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Bezier Interpolation for 3-D Freehand Ultrasound

Freehand 3-D ultrasound (US) produces 3-D volume data of anatomical objects from a sequence of irregularly located 2-D B-mode US images (B-scans). In 3-D US, the voxel intensities are calculated by interpolating those pixels from raw B-scans. Current interpolation algorithms do not consider sparsity of the raw data and are time consuming in computation. In this paper, we aim to perform the 3-D reconstruction of freehand US with sparse raw data in a more efficient manner. A novel interpolation algorithm takes advantage of Bezier curves. A single sweep of raw B-scans is collected, and the third-order Bezier curves are employed for approximating the voxels located in a control window. In in vitro and in vivo experiments, a fetus phantom and a subject's forearm were scanned using the freehand 3-D US system and reconstructed using the proposed Bezier interpolation algorithm and three popular interpolation algorithms, respectively. The results showed that the proposed algorithm significantly outperformed the other three algorithms when the raw B-scans were relatively sparse and the interpolation error in gray level can be reduced by 0.51-5.07. The speed for 3-D reconstruction can be improved by 90.6-97.2 because a single third-order Bezier curve using four control points (i.e., the pixel points) is able to estimate more than four voxels, whereas the estimation of a voxel value often requires a number of pixels in conventional techniques.