# Iterative 2D Tissue Motion Tracking in Ultrafast Ultrasound Imaging
## 4 Discussion
In ultrafast ultrasound imaging, the signal-to-noise ratio is the most important factor whereas the others mainly have an effect at larger movements per frame. We expect that the proposed tracking scheme will be affected by these factors and the size of the kernel in the same manner as other block-matching methods [26; 28; 31]. It is well known that larger kernel sizes give more robust motion estimations [31]. In the phantom study, we use a kernel size of 1 \(\times\) 1 mm\({}^{2}\), which can be regarded to be a relatively small kernel size and might explain some of the standard deviations of the motion estimations in this study. These issues need further studies. The main finding of the phantom study is that a large length of iteration (large \(k\)) reduces the mean estimation error and the standard deviation. However, the results are complex. Figures 4-7 show the following:  
* Using a small initial length of iteration (\(k\leq 2\)) gave rather small mean estimation errors but gave large standard deviations. Each of the motion estimations in the first iteration gave a very small error, but they accumulated to rather large errors and did so along different paths. * Using a medium initial length of iteration (\(k=4\)-\(32\)) gave larger mean estimation errors but smaller standard deviations. All estimations were roughly equal, but the initial motion estimations underestimated the motions. The later iterations gave accurate estimations for the in-between frames, but their starting points from the first iteration were incorrect. * Using a large initial length of iteration (\(k\geq 64\)) gave small mean estimation errors and small standard deviations. The distance moved between each frame in the first iteration was large enough for the motion estimations to be accurate and for the later iterations to give accurate estimations for the in-between frames. It could be expected that the motion estimation errors were the same when using the initial length of iteration \(k\) for a velocity \(v\) or when using \(k\) divided by \(2\) for a velocity two times \(v\) as the movement per frame in the initial tracking is equal. One possible explanation for the different errors, shown in Figures 6 and 7, is the fact that an estimation using \(k\) divided by two uses one iteration less than an estimation using \(k\). Overall, as stated above, more iterations give less estimation errors in the phantom measurements; however, this issue needs further studies. The motion estimations of the proposed tracking scheme were compared to state-of-the-art low frame rate motion estimates as this is the gold standard when estimating the longitudinal wall movement of the arterial wall [26; 28; 32; 33; 34; 35; 36]. The optimal frame rate using low frame rate imaging with a conventional linear scan scheme depends on, e.g., the signal-to-noise ratio, speckle decorrelation, out-of-plane movement, and biasing. Somewhat depending on the ultrasound scanner, we regard a frame rate of 50-90 Hz to be the optimal using a conventional linear scan scheme. Considering the large estimation errors when tracking frame-to-frame using ultrafast ultrasound imaging (\(k=1\) in Tables 1-4), the motion estimation errors when using initial length of iteration \(k=128\) are promising as they are of the same order of magnitude as the results using low frame rate cine loops. The effect of using transducers with different pitch (Figures 4 and 6) was anticipated in effect if not in amplitude, i.e., tracking using a smaller pitch (\(\lambda/2\)) gives more accurate motion estimations than using the larger pitch (\(\lambda\)). This depends probably on both higher pixel density in the lateral direction in the resulting B-mode image and improved beamforming because of the smaller pitch. Further studies are needed to evaluate this. The tracking performance using a low frame rate and the larger pitch was unexpectedly poor, raising the question of whether low frame rate tracking using the 200-\(\upmu\)m-pitch transducer can work in vivo.