## 3 Results
### Birefringence Analysis and Collagen Fraction Quantification  
A representative example of the birefringence analysis is shown in Figure 4 for the same section shown in Figure 3. The intensity of the original dark-field image \(A_{c}^{i}\) (Figure 4a) is affected by source illumination, acquisition exposure, sample transmittance, and a nonzero transmittance \(T_{c}\) of the crossed polarizers. These factors create a background illumination, which could interfere with birefringence detection. The corrections applied through the processing pipeline up to Equation (13) isolated the birefringence signal produced by the sample (Figure 4b), reducing the aforementioned artifacts. The subsequent application of Equation (14) compensated for the effects of section thickness variability. As shown in Figure 4c, the signal was normalized to unitary average optical thickness, producing the RGB image \(S_{bir}^{i}\), which was representative of collagen density in the tissue. The RGB collagen signal was transformed into a greyscale image \(S_{col}^{i}\) (Figure 4d), suitable for segmentation of the high-collagen tissue in the sample by thresholding according to \(t_{col}\). The collagen segmentation mask \(mask_{col}^{i}\) produced for the threshold \(t_{col}\) = 0.152 (see next Section) is highlighted in yellow in Figure 4d. Combining the collagen mask with the tissue mask \(mask_{tis}^{i}\), the collagen fraction \(c^{i}\) of the sample was computed according to Equation (17), giving a value of 14.3% for the shown example. Figure 5 shows an example of the algorithm capability to compensate artifactual variability related to sample thickness. Two spatially close tissue sections, characterized by similar tissue composition but different thickness, were compared. At visual inspection, the tissue profile and the red stain distribution followed similar patterns, while the different section thickness affected the transmittance values (Figure 5a,b). In the original dark-field images, a difference in birefringent signal intensity was observed (Figure 5c,d), where the thicker section emitted a redder and more intense birefringent light. After thickness correction, the RGB birefringence images \(S^{i}_{bir}\) (Figure 5e,f) were more balanced in  
Figure 3: Segmentation of tissue from luminal area and calculation of the transmittance in a representative tissue slice: (**a**) Smoothed histogram of the original bright-field image \(A^{i}_{p}\) separated in the red (R), green (G), and blue (B) channels. The nonuniform illumination causes the values of the luminal area to overlap with those corresponding to the tissue area; (**b**) Original bright-field image \(A^{i}_{p}\) (windowed 0-65,535), affected by nonuniform illumination; (**c**) Smoothed histogram of the bright-field image \(B^{i}\) separated in the red (R), green (G), and blue (B) channels. For each channel, the corrected illumination allows the separation of the lumen peak at \(x_{lum}\) (grey line) from the tissue peak at \(x_{tis}\) (black line) by the threshold \(t_{seg}\) (magenta line); (**d**) Sample transmittance image \(T^{i}_{s}\) obtained by white-balancing \(B^{i}\) according to the white point \(x_{lum}\). The black contour indicates the border of \(mask^{i}_{tis}\), obtained by thresholding \(B^{i}\) at \(t_{seg}\). The threshold separates the luminal and tissue area, represented by the right and left portions of the histogram with respect to the magenta line in (**c**). terms of intensity and chroma. The threshold \(t_{col}\) = 0.152 on the greyscale collagen signal (Figure 5g,h) produced comparable fractions of collagen content (8.1% and 11.1%, respectively). It is to notice that a more fragmented collagen distribution was present in the thinner section, while in the thicker one the signal formed larger clusters, probably owing to the additive effects of a larger number of myocardial tissue layers.