Multi-dimensional sub-sample motion estimation: Initial results

Motion estimation in ultrasound images lies at the heart of many modern signal processing applications. Therefore, its computational cost, accuracy, and precision are of significant importance. In this work, we consider the problem of 3D subsample motion estimation. Extending our previous 2D work, we define a 3D polynomial interpolation function that fits the discrete pattern matching coefficients obtained from digitized 3D echo data. A joint estimation of the axial, lateral and elevational motion is obtained by finding the extremum of this 3D polynomial fit. We study this method using a synthetic phantom and the Field II ultrasound simulation software. The mean absolute axial, lateral, and elevational biases of the proposed 3D polynomial fitting were found to be 0.0066, 0.0075, and 0.0047 of a sample (corresponding to 127 nm, 2.25 ¿m, and 710 nm), respectively, for an axial sampling of 40 MHz (¿ 19.3 ¿m), a lateral sampling of 300 ¿m, and an elevational sampling of 150 ¿m. The mean axial, lateral, and elevational standard deviations of the proposed 3D polynomial fitting were found to be 0.0130, 0.0290, and 0.0569 of a sample (corresponding to 250 nm, 8.71 ¿m, and 8.54 ¿m), respectively. Experimental results demonstrating the viability of the proposed method are also presented.