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DOC: dicom orientation (-1 + N) -> (N - 1)
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doc/source/dicom/dicom_orientation.rst

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@@ -307,13 +307,13 @@ first voxel in the last (slice index = $N-1$) slice to mm space. So:
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.. math::
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\left(\begin{smallmatrix}T^N\\1\end{smallmatrix}\right) = A \left(\begin{smallmatrix}0\\0\\-1 + N\\1\end{smallmatrix}\right)
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\left(\begin{smallmatrix}T^N\\1\end{smallmatrix}\right) = A \left(\begin{smallmatrix}0\\0\\N - 1\\1\end{smallmatrix}\right)
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From this it follows that:
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.. math::
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\begin{Bmatrix}k_{{1}} : \frac{T^{1}_{{1}} - T^{N}_{{1}}}{1 - N}, & k_{{2}} : \frac{T^{1}_{{2}} - T^{N}_{{2}}}{1 - N}, & k_{{3}} : \frac{T^{1}_{{3}} - T^{N}_{{3}}}{1 - N}\end{Bmatrix}
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\begin{Bmatrix}k_{{1}} : \frac{T^{N}_{{1}} - T^{1}_{{1}}}{N - 1}, & k_{{2}} : \frac{T^{N}_{{2}} - T^{1}_{{2}}}{N - 1}, & k_{{3}} : \frac{T^{N}_{{3}} - T^{1}_{{3}}}{N - 1}\end{Bmatrix}
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and therefore:
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@@ -324,7 +324,7 @@ and therefore:
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.. math::
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A_{multi} = \left(\begin{smallmatrix}F_{{11}} \Delta{r} & F_{{12}} \Delta{c} & \frac{T^{1}_{{1}} - T^{N}_{{1}}}{1 - N} & T^{1}_{{1}}\\F_{{21}} \Delta{r} & F_{{22}} \Delta{c} & \frac{T^{1}_{{2}} - T^{N}_{{2}}}{1 - N} & T^{1}_{{2}}\\F_{{31}} \Delta{r} & F_{{32}} \Delta{c} & \frac{T^{1}_{{3}} - T^{N}_{{3}}}{1 - N} & T^{1}_{{3}}\\0 & 0 & 0 & 1\end{smallmatrix}\right)
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A_{multi} = \left(\begin{smallmatrix}F_{{11}} \Delta{r} & F_{{12}} \Delta{c} & \frac{T^{N}_{{1}} - T^{1}_{{1}}}{N - 1} & T^{1}_{{1}}\\F_{{21}} \Delta{r} & F_{{22}} \Delta{c} & \frac{T^{N}_{{2}} - T^{1}_{{2}}}{N - 1} & T^{1}_{{2}}\\F_{{31}} \Delta{r} & F_{{32}} \Delta{c} & \frac{T^{N}_{{3}} - T^{1}_{{3}}}{N - 1} & T^{1}_{{3}}\\0 & 0 & 0 & 1\end{smallmatrix}\right)
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A_{single} = \left(\begin{smallmatrix}F_{{11}} \Delta{r} & F_{{12}} \Delta{c} & \Delta{s} n_{{1}} & T^{1}_{{1}}\\F_{{21}} \Delta{r} & F_{{22}} \Delta{c} & \Delta{s} n_{{2}} & T^{1}_{{2}}\\F_{{31}} \Delta{r} & F_{{32}} \Delta{c} & \Delta{s} n_{{3}} & T^{1}_{{3}}\\0 & 0 & 0 & 1\end{smallmatrix}\right)
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