Intensity variations in image texture can provide powerful quantitative information about physical properties of biological tissue. However, tissue patterns can vary according to the utilized imaging system and are intrinsically correlated to the scale of analysis. In the case of ultrasound, the Nakagami distribution is a general model of the ultrasonic backscattering envelope under various scattering conditions and densities where it can be employed for characterizing image texture, but the subtle intra-heterogeneities within a given mass are difficult to capture via this model as it works at a single spatial scale. This paper proposes a locally adaptive 3D multi-resolution Nakagami-based fractal feature descriptor that extends Nakagami-based texture analysis to accommodate subtle speckle spatial frequency tissue intensity variability in volumetric scans. Local textural fractal descriptors – which are invariant to affine intensity changes – are extracted from volumetric patches at different spatial resolutions from voxel lattice-based generated shape and scale Nakagami parameters. Using ultrasound radio-frequency datasets we found that after applying an adaptive fractal decomposition label transfer approach on top of the generated Nakagami voxels, tissue characterization results were superior to the state of art. Experimental results on real 3D ultrasonic pre-clinical and clinical datasets suggest that describing tumor intra-heterogeneity via this descriptor may facilitate improved prediction of therapy response and disease characterization. 
Quantification of ultrasonic texture intra-heterogeneity via volumetric stochastic modeling for tissue characterization