Estimation of surface pose with a physically-based ultrasonic image model

State-of-the-art approaches to shape analysis in medical images use a variety of sophisticated models for object shape. We have developed an image model that permits the application of these approaches to ultrasonic images, with detailed methods for representing rough surfaces. Our physically-based, probabilistic image model incorporates the combined effects of the system point-spread function (PSF), the tissue microstructure, and the gross tissue shape. At each image pixel, the amplitude mean and variance are computed directly from the model, characterizing the combined influence of shape, microstructure, and system PSF. Calculation of the SNR0 is used to further classify each pixel as Rayleigh- or non-Rayleigh-distributed. This characterization was used here to generate a data likelihood representing any set of images of a given surface by a probability density conditioned on the surface pose, or rotation and translation. The utility of this likelihood was demonstrated by applying maximum likelihood estimation to infer the pose of a cadaveric vertebra from simulated images of its surface. Successful results were achieved using derivative-based optimization algorithms for a data set of only three images. With a quasi-Newton BFGS algorithm, error in 15 of 20 trials was less than 0.4 degrees in rotation and 0.2 mm in translation. Estimation was inaccurate in only 1 of 20 trials. These results illustrate the potential of a physically-based image model in a rigorous approach to image analysis and also serve as an example of quantitative assessment of the model via performance in a specific application.