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- Data Visualization (`astropy.visualization`) »
- Image stretching and normalization

# 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

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])
    (1, 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`, and `AsymmetricPercentileInterval`. For these three, 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])
    (3.0, 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 provide 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 stretches and intervals can be chained by using the `+` operator, which returns a new transformation. 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 showing data, and requires a `Normalize` object to be passed to e.g. `imshow()`. The `astropy.visualization` module provides a class, `ImageNormalize`, which wraps the stretch functions from Stretching into an object Matplotlib understands. The `ImageNormalize` class takes the limits (which you can determine from the Intervals and Normalization classes) and the stretch instance:

    import numpy as np
    import matplotlib.pyplot as plt

    from astropy.visualization import SqrtStretch
    from astropy.visualization.mpl_normalize import ImageNormalize

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

    # Create normalizer object
    norm = ImageNormalize(vmin=0., vmax=65536, stretch=SqrtStretch())

    # Make the figure
    fig = plt.figure()
    ax = fig.add_subplot(1, 1, 1)
    im = ax.imshow(image, origin='lower', norm=norm)
    fig.colorbar(im)

(Source code, png, hires.png, pdf)

As shown above, the colorbar ticks are automatically adjusted.