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# Image stretching and normalization

The `astropy.visualization` module provides a framework for transforming values in images (and more generally any arrays), typically for the purpose of visualization. Two main types of transformations are provided:

- Normalization to the [0:1] range using lower and upper limits where \(x\) represents the values in the original image:

\[y = \frac{x - v_{\rm min}}{v_{\rm max} - v_{\rm min}}\]

- Stretching of values in the [0:1] range to the [0:1] range using a linear or non-linear function:

\[z = f(y)\]

In addition, classes are provided in order to identify lower and upper limits for a dataset based on specific algorithms (such as using percentiles).

Identifying lower and upper limits, as well as re-normalizing, is described in the Intervals and Normalization section, while stretching is described in the Stretching section.

## Intervals and Normalization

### The Quick Way

`astropy` provides a convenience `simple_norm()` function and a `SimpleNorm` class that can be useful for quick interactive analysis. These convenience tools create a `ImageNormalize` normalization object that can be used with Matplotlib’s `imshow()` method

Here’s an example using the `simple_norm()` function:

    import numpy as np
    import matplotlib.pyplot as plt
    from astropy.visualization import simple_norm

    # Generate a test image
    image = np.arange(65536).reshape((256, 256))

    # Create an ImageNormalize object
    norm = simple_norm(image, 'sqrt')

    # Display the image
    fig, ax = plt.subplots()
    im = ax.imshow(image, origin='lower', norm=norm)
    fig.colorbar(im)

(`png`, `svg`, `pdf`)

Here’s an example using the `SimpleNorm` class with its `imshow()` method:

    import numpy as np
    import matplotlib.pyplot as plt
    from astropy.visualization import SimpleNorm

    # Generate a test image
    image = np.arange(65536).reshape((256, 256))

    # Create an ImageNormalize object
    snorm = SimpleNorm('sqrt', percent=98)

    # Display the image
    fig, ax = plt.subplots()
    axim = snorm.imshow(image, ax=ax, origin='lower')
    fig.colorbar(axim)

(`png`, `svg`, `pdf`)

### The detailed way

Several classes are provided for determining intervals and for normalizing values in this interval to the [0:1] range. One of the simplest examples is the `MinMaxInterval` which determines the limits of the values based on the minimum and maximum values in the array. The class is instantiated with no arguments:

    >>> from astropy.visualization import MinMaxInterval
    >>> interval = MinMaxInterval()

and the limits can be determined by calling the `get_limits()` method, which takes the array of values:

    >>> interval.get_limits([1, 3, 4, 5, 6])
    (np.int64(1), np.int64(6))

The `interval` instance can also be called like a function to actually normalize values to the range:

    >>> interval([1, 3, 4, 5, 6])
    array([0. , 0.4, 0.6, 0.8, 1. ])

Other interval classes include `ManualInterval`, `PercentileInterval`, `AsymmetricPercentileInterval`, and `ZScaleInterval`. For these, values in the array can fall outside of the limits given by the interval. A `clip` argument is provided to control the behavior of the normalization when values fall outside the limits:

    >>> from astropy.visualization import PercentileInterval
    >>> interval = PercentileInterval(50.)
    >>> interval.get_limits([1, 3, 4, 5, 6])
    (np.float64(3.0), np.float64(5.0))
    >>> interval([1, 3, 4, 5, 6])  # default is clip=True
    array([0. , 0. , 0.5, 1. , 1. ])
    >>> interval([1, 3, 4, 5, 6], clip=False)
    array([-1. ,  0. ,  0.5,  1. ,  1.5])

## Stretching

In addition to classes that can scale values to the [0:1] range, a number of classes are provided to ‘stretch’ the values using different functions. These map a [0:1] range onto a transformed [0:1] range. A simple example is the `SqrtStretch` class:

    >>> from astropy.visualization import SqrtStretch
    >>> stretch = SqrtStretch()
    >>> stretch([0., 0.25, 0.5, 0.75, 1.])
    array([0.        , 0.5       , 0.70710678, 0.8660254 , 1.        ])

As for the intervals, values outside the [0:1] range can be treated differently depending on the `clip` argument. By default, output values are clipped to the [0:1] range:

    >>> stretch([-1., 0., 0.5, 1., 1.5])
    array([0.       , 0.        , 0.70710678, 1.        , 1.        ])

but this can be disabled:

    >>> stretch([-1., 0., 0.5, 1., 1.5], clip=False)
    array([       nan, 0.        , 0.70710678, 1.        , 1.22474487])

Note

The stretch functions are similar but not always strictly identical to those used in e.g. DS9 (although they should have the same behavior). The equations for the DS9 stretches can be found here and can be compared to the equations for our stretches provided in the `astropy.visualization` API section. The main difference between our stretches and DS9 is that we have adjusted them so that the [0:1] range always maps exactly to the [0:1] range.

## Combining transformations

Any intervals and stretches can be chained by using the `+` operator, which returns a new transformation. When combining intervals and stretches, the stretch object must come before the interval object. For example, to apply normalization based on a percentile value, followed by a square root stretch, you can do:

    >>> transform = SqrtStretch() + PercentileInterval(90.)
    >>> transform([1, 3, 4, 5, 6])
    array([0.        , 0.60302269, 0.76870611, 0.90453403, 1.        ])

As before, the combined transformation can also accept a `clip` argument (which is `True` by default).

## Matplotlib normalization

Matplotlib allows a custom normalization and stretch to be used when displaying data by passing a `matplotlib.colors.Normalize` object, e.g. to `imshow()`. The `astropy.visualization` module provides an `ImageNormalize` class that wraps the interval (see Intervals and Normalization) and stretch (see Stretching) objects into an object Matplotlib understands.

The inputs to the `ImageNormalize` class are the data and the interval and stretch objects:

    import numpy as np
    import matplotlib.pyplot as plt

    from astropy.visualization import (MinMaxInterval, SqrtStretch,
                                       ImageNormalize)

    # Generate a test image
    image = np.arange(65536).reshape((256, 256))

    # Create an ImageNormalize object
    norm = ImageNormalize(image, interval=MinMaxInterval(),
                          stretch=SqrtStretch())

    # or equivalently using positional arguments
    # norm = ImageNormalize(image, MinMaxInterval(), SqrtStretch())

    # Display the image
    fig, ax = plt.subplots()
    im = ax.imshow(image, origin='lower', norm=norm)
    fig.colorbar(im)

(`png`, `svg`, `pdf`)

As shown above, the colorbar ticks are automatically adjusted.

Please note that one should not use `ax.imshow(norm(image))` because the colorbar ticks marks will represent normalized image values (on a linear scale), not the actual image values. Also, the image displayed by `ax.imshow(norm(image))` is not exactly equivalent to `ax.imshow(image, norm=norm)` if the image contains `NaN` or `inf` values. The exact equivalent is `ax.imshow(norm(np.ma.masked_invalid(image))`.

The input image to `ImageNormalize` is typically the one to be displayed, so there is a convenience function `imshow_norm()` to ease this use case:

    import numpy as np
    import matplotlib.pyplot as plt

    from astropy.visualization import imshow_norm, MinMaxInterval, SqrtStretch

    # Generate a test image
    image = np.arange(65536).reshape((256, 256))

    # Display the exact same thing as the above plot
    fig, ax = plt.subplots()
    im, norm = imshow_norm(image, ax, origin='lower',
                           interval=MinMaxInterval(), stretch=SqrtStretch())
    fig.colorbar(im)

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While this is the simplest case, it is also possible for a completely different image to be used to establish the normalization (e.g. if one wants to display several images with exactly the same normalization and stretch).

The inputs to the `ImageNormalize` class can also be the vmin and vmax limits, which you can determine from the Intervals and Normalization classes, and the stretch object:

    import numpy as np
    import matplotlib.pyplot as plt

    from astropy.visualization import (MinMaxInterval, SqrtStretch,
                                       ImageNormalize)

    # Generate a test image
    image = np.arange(65536).reshape((256, 256))

    # Create interval object
    interval = MinMaxInterval()
    vmin, vmax = interval.get_limits(image)

    # Create an ImageNormalize object using a SqrtStretch object
    norm = ImageNormalize(vmin=vmin, vmax=vmax, stretch=SqrtStretch())

    # Display the image
    fig, ax = plt.subplots()
    im = ax.imshow(image, origin='lower', norm=norm)
    fig.colorbar(im)

(`png`, `svg`, `pdf`)

## Combining stretches and Matplotlib normalization

Stretches can also be combined with other stretches, just like transformations. The resulting `CompositeStretch` can be used to normalize Matplotlib images like any other stretch. For example, a composite stretch can stretch residual images with negative values:

    import numpy as np
    import matplotlib.pyplot as plt
    from astropy.visualization.stretch import SinhStretch, LinearStretch
    from astropy.visualization import ImageNormalize

    # Transforms normalized values [0,1] to [-1,1] before stretch and then back
    stretch = LinearStretch(slope=0.5, intercept=0.5) + SinhStretch() + \
        LinearStretch(slope=2, intercept=-1)

    # Image of random Gaussian noise
    rng = np.random.default_rng()
    image = rng.normal(size=(64, 64))
    fig, ax = plt.subplots()
    # ImageNormalize normalizes values to [0,1] before applying the stretch
    norm = ImageNormalize(stretch=stretch, vmin=-5, vmax=5)
    im = ax.imshow(image, origin='lower', norm=norm, cmap='gray')
    fig.colorbar(im)

(`png`, `svg`, `pdf`)