Visualizing positional uncertainty in freehand 3D ultrasound

The freehand 3D ultrasound technique relies on position sensors attached to the probe to register the location of each image to a 3D space. However, the imprecision of the position sensors reduces the reliability of estimated image locations. In this paper, we propose a novel method to compute the positional uncertainty of an image plane. First, we use rigid body point-based registration to compute the error produced by each pixel of the image during the tracking. The Target Registration Error (TRE) is used to compute the covariance matrix of errors at each pixel position. This covariance matrix is then decomposed as a 3D orientation error, in the x, y and z directions. Considering a volume around the image, we introduce the Image Plane Crossing Probability (IPCP) to determine the probability that the plane passes through each voxel. The result is a point cloud probability around the image plane, where each voxel contains the crossing probability and the contribution of each direction of the error. Finally, a simple volume rendering technique is used to visualize the uncertainty of the plane position. The results are validated in two steps. The first step is a Monte Carlo simulation to validate the estimate of the TRE covariance for the tracking errors. The second step simulates TRE errors on a plane and validates the associated positional uncertainty.