A discrete-scatterer model for ultrasonic images of rough surfaces

Automated analysis of ultrasonic images could be greatly improved with model-based Bayesian methods for image analysis. Such an approach would require an accurate probabilistic image model representing ultrasonic images in terms of the gross shape of underlying anatomical structure. Existing probabilistic models for ultrasonic image data do not adequately incorporate structure shape or system characteristics; thus, a substantially new approach is warranted. Toward that goal, we have developed models for the imaging system and rough surface with the following objectives: (1) accuracy in representation of basic image characteristics such as the texture and intensity, (2) a minimum of computational requirements, and (3) a form that is naturally extendable to an appropriate probabilistic image model. The imaging system was modeled as a linear system with a separable three-dimensional point-spread function with an envelope of Gaussian curves in each dimension. The rough surface was modeled as a collection of discrete scatterers placed on the continuum and parametrized by a surface roughness and scatterer concentration. Models were evaluated by a visual comparison of actual and simulated images of a cadaveric lumbar vertebra. The gross shape of the vertebral surface was estimated from computed tomography images of the vertebra, and simulated images were generated using the models and the gross surface shape. Actual images were registered with the surface and simulated images to within 2 mm. The similarity of the actual and simulated images was quite remarkable considering the simplicity of the models. Differences between the images were less than those between two simulated images separated by 0.4 mm or one-fifth the registration error. Further assessment of the models would require a statistical approach not yet available. The models do, however, provide the basis for the development of a computationally tractable probabilistic image model for image analysis. Such a mod- l will provide the means for a statistical evaluation of the system and surface models.