The black-box nature of deep learning (DL) models presents a significant challenge for their adoption in clinical settings. The field of explainable artificial intelligence (XAI) has emerged to improve the transparency and interpretability of models. However, current techniques do not adequately describe the reasoning underpinning DL models. This study replicates and extends previous research on the use of texture analysis to improve interpretability in clinically geared segmentation tasks. We evaluate Law's Texture Energy Measures (LTEMs) in the learning and decision-making processes of different DL architectures. We extend the work to include breast cancer, skin lesion, and gastrointestinal polyp datasets, as well as CLAHE-enhanced datasets to identify any divergence in learning. Experimental results reiterate that LTEMs, specifically level-edge convolution masks, are highly influential across multiple DL architectures. Additionally, Gray-Level Co-occurrence Matrix (GLCM) analysis highlights autocorrelation as a key descriptor. The results confirm that texture-based representations, learned primarily in the early layers of the network, are sufficient for robust learning. Through LTEMs, we can characterize the patterns learned in DL and associate these patterns with verbal descriptions and clinically objective measures, thus translating the DL learning into human terms. This psychophysical approach eases the clinical interpretability of DL models. Code availability: https://github.com/xrai-lib/xai-texture.