A fast normalized cross-correlation calculation method for motion estimation

High-precision motion estimation has become essential in ultrasound-based techniques such as time-domain Doppler and elastography. Normalized cross-correlation (NCC) has been shown as one of the best motion estimators. However, a significant drawback is its associated computational cost, especially when RF signals are used. In this paper, a method based on sum tables developed elsewhere is adapted for fast NCC calculation in ultrasound-based motion estimation, and is tested with respect to the speed enhancement of the specific application of ultrasound-based motion estimation. Both the numerator and denominator in the NCC definition are obtained through pre-calculated sum tables to eliminate redundancy of repeated NCC calculations. Unlike a previously reported method, a search region following the principle of motion estimation is applied in the construction of sum tables. Because an exhaustive search and high window overlap are typically used for highest quality imaging, the computational cost of the proposed method is significantly lower than that of the direct method using the NCC definition, without increasing bias and variance characteristics of the motion estimation or sacrificing the spatial resolution. Therefore, high quality, high spatial resolution, and high calculation speed can be all simultaneously obtained using the proposed methodology. The high efficiency of this method was verified using RF signals from a human abdominal aorta in vivo. For the parameters typically used, a real-time, very high frame rate of 310 frames/s was achieved for the motion estimation. The proposed method was also extended to 2-D NCC motion estimation and motion estimation with other algorithms. The technique could thus prove very useful and flexible for real-time motion estimation as well as in other fields such as optical flow and image registration.