A closed-form differential formulation for ultrasound spatial calibration

Abstract

Purpose: Calibration is essential in tracked freehand 3D ultrasound (US) to find the spatial transformation from the image coordinates to the reference coordinate system. Calibration accuracy is especially important in image-guided interventions. Method: We introduce a new mathematical framework that substantially improves the US calibration accuracy. It achieves this by using accurate measurements of axial differences in 1D US signals of a multi-wedge phantom, in a closed-form solution. Results: We report a point reconstruction accuracy of 0.3 mm using 300 independent measurements. Conclusion: The measured calibration errors significantly outperform the currently reported calibration accuracies. © 2012 Springer-Verlag.