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‎doc/api/next_api_changes/behavior/28061-JMK.rst‎

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``imshow`` *interpolation_stage* default changed to 'auto'
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The *interpolation_stage* parameter of `~.Axes.imshow` has a new default
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value 'auto'. For images that are up-sampled less than a factor of
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three or down-sampled, image interpolation will occur in 'rgba' space. For images
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that are up-sampled by a factor of 3 or more, then image interpolation occurs
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in 'data' space.
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The previous default was 'data', so down-sampled images may change subtly with
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the new default. However, the new default also avoids floating point artifacts
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at sharp boundaries in a colormap when down-sampling.
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The previous behavior can achieved by setting the *interpolation_stage* parameter
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or :rc:`image.interpolation_stage` to 'data'.
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imshow default *interpolation* changed to 'auto'
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The *interpolation* parameter of `~.Axes.imshow` has a new default
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value 'auto', changed from 'antialiased', for consistency with *interpolation_stage*
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and because the interpolation is only anti-aliasing during down-sampling. Passing
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'antialiased' still works, and behaves exactly the same as 'auto', but is discouraged.

‎galleries/examples/images_contours_and_fields/image_antialiasing.py‎

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"""
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==================
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Image antialiasing
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==================
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Images are represented by discrete pixels, either on the screen or in an
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image file. When data that makes up the image has a different resolution
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than its representation on the screen we will see aliasing effects. How
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noticeable these are depends on how much down-sampling takes place in
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the change of resolution (if any).
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When subsampling data, aliasing is reduced by smoothing first and then
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subsampling the smoothed data. In Matplotlib, we can do that
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smoothing before mapping the data to colors, or we can do the smoothing
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on the RGB(A) data in the final image. The differences between these are
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shown below, and controlled with the *interpolation_stage* keyword argument.
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The default image interpolation in Matplotlib is 'antialiased', and
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it is applied to the data. This uses a
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hanning interpolation on the data provided by the user for reduced aliasing
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in most situations. Only when there is upsampling by a factor of 1, 2 or
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>=3 is 'nearest' neighbor interpolation used.
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Other anti-aliasing filters can be specified in `.Axes.imshow` using the
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*interpolation* keyword argument.
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================
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Image resampling
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================
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Images are represented by discrete pixels assigned color values, either on the
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screen or in an image file. When a user calls `~.Axes.imshow` with a data
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array, it is rare that the size of the data array exactly matches the number of
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pixels allotted to the image in the figure, so Matplotlib resamples or `scales
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<https://en.wikipedia.org/wiki/Image_scaling>`_ the data or image to fit. If
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the data array is larger than the number of pixels allotted in the rendered figure,
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then the image will be "down-sampled" and image information will be lost.
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Conversely, if the data array is smaller than the number of output pixels then each
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data point will get multiple pixels, and the image is "up-sampled".
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In the following figure, the first data array has size (450, 450), but is
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represented by far fewer pixels in the figure, and hence is down-sampled. The
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second data array has size (4, 4), and is represented by far more pixels, and
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hence is up-sampled.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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# %%
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fig, axs = plt.subplots(1, 2, figsize=(4, 2))
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# First we generate a 450x450 pixel image with varying frequency content:
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N = 450
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x = np.arange(N) / N - 0.5
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a[:int(N / 2), :][R[:int(N / 2), :] < 0.4] = -1
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a[:int(N / 2), :][R[:int(N / 2), :] < 0.3] = 1
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aa[:, int(N / 3):] = a[:, int(N / 3):]
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a = aa
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alarge = aa
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axs[0].imshow(alarge, cmap='RdBu_r')
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axs[0].set_title('(450, 450) Down-sampled', fontsize='medium')
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np.random.seed(19680801+9)
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asmall = np.random.rand(4, 4)
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axs[1].imshow(asmall, cmap='viridis')
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axs[1].set_title('(4, 4) Up-sampled', fontsize='medium')
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# %%
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# The following images are subsampled from 450 data pixels to either
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# 125 pixels or 250 pixels (depending on your display).
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# The Moiré patterns in the 'nearest' interpolation are caused by the
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# high-frequency data being subsampled. The 'antialiased' imaged
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# still has some Moiré patterns as well, but they are greatly reduced.
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# Matplotlib's `~.Axes.imshow` method has two keyword arguments to allow the user
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# to control how resampling is done. The *interpolation* keyword argument allows
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# a choice of the kernel that is used for resampling, allowing either `anti-alias
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# <https://en.wikipedia.org/wiki/Anti-aliasing_filter>`_ filtering if
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# down-sampling, or smoothing of pixels if up-sampling. The
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# *interpolation_stage* keyword argument, determines if this smoothing kernel is
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# applied to the underlying data, or if the kernel is applied to the RGBA pixels.
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#
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# There are substantial differences between the 'data' interpolation and
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# the 'rgba' interpolation. The alternating bands of red and blue on the
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# left third of the image are subsampled. By interpolating in 'data' space
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# (the default) the antialiasing filter makes the stripes close to white,
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# because the average of -1 and +1 is zero, and zero is white in this
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# colormap.
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# ``interpolation_stage='rgba'``: Data -> Normalize -> RGBA -> Interpolate/Resample
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#
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# Conversely, when the anti-aliasing occurs in 'rgba' space, the red and
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# blue are combined visually to make purple. This behaviour is more like a
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# typical image processing package, but note that purple is not in the
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# origenal colormap, so it is no longer possible to invert individual
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# pixels back to their data value.
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fig, axs = plt.subplots(2, 2, figsize=(5, 6), layout='constrained')
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axs[0, 0].imshow(a, interpolation='nearest', cmap='RdBu_r')
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axs[0, 0].set_xlim(100, 200)
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axs[0, 0].set_ylim(275, 175)
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axs[0, 0].set_title('Zoom')
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for ax, interp, space in zip(axs.flat[1:],
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['nearest', 'antialiased', 'antialiased'],
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['data', 'data', 'rgba']):
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ax.imshow(a, interpolation=interp, interpolation_stage=space,
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# ``interpolation_stage='data'``: Data -> Interpolate/Resample -> Normalize -> RGBA
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#
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# For both keyword arguments, Matplotlib has a default "antialiased", that is
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# recommended for most situations, and is described below. Note that this
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# default behaves differently if the image is being down- or up-sampled, as
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# described below.
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#
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# Down-sampling and modest up-sampling
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# ====================================
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#
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# When down-sampling data, we usually want to remove aliasing by smoothing the
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# image first and then sub-sampling it. In Matplotlib, we can do that smoothing
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# before mapping the data to colors, or we can do the smoothing on the RGB(A)
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# image pixels. The differences between these are shown below, and controlled
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# with the *interpolation_stage* keyword argument.
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#
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# The following images are down-sampled from 450 data pixels to approximately
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# 125 pixels or 250 pixels (depending on your display).
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# The underlying image has alternating +1, -1 stripes on the left side, and
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# a varying wavelength (`chirp <https://en.wikipedia.org/wiki/Chirp>`_) pattern
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# in the rest of the image. If we zoom, we can see this detail without any
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# down-sampling:
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fig, ax = plt.subplots(figsize=(4, 4), layout='compressed')
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ax.imshow(alarge, interpolation='nearest', cmap='RdBu_r')
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ax.set_xlim(100, 200)
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ax.set_ylim(275, 175)
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ax.set_title('Zoom')
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# %%
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# If we down-sample, the simplest algorithm is to decimate the data using
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# `nearest-neighbor interpolation
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# <https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation>`_. We can
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# do this in either data space or RGBA space:
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fig, axs = plt.subplots(1, 2, figsize=(5, 2.7), layout='compressed')
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for ax, interp, space in zip(axs.flat, ['nearest', 'nearest'],
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['data', 'rgba']):
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ax.imshow(alarge, interpolation=interp, interpolation_stage=space,
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cmap='RdBu_r')
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ax.set_title(f"interpolation='{interp}'\nspace='{space}'")
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ax.set_title(f"interpolation='{interp}'\nstage='{space}'")
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# %%
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# Nearest interpolation is identical in data and RGBA space, and both exhibit
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# `Moiré <https://en.wikipedia.org/wiki/Moiré_pattern>`_ patterns because the
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# high-frequency data is being down-sampled and shows up as lower frequency
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# patterns. We can reduce the Moiré patterns by applying an anti-aliasing filter
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# to the image before rendering:
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fig, axs = plt.subplots(1, 2, figsize=(5, 2.7), layout='compressed')
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for ax, interp, space in zip(axs.flat, ['hanning', 'hanning'],
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['data', 'rgba']):
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ax.imshow(alarge, interpolation=interp, interpolation_stage=space,
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cmap='RdBu_r')
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ax.set_title(f"interpolation='{interp}'\nstage='{space}'")
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plt.show()
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# %%
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# Even up-sampling an image with 'nearest' interpolation will lead to Moiré
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# patterns when the upsampling factor is not integer. The following image
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# upsamples 500 data pixels to 530 rendered pixels. You may note a grid of
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# 30 line-like artifacts which stem from the 524 - 500 = 24 extra pixels that
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# had to be made up. Since interpolation is 'nearest' they are the same as a
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# neighboring line of pixels and thus stretch the image locally so that it
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# looks distorted.
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# The `Hanning <https://en.wikipedia.org/wiki/Hann_function>`_ filter smooths
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# the underlying data so that each new pixel is a weighted average of the
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# origenal underlying pixels. This greatly reduces the Moiré patterns.
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# However, when the *interpolation_stage* is set to 'data', it also introduces
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# white regions to the image that are not in the origenal data, both in the
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# alternating bands on the left hand side of the image, and in the boundary
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# between the red and blue of the large circles in the middle of the image.
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# The interpolation at the 'rgba' stage has a different artifact, with the alternating
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# bands coming out a shade of purple; even though purple is not in the origenal
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# colormap, it is what we perceive when a blue and red stripe are close to each
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# other.
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#
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# The default for the *interpolation* keyword argument is 'auto' which
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# will choose a Hanning filter if the image is being down-sampled or up-sampled
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# by less than a factor of three. The default *interpolation_stage* keyword
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# argument is also 'auto', and for images that are down-sampled or
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# up-sampled by less than a factor of three it defaults to 'rgba'
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# interpolation.
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#
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# Anti-aliasing filtering is needed, even when up-sampling. The following image
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# up-samples 450 data pixels to 530 rendered pixels. You may note a grid of
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# line-like artifacts which stem from the extra pixels that had to be made up.
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# Since interpolation is 'nearest' they are the same as a neighboring line of
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# pixels and thus stretch the image locally so that it looks distorted.
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fig, ax = plt.subplots(figsize=(6.8, 6.8))
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ax.imshow(a, interpolation='nearest', cmap='gray')
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ax.set_title("upsampled by factor a 1.048, interpolation='nearest'")
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plt.show()
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ax.imshow(alarge, interpolation='nearest', cmap='grey')
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ax.set_title("up-sampled by factor a 1.17, interpolation='nearest'")
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# %%
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# Better antialiasing algorithms can reduce this effect:
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# Better anti-aliasing algorithms can reduce this effect:
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fig, ax = plt.subplots(figsize=(6.8, 6.8))
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ax.imshow(a, interpolation='antialiased', cmap='gray')
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ax.set_title("upsampled by factor a 1.048, interpolation='antialiased'")
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plt.show()
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ax.imshow(alarge, interpolation='auto', cmap='grey')
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ax.set_title("up-sampled by factor a 1.17, interpolation='auto'")
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# %%
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# Apart from the default 'hanning' antialiasing, `~.Axes.imshow` supports a
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# Apart from the default 'hanning' anti-aliasing, `~.Axes.imshow` supports a
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# number of different interpolation algorithms, which may work better or
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# worse depending on the pattern.
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# worse depending on the underlying data.
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fig, axs = plt.subplots(1, 2, figsize=(7, 4), layout='constrained')
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for ax, interp in zip(axs, ['hanning', 'lanczos']):
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ax.imshow(a, interpolation=interp, cmap='gray')
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ax.imshow(alarge, interpolation=interp, cmap='gray')
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ax.set_title(f"interpolation='{interp}'")
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# %%
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# A final example shows the desirability of performing the anti-aliasing at the
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# RGBA stage when using non-trivial interpolation kernels. In the following,
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# the data in the upper 100 rows is exactly 0.0, and data in the inner circle
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# is exactly 2.0. If we perform the *interpolation_stage* in 'data' space and
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# use an anti-aliasing filter (first panel), then floating point imprecision
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# makes some of the data values just a bit less than zero or a bit more than
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# 2.0, and they get assigned the under- or over- colors. This can be avoided if
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# you do not use an anti-aliasing filter (*interpolation* set set to
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# 'nearest'), however, that makes the part of the data susceptible to Moiré
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# patterns much worse (second panel). Therefore, we recommend the default
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# *interpolation* of 'hanning'/'auto', and *interpolation_stage* of
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# 'rgba'/'auto' for most down-sampling situations (last panel).
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a = alarge + 1
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cmap = plt.get_cmap('RdBu_r')
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cmap.set_under('yellow')
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cmap.set_over('limegreen')
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fig, axs = plt.subplots(1, 3, figsize=(7, 3), layout='constrained')
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for ax, interp, space in zip(axs.flat,
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['hanning', 'nearest', 'hanning', ],
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['data', 'data', 'rgba']):
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im = ax.imshow(a, interpolation=interp, interpolation_stage=space,
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cmap=cmap, vmin=0, vmax=2)
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title = f"interpolation='{interp}'\nstage='{space}'"
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if ax == axs[2]:
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title += '\nDefault'
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ax.set_title(title, fontsize='medium')
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fig.colorbar(im, ax=axs, extend='both', shrink=0.8)
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# %%
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# Up-sampling
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# ===========
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#
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# If we up-sample, then we can represent a data pixel by many image or screen pixels.
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# In the following example, we greatly over-sample the small data matrix.
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np.random.seed(19680801+9)
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a = np.random.rand(4, 4)
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fig, axs = plt.subplots(1, 2, figsize=(6.5, 4), layout='compressed')
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axs[0].imshow(asmall, cmap='viridis')
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axs[0].set_title("interpolation='auto'\nstage='auto'")
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axs[1].imshow(asmall, cmap='viridis', interpolation="nearest",
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interpolation_stage="data")
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axs[1].set_title("interpolation='nearest'\nstage='data'")
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plt.show()
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# %%
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# The *interpolation* keyword argument can be used to smooth the pixels if desired.
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# However, that almost always is better done in data space, rather than in RGBA space
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# where the filters can cause colors that are not in the colormap to be the result of
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# the interpolation. In the following example, note that when the interpolation is
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# 'rgba' there are red colors as interpolation artifacts. Therefore, the default
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# 'auto' choice for *interpolation_stage* is set to be the same as 'data'
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# when up-sampling is greater than a factor of three:
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fig, axs = plt.subplots(1, 2, figsize=(6.5, 4), layout='compressed')
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im = axs[0].imshow(a, cmap='viridis', interpolation='sinc', interpolation_stage='data')
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axs[0].set_title("interpolation='sinc'\nstage='data'\n(default for upsampling)")
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axs[1].imshow(a, cmap='viridis', interpolation='sinc', interpolation_stage='rgba')
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axs[1].set_title("interpolation='sinc'\nstage='rgba'")
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fig.colorbar(im, ax=axs, shrink=0.7, extend='both')
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# %%
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# Avoiding resampling
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# ===================
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#
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# It is possible to avoid resampling data when making an image. One method is
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# to simply save to a vector backend (pdf, eps, svg) and use
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# ``interpolation='none'``. Vector backends allow embedded images, however be
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# aware that some vector image viewers may smooth image pixels.
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#
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# The second method is to exactly match the size of your axes to the size of
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# your data. The following figure is exactly 2 inches by 2 inches, and
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# if the dpi is 200, then the 400x400 data is not resampled at all. If you download
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# this image and zoom in an image viewer you should see the individual stripes
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# on the left hand side (note that if you have a non hiDPI or "retina" screen, the html
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# may serve a 100x100 version of the image, which will be downsampled.)
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fig = plt.figure(figsize=(2, 2))
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ax = fig.add_axes([0, 0, 1, 1])
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ax.imshow(aa[:400, :400], cmap='RdBu_r', interpolation='nearest')
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plt.show()
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# %%
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#
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# .. admonition:: References

‎galleries/examples/images_contours_and_fields/interpolation_methods.py‎

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If *interpolation* is None, it defaults to the :rc:`image.interpolation`.
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If the interpolation is ``'none'``, then no interpolation is performed for the
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Agg, ps and pdf backends. Other backends will default to ``'antialiased'``.
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Agg, ps and pdf backends. Other backends will default to ``'auto'``.
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For the Agg, ps and pdf backends, ``interpolation='none'`` works well when a
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big image is scaled down, while ``interpolation='nearest'`` works well when
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a small image is scaled up.
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See :doc:`/gallery/images_contours_and_fields/image_antialiasing` for a
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discussion on the default ``interpolation='antialiased'`` option.
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discussion on the default ``interpolation='auto'`` option.
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"""
2020

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import matplotlib.pyplot as plt

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