---
title: Multi-Scale SSIM
description: 'Compute MultiScaleSSIM, Multi-scale Structural Similarity Index Measure.'
canonical: >-
  https://lightning.ai/docs/torchmetrics/stable/image/multi_scale_structural_similarity
---
# Multi-Scale SSIM {#multi-scale-ssim}

## Module Interface {#module-interface}

### `class torchmetrics.image.MultiScaleStructuralSimilarityIndexMeasure(gaussian_kernel=True, kernel_size=11, sigma=1.5, reduction='elementwise_mean', data_range=None, k1=0.01, k2=0.03, betas=(0.0448, 0.2856, 0.3001, 0.2363, 0.1333), normalize='relu', **kwargs)` {#torchmetrics.image.MultiScaleStructuralSimilarityIndexMeasure}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/ssim.py#L242-L453)

Compute [MultiScaleSSIM](https://ieeexplore.ieee.org/abstract/document/1292216), Multi-scale Structural Similarity Index Measure.

This metric is is a generalization of Structural Similarity Index Measure by incorporating image details at different resolution scores.

As input to `forward` and `update` the metric accepts the following input

*   `preds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Predictions from model
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Ground truth values
    

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

*   `msssim` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): if `reduction!='none'` returns float scalar tensor with average MSSSIM value over sample else returns tensor of shape `(N,)` with SSIM values per sample
    

Parameters:

*   **gaussian\_kernel** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – If `True` (default), a gaussian kernel is used, if false a uniform kernel is used
    
*   **kernel\_size** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]\]) – size of the gaussian kernel
    
*   **sigma** (`Union`\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\]\]) – Standard deviation of the gaussian kernel
    
*   **reduction** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'elementwise_mean'`, `'sum'`, `'none'`, `None`\]) –
    
    a method to reduce metric score over labels.
    
    *   `'elementwise_mean'`: takes the mean
        
    *   `'sum'`: takes the sum
        
    *   `'none'` or `None`: no reduction will be applied
        
    
*   **data\_range** (`Union`\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – the range of the data. If None, it is determined from the data (max - min). If a tuple is provided then the range is calculated as the difference and input is clamped between the values. The `data_range` must be given when `dim` is not None.
    
*   **k1** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Parameter of structural similarity index measure.
    
*   **k2** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Parameter of structural similarity index measure.
    
*   **betas** ([`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`...`](https://docs.python.org/3/builtins/constants.html#Ellipsis "(in Python v3.15)")\]) – Exponent parameters for individual similarities and contrastive sensitivities returned by different image resolutions.
    
*   **normalize** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'relu'`, `'simple'`, `None`\]) – When MultiScaleStructuralSimilarityIndexMeasure loss is used for training, it is desirable to use normalizes to improve the training stability. This normalize argument is out of scope of the original implementation \[1\], and it is adapted from [https://github.com/jorge-pessoa/pytorch-msssim](https://github.com/jorge-pessoa/pytorch-msssim) instead.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Returns:

Tensor with Multi-Scale SSIM score

Raises:

*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `kernel_size` is not an int or a Sequence of ints with size 2 or 3.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `betas` is not a tuple of floats with length 2.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `normalize` is neither None, ReLU nor simple.
    

Example

```python
>>> from torch import rand
>>> from torchmetrics.image import MultiScaleStructuralSimilarityIndexMeasure
>>> preds = torch.rand([3, 3, 256, 256])
>>> target = preds * 0.75
>>> ms_ssim = MultiScaleStructuralSimilarityIndexMeasure(data_range=1.0)
>>> ms_ssim(preds, target)
tensor(0.9628)
```

#### `plot(val=None, ax=None)` {#torchmetrics.image.MultiScaleStructuralSimilarityIndexMeasure.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/ssim.py#L409-L453)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> # Example plotting a single value
>>> from torch import rand
>>> from torchmetrics.image import MultiScaleStructuralSimilarityIndexMeasure
>>> preds = rand([3, 3, 256, 256])
>>> target = preds * 0.75
>>> metric = MultiScaleStructuralSimilarityIndexMeasure(data_range=1.0)
>>> metric.update(preds, target)
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/multi\_scale\_structural\_similarity-1.png](/docs/torchmetrics/1.9.0/static/_images/multi_scale_structural_similarity-1.png)](/docs/torchmetrics/1.9.0/static/_images/multi_scale_structural_similarity-1.png)

```python
>>> # Example plotting multiple values
>>> from torch import rand
>>> from torchmetrics.image import MultiScaleStructuralSimilarityIndexMeasure
>>> preds = rand([3, 3, 256, 256])
>>> target = preds * 0.75
>>> metric = MultiScaleStructuralSimilarityIndexMeasure(data_range=1.0)
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(preds, target))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/multi\_scale\_structural\_similarity-2.png](/docs/torchmetrics/1.9.0/static/_images/multi_scale_structural_similarity-2.png)](/docs/torchmetrics/1.9.0/static/_images/multi_scale_structural_similarity-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.image.multiscale_structural_similarity_index_measure(preds, target, gaussian_kernel=True, sigma=1.5, kernel_size=11, reduction='elementwise_mean', data_range=None, k1=0.01, k2=0.03, betas=(0.0448, 0.2856, 0.3001, 0.2363, 0.1333), normalize='relu')` {#torchmetrics.functional.image.multiscale_structural_similarity_index_measure}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/image/ssim.py#L449-L529)

Compute [MultiScaleSSIM](https://ieeexplore.ieee.org/abstract/document/1292216), Multi-scale Structural Similarity Index Measure.

This metric is a generalization of Structural Similarity Index Measure by incorporating image details at different resolution scores.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Predictions from model of shape `[N, C, H, W]`
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Ground truth values of shape `[N, C, H, W]`
    
*   **gaussian\_kernel** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – If true, a gaussian kernel is used, if false a uniform kernel is used
    
*   **sigma** (`Union`\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\]\]) – Standard deviation of the gaussian kernel
    
*   **kernel\_size** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]\]) – size of the gaussian kernel
    
*   **reduction** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'elementwise_mean'`, `'sum'`, `'none'`, `None`\]) –
    
    a method to reduce metric score over labels.
    
    *   `'elementwise_mean'`: takes the mean
        
    *   `'sum'`: takes the sum
        
    *   `'none'` or `None`: no reduction will be applied
        
    
*   **data\_range** (`Union`\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – the range of the data. If None, it is determined from the data (max - min). If a tuple is provided then the range is calculated as the difference and input is clamped between the values.
    
*   **k1** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Parameter of structural similarity index measure.
    
*   **k2** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Parameter of structural similarity index measure.
    
*   **betas** ([`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)"), [`...`](https://docs.python.org/3/builtins/constants.html#Ellipsis "(in Python v3.15)")\]) – Exponent parameters for individual similarities and contrastive sensitivities returned by different image resolutions.
    
*   **normalize** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'relu'`, `'simple'`\]\]) – When MultiScaleSSIM loss is used for training, it is desirable to use normalizes to improve the training stability. This normalize argument is out of scope of the original implementation \[1\], and it is adapted from [https://github.com/jorge-pessoa/pytorch-msssim](https://github.com/jorge-pessoa/pytorch-msssim) instead.
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

Returns:

Tensor with Multi-Scale SSIM score

Raises:

*   [**TypeError**](https://docs.python.org/3/builtins/exceptions.html#TypeError "(in Python v3.15)") – If `preds` and `target` don’t have the same data type.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `preds` and `target` don’t have `BxCxHxW shape`.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If the length of `kernel_size` or `sigma` is not `2`.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If one of the elements of `kernel_size` is not an `odd positive number`.
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If one of the elements of `sigma` is not a `positive number`.
    

Example

```python
>>> from torch import rand
>>> from torchmetrics.functional.image import multiscale_structural_similarity_index_measure
>>> preds = rand([3, 3, 256, 256])
>>> target = preds * 0.75
>>> multiscale_structural_similarity_index_measure(preds, target, data_range=1.0)
tensor(0.9628)
```

References

\[1\] Multi-Scale Structural Similarity For Image Quality Assessment by Zhou Wang, Eero P. Simoncelli and Alan C. Bovik [MultiScaleSSIM](https://ieeexplore.ieee.org/abstract/document/1292216)

---

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