  Three-dimensional (3D) freehand ultrasound (US) reconstruction without a
tracker can be advantageous over its two-dimensional or tracked counterparts in
many clinical applications. In this paper, we propose to estimate 3D spatial
transformation between US frames from both past and future 2D images, using
feed-forward and recurrent neural networks (RNNs). With the temporally
available frames, a further multi-task learning algorithm is proposed to
utilise a large number of auxiliary transformation-predicting tasks between
them. Using more than 40,000 US frames acquired from 228 scans on 38 forearms
of 19 volunteers in a volunteer study, the hold-out test performance is
quantified by frame prediction accuracy, volume reconstruction overlap,
accumulated tracking error and final drift, based on ground-truth from an
optical tracker. The results show the importance of modelling the
temporal-spatially correlated input frames as well as output transformations,
with further improvement owing to additional past and/or future frames. The
best performing model was associated with predicting transformation between
moderately-spaced frames, with an interval of less than ten frames at 20 frames
per second (fps). Little benefit was observed by adding frames more than one
second away from the predicted transformation, with or without LSTM-based RNNs.
Interestingly, with the proposed approach, explicit within-sequence loss that
encourages consistency in composing transformations or minimises accumulated
error may no longer be required. The implementation code and volunteer data
will be made publicly available ensuring reproducibility and further research.
