Nonrigid Reconstruction of Freehand Ultrasound without a Tracker

Reconstructing 2D freehand Ultrasound (US) frames into 3D space without using a tracker has recently seen advances with deep learning. Predicting good frame-to-frame rigid transformations is often accepted as the learning objective, especially when the ground-truth labels from spatial tracking devices are inherently rigid transformations. Motivated by a) the observed nonrigid deformation due to soft tissue motion during scanning, and b) the highly sensitive prediction of rigid transformation, this study investigates the methods and their benefits in predicting nonrigid transformations for reconstructing 3D US. We propose a novel co-optimisation algorithm for simultaneously estimating rigid transformations among US frames, supervised by ground-truth from a tracker, and a nonrigid deformation, optimised by a regularised registration network. We show that these two objectives can be either optimised using meta-learning or combined by weighting. A fast scattered data interpolation is also developed for enabling frequent reconstruction and registration of non-parallel US frames, during training. With a new data set containing over 357,000 frames in 720 scans, acquired from 60 subjects, the experiments demonstrate that, due to an expanded thus easier-to-optimise solution space, the generalisation is improved with the added deformation estimation, with respect to the rigid ground-truth. The global pixel reconstruction error (assessing accumulative prediction) is lowered from 18.48 to 16.51 mm, compared with baseline rigid-transformation-predicting methods. Using manually identified landmarks, the proposed co-optimisation also shows potentials in compensating nonrigid tissue motion at inference, which is not measurable by tracker-provided ground-truth. The code and data used in this paper are made publicly available at https://github.com/QiLi111/NR-Rec-FUS.