Total Variation Regularization of Pose Signals with an Application to 3D Freehand Ultrasound

Three-dimensional freehand imaging techniques are gaining wider adoption due to their ?exibility and cost ef?ciency. Typical examples for such a combination of a tracking system with an imaging device are freehand SPECT or freehand 3D ultrasound. However, the quality of the resulting image data is heavily dependent on the skill of the human operator and on the level of noise of the tracking data. The latter aspect can introduce blur or strong artifacts, which can signi?cantly hamper the interpretation of image data. Unfortunately, the most commonly used tracking systems to date, i.e. optical and electromagnetic, present a trade-off between invading the surgeon's workspace (due to line-of-sight requirements) and higher levels of noise and sensitivity due to the interference of surrounding metallic objects. In this work, we propose a novel approach for total variation regularization of data from tracking systems (which we term pose signals) based on a variational formulation in the manifold of Euclidean transformations. The performance of the proposed approach was evaluated using synthetic data as well as real ultrasound sweeps executed on both a Lego phantom and human anatomy, showing signi?cant improvement in terms of tracking data quality and compounded ultrasound images. Source code can be found at https://github.com/IFL-CAMP/pose_regularization.