## 3 Results  
### Comparisons of Accuracy Among Different Implementations  
Displacement estimates obtained from using the **NCC-CPU** of the block-matching algorithm were compared to other five above-mentioned implementations: **Lou-konofagou-CPU**, **Lewis-CPU**, **NCC-GPU**, **Lou-Konofagou-GPU**, **Lewis-GPU**. In Figure 4, the standard-NCC-CPU implementation yielded exactly same displacements as compared to the Lou-Konofagou-CPU implementation (see the second row). The differences between the standard-NCC-CPU and Lewis-CPU implementations were neglectable (\(<\)10\({}^{-15}\) mm), as shown in the third row of Figure 4. However, when comparing three GPU implementations (NCC-GPU, Lou-Konofagou-GPU and Lewis-GPU) to the standard-NCC-CPU implementation, small differences exist (see the fourth to sixth rows in Figure 4). The differences are quantitatively analyzed from 30 (elevational) slices of ultrasound displacement data and the result is shown in Figure 5.  
It is clear from Figure 5 that all three GPU implementations produced slightly different displacement results. However, the difference was small (10\({}^{-6}\)-10\({}^{-4}\) mm). Such a small difference did not result in visible differences on respective axial strain images (see the fourth column in Figure 4). Computational Efficiency  
The influence of the tracking kernel size was investigated for six implementations and the results are shown in Figure 6. The search range was set to \((5\,\mathrm{[lateral]}\times 18\,\mathrm{[axial]}\times 3\,\mathrm{[elevational]})\) for tracking approximately 1.5% tissue deformation, and the size of tracking kernel varied as stated in those figures. For reference, 18, 61 and 69 axial samples are equivalent to 0.36 mm, 1.16 mm, and 1.35 mm, respectively, while 7, 9 and 11 beamlines are 0.83 mm, 1.07 mm and 1.31 mm, respectively. Three elevation planes equal to 0.64 mm in space. We found that the Lou-Konofagou method can substantially reduce the computing time under the CPU environment (i.e., \(>\)95% reduction between Lou-Konofagou-CPU and NCC-CPU). However, under the GPU environment, the reductions become small but still noticeable (between 17-46%). It is interesting to note that, under the GPU environment, [PERSON]'s method reduces the computing time at a lower rate (between 7-23%), as compared to Lou-Konofagou method. Figure 4: In the first row, (**A**) lateral, (**B**) axial and (**C**) elevational displacements estimated from a TM phantom using the CPU-Version of the standard NCC method. The (displacement) difference images from the first three columns of the second to the sixth rows showing the displacement difference between the stand-NCC-CPU method and one of the other five methods: [second row] Lou-Konofagou-CPU, [third row] Lewis-CPU, [fourth row] NCC-GPU, [fifth row] Lou-Konofagou-GPU and [sixth row] Lewis-GPU. Estimated displacement differences are displayed in a compressed (log\({}_{10}\)) fashion except for the results in the second row in which the differences are zeros. Disp. is an abbreviation of displacement. Axial strain images (**D**, **H**, **L**, **P**, **T**, and **X**) obtained by six implementations are shown in the fourth column. Figure 5: Clustered box plots illustrating absolute displacement difference values obtained from the standard-NCC-CPU implementation and three different GPU implementations (standard-NCC-GPU, Lou-Konofagou-GPU, Lewis-GPU). The top and bottom of the boxes indicate 75 and 25 percentiles, respectively. The line through the middle of each box represents the median. The error bars show the minimum and maximum values. The gray “dot-shaped” markers indicate outliers. When the tracking kernel was fixed at 9 [1.07 mm; lateral] \(\times\) 69 [1.35 mm; axial] \(\times\) 3 [0.64 mm; elevational]]. The computational efficiency was also examined when the search range had been varied. It is common to change the search range in USE to accommodate different frame-to-frame (2D) or volume-to-volume (3-D) strain levels occurring in vivo.