than diagnostic. The cross-modality comparison was not a clinical validation, the SLIC-based feature extraction was not optimized for polarimetric images, and the sample cohort was small and drawn from a single animal model. The depolarization finding does not establish a direct biological or causal relationship with tumor structure, only a consistent association across numerical distributions, spatial heterogeneity and visual enhancement. The treated specimens reflect treatment-associated alterations in the tumor microenvironment in a controlled preclinical setting, not evidence of clinical benefit in patients.

Even so, the study demonstrates a feasible route toward bridging conventional histological observation and quantitative physical tissue descriptors. By combining large-field polarimetric imaging, physically grounded parameter extraction and intuitive visualization, the framework establishes quantitative links between histological appearance and interpretable optical properties, providing a foundation the authors say will next be tested on larger pathologist-annotated cohorts and integrated with machine-learning approaches for automated tissue characterization and treatment-response prediction.

Subject of Research: Differential Mueller matrix polarimetric microscopy for mapping melanoma tissue structure

Article Title: Computational Mueller matrix microscopic pathology based on differential decomposition for medical reference mapping

Article References: Mao, Y., Estevéz, I., Pérez-Torres, A., Campos, J., & Lizana, A. (2026). Computational Mueller matrix microscopic pathology based on differential decomposition for medical reference mapping. Frontiers in Bioinformatics, 6, Article 1953765. https://doi.org/10.3389/fbinf.2026.1953765

Image Credits: AI Generated

DOI: 10.3389/fbinf.2026.1953765

Keywords: Mueller matrix polarimetry, differential decomposition, computational pathology, label-free imaging, image stitching, pseudo-color mapping, depolarization, melanoma, histopathology, birefringence, tumor microenvironment, quantitative imaging