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# Error Relative Global Dim. Synthesis (ERGAS)¶

## Module Interface¶

class torchmetrics.image.ErrorRelativeGlobalDimensionlessSynthesis(ratio=4, reduction='elementwise_mean', **kwargs)[source]

Calculate the Error relative global dimensionless synthesis (ERGAS) metric.

This metric is used to calculate the accuracy of Pan sharpened image considering normalized average error of each band of the result image. It is defined as:

$ERGAS = 100 \cdot \frac{h}{l} \cdot \sqrt{\frac{1}{N} \sum_{k=1}^{N} \frac{RMSE(B_k)^2}{\mu_k^2}}$

where $$h$$ and $$l$$ denote the spatial resolution (pixel size) of the high and low resolution images, often shorted to the ratio between them $$r=h/l$$. $$N$$ is the number of spectral bands, $$RMSE(B_k)$$ is the root mean square error of the k-th band between low and high resolution images, and $$\\mu_k$$ 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

As output of forward and compute the metric returns the following output

• ergas (Tensor): if reduction!='none' returns float scalar tensor with average ERGAS value over sample else returns tensor of shape (N,) with ERGAS values per sample

Parameters:
• ratio (float) – ratio of high resolution to low resolution.

• reduction (Literal['elementwise_mean', 'sum', 'none', None]) –

a method to reduce metric score over labels.

• 'elementwise_mean': takes the mean (default)

• 'sum': takes the sum

• 'none' or None: no reduction will be applied

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Example

>>> import torch
>>> from torchmetrics.image import ErrorRelativeGlobalDimensionlessSynthesis
>>> preds = torch.rand([16, 1, 16, 16], generator=torch.manual_seed(42))
>>> target = preds * 0.75
>>> ergas = ErrorRelativeGlobalDimensionlessSynthesis()
>>> torch.round(ergas(preds, target))
tensor(10.)

plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.image import ErrorRelativeGlobalDimensionlessSynthesis
>>> preds = torch.rand([16, 1, 16, 16], generator=torch.manual_seed(42))
>>> target = preds * 0.75
>>> metric = ErrorRelativeGlobalDimensionlessSynthesis()
>>> metric.update(preds, target)
>>> fig_, ax_ = metric.plot()

>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.image import ErrorRelativeGlobalDimensionlessSynthesis
>>> preds = torch.rand([16, 1, 16, 16], generator=torch.manual_seed(42))
>>> target = preds * 0.75
>>> metric = ErrorRelativeGlobalDimensionlessSynthesis()
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(preds, target))
>>> fig_, ax_ = metric.plot(values)


## Functional Interface¶

torchmetrics.functional.image.error_relative_global_dimensionless_synthesis(preds, target, ratio=4, reduction='elementwise_mean')[source]

Calculates Error relative global dimensionless synthesis (ERGAS) metric.

Parameters:
• preds (Tensor) – estimated image

• target (Tensor) – ground truth image

• ratio (float) – ratio of high resolution to low resolution

• reduction (Literal['elementwise_mean', 'sum', 'none', None]) –

a method to reduce metric score over labels.

• 'elementwise_mean': takes the mean (default)

• 'sum': takes the sum

• 'none' or None: no reduction will be applied

Return type:

Tensor

Returns:

Tensor with RelativeG score

Raises:
• TypeError – If preds and target don’t have the same data type.

• ValueError – If preds and target don’t have BxCxHxW shape.

Example

>>> from torchmetrics.functional.image import error_relative_global_dimensionless_synthesis
>>> gen = torch.manual_seed(42)
>>> preds = torch.rand([16, 1, 16, 16], generator=gen)
>>> target = preds * 0.75
>>> error_relative_global_dimensionless_synthesis(preds, target)
tensor(9.6193)