4-D x 3-D ultrasound: real-time scan conversion, filtering, and display of displacement vectors with a motorized curvilinear transducer

Recent research in the field of elastography has sought to expand displacement tracking to three dimensions. Once the 3-D volumes of displacement data have been obtained, they must be scan converted so that further processing, such as inversion methods to obtain tissue elasticity, can take place in Cartesian coordinates. This paper details an efficient and geometrically accurate algorithm to scan convert 3-D volumes of displacement vectors obtained from a motorized sector transducer. The proposed algorithm utilizes the physical scan geometry to convert the 3-D volumes of displacement data to both Cartesian coordinates and Cartesian displacements. Spatially varying filters are also proposed to prevent aliasing while minimizing data loss. Validation of the system has shown the algorithm to be correct to floating point precision, and the 3-D scan conversion and filtering can be performed faster than the native rate of data acquisition for the motorized transducer.