1 Correction to: Math Geosci https://doi.org/10.1007/s11004-019-09818-4
The original version of this article unfortunately contained mistakes in Eqs. 9, 10, 12 and 13.
The correct versions are
$$ D(d_{V} ({\mathbf{u}}_{i} ),d_{V}^{(t)} ({\mathbf{u}})) = \left( {\sum\limits_{j = 0}^{{n_{V} }} \lambda ({\mathbf{h}}_{j} )\left[ {r_{V} ({\mathbf{u}}_{i} + {\mathbf{h}}_{j} ) - r_{V}^{(t)} ({\mathbf{u}} + {\mathbf{h}}_{j} )} \right]^{2} } \right)^{1/2} , $$
(9)
$$ D(d_{v} ({\mathbf{u}}_{i} ),d_{v}^{(t)} ({\mathbf{u}})) = \left( {\sum\limits_{j = 1}^{{n_{v} ({\mathbf{u}}_{i} )}} \lambda ({\mathbf{h}}_{j} )\left[ {r_{v}^{(s)} ({\mathbf{u}}_{i} + {\mathbf{h}}_{j} ) - r_{v}^{(t)} ({\mathbf{u}} + {\mathbf{h}}_{j} )} \right]^{2} } \right)^{1/2} , $$
(10)
$$ \begin{aligned} & { \Pr }\{ {\mathbf{R}}_{v} ({\mathbf{u}}_{i} ) = {\mathbf{r}}_{v} |\varOmega_{i - 1} \} \approx { \Pr }\{ {\mathbf{R}}_{v} ({\mathbf{u}}_{i} ) = {\mathbf{r}}_{v}^{(t)} ({\mathbf{u}}_{k} )|d_{V} ({\mathbf{u}}_{i} ),d_{v} ({\mathbf{u}}_{i} )\} \\ & \propto { \Pr }\{ {\mathbf{R}}_{v} ({\mathbf{u}}_{i} ) = {\mathbf{r}}_{v}^{(t)} ({\mathbf{u}}_{k} )|d_{V} ({\mathbf{u}}_{i} )\}^{{1 - \alpha_{i} }} \cdot { \Pr }\{ {\mathbf{R}}_{v} ({\mathbf{u}}_{i} ) = {\mathbf{r}}_{v}^{(t)} ({\mathbf{u}}_{k} )|d_{v} ({\mathbf{u}}_{i} )\}^{{\alpha_{i} }} , \\ \end{aligned} $$
(12)
$$ \lambda ({\mathbf{h}}_{j} ) = \frac{1}{{2\pi \sigma^{2} \beta }}\exp \left( { - \frac{{\left\| {{\mathbf{h}}_{j} - {\mathbf{h}}_{0} } \right\|_{2}^{2} }}{{2\sigma^{2} }}} \right). $$
(13)
Please note that the correct versions of the equations were used in the computations, therefore, the results remain unchanged.
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Rasera, L.G., Gravey, M., Lane, S.N. et al. Correction to: Downscaling Images with Trends Using Multiple-Point Statistics Simulation: An Application to Digital Elevation Models. Math Geosci 52, 189 (2020). https://doi.org/10.1007/s11004-019-09831-7
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DOI: https://doi.org/10.1007/s11004-019-09831-7