Similarity Registration Problems for 2D/3D Ultrasound Calibration

TL;DR

This paper introduces minimal algorithms for similarity registration of 3D lines and points, enabling accurate calibration of ultrasound probes with tracked needles, demonstrated through synthetic and real data.

Contribution

It presents novel minimal solutions for similarity registration problems, specifically for ultrasound calibration involving 3D lines and points, improving over non-minimal methods.

Findings

Minimal solutions solve registration with fewer correspondences.

Algorithms outperform non-minimal linear formulations.

Validated with synthetic and real ultrasound data.

Abstract

We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with a minimum of 2 line-line correspondences, while the second is solved up to 4 discrete solutions using 4 point-line correspondences. We use these algorithms to perform the extrinsic calibration between a pose tracking sensor and a 2D/3D ultrasound (US) curvilinear probe using a tracked needle as calibration target. The needle is tracked as a 3D line, and is scanned by the ultrasound as either a 3D line (3D US) or as a 2D point (2D US). Since the scale factor that converts US scan units to metric coordinates is unknown, the calibration is formulated as a similarity registration problem. We present results with both synthetic and real data and show that the minimum solutions outperform the correspondent non-minimal linear formulations.