A pointwise contextual multiscale texture operator and its application to 3D medical image segmentation

We introduce a pointwise multiscale texture operator providing a mathematically grounded and interpretable description of how local image context evolves across observation scales. The operator is defined through the scale evolution of a contextual multiscale signature derived from Gaussian scale-space representations, thereby establishing direct connections with diffusion processes and multiresolution analysis. This formulation yields a stable descriptor of texture transitions that is robust to moderate noise, blurring, and acquisition variability, while remaining independent of any specific segmentation strategy. As a demonstration of its practical utility, we embed the proposed operator within a texture-coherence-driven region-growing framework for image segmentation. The resulting algorithm is dimension independent, computationally tractable, and does not rely on training data or complex architectural design. We illustrate its performance on 3D cone-beam computed tomography (CBCT) datasets, where it enables coherent segmentation and volumetric reconstruction of the dental pulp chamber under clinically relevant conditions involving low contrast, partial volume effects, and heterogeneous textures. Beyond this specific application, the proposed operator constitutes a general framework for multiscale texture analysis and structural characterization, particularly suited to imaging scenarios where interpretability, robustness to acquisition degradation, and limited annotated data are critical.