Fast surface and volume estimation from non-parallel cross-sections, for freehand three-dimensional ultrasound

Volume measurements from ultrasound B-scans are useful in many clinical areas. It has been demonstrated previously that using three-dimensional (3-D) ultrasound can greatly increase the accuracy of these measurements. Freehand 3-D ultrasound allows freedom of movement in scanning, but the processing is complicated by having non-parallel scan planes. Two techniques are proposed for volume measurement from such data, which also improve surface and volume estimation from data acquired on parallel planes. Cubic planimetry is a more accurate extension of a volume measurement technique involving vector areas and centroids of cross-sections. Maximal-disc shape-based interpolation is an extension of shape-based interpolation which uses maximal disc representations to adjust the interpolation direction locally and hence improve the quality of the surface generated. Both methods are tested in simulation and in vivo. Volumes estimated using cubic planimetry are more accurate than step-section planimetry, and require fewer cross-sections, even for complex objects. Maximal-disc shape-based interpolation provides a reliable means of reconstructing surfaces from a handful of cross-sections, and can therefore be used to give confidence in the segmentation and hence also the cubic planimetry volume.