Application of the hierarchical texture-descriptor tensor to histological muscle sections of Poecilia reticulata

Histological assessment of fish skeletal muscle is mostly qualitative, and texture descriptors are usually reported at a single scale and averaged over orientation. This study applies a hierarchical texture-descriptor tensor, indexed by descriptor channel, Gaussian scale, orientation and region of interest (ROI), to two haematoxylin and eosin (HE) panels of guppy (Poecilia reticulata) muscle published under an open licence: a control panel and a panel from fish affected by Tetrahymena pyriformis. Ten channels were evaluated at four scales (1, 2, 4, 8 px) and four orientations, for one ROI (160 entries per image) and four ROIs (640 entries). The anisotropy index A and the texture axis were obtained exactly from the structure matrix and interpreted as circular statistics of the doubled gradient directions; a dilation-covariance relation was used to compare the panels at equal physical scale despite their different pixel sizes (0.75 and 0.96 μm px-1). At s = 2 px, the control muscle was strongly oriented (A = 0.597, 95% CI 0.552-0.648), and its texture axis agreed within 4.2° with the orientation of the interfibre spaces segmented independently. The affected muscle was less oriented (A = 0.377, 95% CI 0.322-0.435); both values exceeded the 95th percentile of isotropic surrogates (≤ 0.034, P ≤ 0.005). At matched physical scales of 1-8 μm, A was 0.57-0.67 in the control and 0.35-0.47 in the affected muscle. The affected panel had a larger characteristic scale (9.9 versus 5.7 μm), a larger area of unstained space (37.5 versus 7.9%), lower co-occurrence contrast and energy and a higher second-derivative amplitude. The results are descriptive, rest on one panel per condition, and do not establish diagnostic value.