  Accurately localizing two-dimensional (2D) ultrasound (US) fetal brain images
in the 3D brain, using minimal computational resources, is an important task
for automated US analysis of fetal growth and development. We propose an
uncertainty-aware deep learning model for automated 3D plane localization in 2D
fetal brain images. Specifically, a multi-head network is trained to jointly
regress 3D plane pose from 2D images in terms of different geometric
transformations. The model explicitly learns to predict uncertainty to allocate
higher weight to inputs with low variances across different transformations to
improve performance. Our proposed method, QAERTS, demonstrates superior pose
estimation accuracy than the state-of-the-art and most of the uncertainty-based
approaches, leading to 9% improvement on plane angle (PA) for localization
accuracy, and 8% on normalized cross-correlation (NCC) for sampled image
quality. QAERTS also demonstrates efficiency, containing 5$\times$ fewer
parameters than ensemble-based approach, making it advantageous in
resource-constrained settings. In addition, QAERTS proves to be more robust to
noise effects observed in freehand US scanning by leveraging rotational
discontinuities and explicit output uncertainties.
