Correction: Displacement detection with sub-pixel accuracy and high spatial resolution using deep learning

Correction: Journal of Medical Ultrasonics (2022) 49:3–15 https://doi.org/10.1007/s10396-021-01162-7

In this article the presentation of the Lucas–Kanade method in the section of Material and Method was incorrectly given as

$$ \left[ {\begin{array}{*{20}l} {u_{x} } \\ {u_{z} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\sum\limits_{{x,z}} {l_{x}^{2} } } & {\sum\limits_{{x,z}} {l_{x} l_{z} } } \\ {\sum\limits_{{x,z}} {l_{x} l_{z} } } & {\sum\limits_{{x,z}} {l_{z}^{2} } } \\ \end{array} } \right]^{{ - 1}} \left( {\left( {I - J} \right)\left[ {\begin{array}{*{20}c} {\sum\limits_{{x,z}} {l_{x} } } \\ {\sum\limits_{{x,z}} {l_{z} } } \\ \end{array} } \right]} \right), $$

but should have been

$$\left[\begin{array}{c}{u}_{x}\\ {u}_{z}\end{array}\right]={\left[\begin{array}{cc}\sum {I}_{x}^{2}& \sum {I}_{x}{I}_{z}\\ \sum {I}_{x}{I}_{z}& \sum {I}_{z}^{2}\end{array}\right]}^{-1}\sum \left[\left(I-J\right)\left[\begin{array}{c}{I}_{x}\\ {I}_{z}\end{array}\right]\right]$$

In Table 1 of this article, the data in row 4 were incorrectly published.

Incorrect version

Table 1 The optimization of network parameters

Corrected version (Table 1)

Table 1 The optimization of network parameters