# 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 that can be useful for quick interactive analysis:

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


(png, svg, pdf) This convenience function combines a Stretch object with an Interval object. We recommend using ImageNormalize directly in scripted programs instead of this convenience function.

### 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])
(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, 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])
(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 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 = plt.figure()
ax = fig.add_subplot(1, 1, 1)
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 = plt.figure()
ax = fig.add_subplot(1, 1, 1)
im, norm = imshow_norm(image, ax, origin='lower',
interval=MinMaxInterval(), stretch=SqrtStretch())
fig.colorbar(im)


(png, svg, pdf) 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 = plt.figure()
ax = fig.add_subplot(1, 1, 1)
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
image = np.random.normal(size=(64, 64))
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
# 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) 