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docs: fix ERGAS metric (#2573)
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SkafteNicki authored May 30, 2024
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9 changes: 4 additions & 5 deletions src/torchmetrics/image/ergas.py
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Expand Up @@ -35,12 +35,11 @@ class ErrorRelativeGlobalDimensionlessSynthesis(Metric):
band of the result image. It is defined as:
.. math::
ERGAS = 100 \cdot \frac{h}{l} \cdot \sqrt{\frac{1}{N} \sum_{k=1}^{N} \frac{RMSE(B_k)^2}{\mu_k^2}}
ERGAS = \frac{100}{r} \cdot \sqrt{\frac{1}{N} \sum_{k=1}^{N} \frac{RMSE(B_k)^2}{\mu_k^2}}
where :math:`h` and :math:`l` denote the spatial resolution (pixel size) of the high and low resolution images,
often shorted to the ratio between them :math:`r=h/l`. :math:`N` is the number of spectral bands, :math:`RMSE(B_k)`
is the root mean square error of the k-th band between low and high resolution images, and :math:`\\mu_k` is the
mean value of the k-th band of the reference image.
where :math:`r=h/l` denote the ratio in spatial resolution (pixel size) between the high and low resolution images.
:math:`N` is the number of spectral bands, :math:`RMSE(B_k)` is the root mean square error of the k-th band between
low and high resolution images, and :math:`\\mu_k` is the mean value of the k-th band of the reference image.
As input to ``forward`` and ``update`` the metric accepts the following input
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