Combinatorial and Probabilistic Fusion of Noisy Correlation Measurements for Untracked Freehand 3-D Ultrasound

In freehand 3-D ultrasound (US), the relative positions of US images are usually measured using a position tracking device despite its cumbersome nature. The probe trajectory can instead be estimated from image data, using registration techniques to recover in-plane motion and speckle decorrelation to recover out-of-plane transformations. The relationship between speckle decorrelation and elevational separation is typically represented by a single curve, estimated from calibration data. Distances read off such a curve are corrupted by bias and uncertainty, and only provide an absolute estimate of elevational displacement. This paper presents a probabilistic model of the relationship between correlation measurements and elevational separation. This representation captures the skewed distribution of distance estimates based on high correlations and the uncertainties attached to each measurement. Multiple redundant correlation measurements can then be integrated within a maximum likelihood estimation framework. This paper also introduces a new method based on the traveling salesman problem for resolving sign ambiguities in data sets resulting from nonmonotonic probe motion and frame intersections. Experiments with real and synthetic US data show that by combining these new methods, out-of-plane US probe motion is recovered with improved accuracy over baseline methods using a deterministic model and fewer measurements.