  Thyroid disorders are most commonly diagnosed using high-resolution
Ultrasound (US). Longitudinal nodule tracking is a pivotal diagnostic protocol
for monitoring changes in pathological thyroid morphology. This task, however,
imposes a substantial cognitive load on clinicians due to the inherent
challenge of maintaining a mental 3D reconstruction of the organ. We thus
present a framework for automated US image slice localization within a 3D shape
representation to ease how such sonographic diagnoses are carried out. Our
proposed method learns a common latent embedding space between US image patches
and the 3D surface of an individual's thyroid shape, or a statistical
aggregation in the form of a statistical shape model (SSM), via contrastive
metric learning. Using cross-modality registration and Procrustes analysis, we
leverage features from our model to register US slices to a 3D mesh
representation of the thyroid shape. We demonstrate that our multi-modal
registration framework can localize images on the 3D surface topology of a
patient-specific organ and the mean shape of an SSM. Experimental results
indicate slice positions can be predicted within an average of 1.2 mm of the
ground-truth slice location on the patient-specific 3D anatomy and 4.6 mm on
the SSM, exemplifying its usefulness for slice localization during sonographic
acquisitions. Code is publically available:
\href{https://github.com/vuenc/slice-to-shape}{https://github.com/vuenc/slice-to-shape}
