ahe

A minimalist Python library for (Contrast Limited) (Adaptive) Histogram Equalization, combining the expressiveness of a user-friendly Python interface with the raw power of a low-level implementation.

• Development status
• Installation
• Usage
  • Simple Histogram Equalization
  • Adaptive Histogram equalization AHE
    • Prioritizing accuracy: sliding-tile
    • Prioritizing performance: tile-interpolation
  • General rules for tiling schemes
• Migrating from scikit-image
  • TL;DR
  • Disclaimer: missing features
  • Dependency Minimalism
  • Better performance
  • Interface Consistency
  • Conservation of transformation invariants
  • Additional features
  • Migration Guide
    • HE
    • AHE with implicit kernel size
    • CLAHE with explicit kernel size
• References

Development status

ahe is currently in alpha. Fundational features are available, and expected to be stable, but the software as a whole may not be feature complete yet.

Installation

$ python -m pip install ahe

Usage

Simple Histogram Equalization

We'll start by defining an image composed of noise.

import ahe
import numpy as np

image_shape = (128, 128)
prng = np.random.default_rng(0)
image = np.clip(
    prng.normal(
        loc=0.5,
        scale=0.25,
        size=np.prod(image_shape),
    ).reshape(image_shape),
    a_min=0.0,
    a_max=1.0,
)

Non-adaptive histogram equalization is performed as follow

image_eq = ahe.equalize_histogram(image)

This method is least expensive in terms of strain put on hardware resources. However, as a single histogram is computed and adjusted over the entire image, this technique is known to amplify noise in near-uniform regions.

Adaptive Histogram equalization (AHE)

Adaptive Histogram Equalization (AHE) was designed to overcome this limitation by instead computing more localized (and numerous) histograms, improving the local contrast in all regions, at the cost of a reduced efficiency. As illustrated in the following, there are two main variants of AHE, sliding-tile and tile-interpolation. As the names suggest, both methods rely on the use of of tiles, also known as contextual regions, that define sub-domains in which different histograms are computed and applied.

Prioritizing accuracy: sliding-tile

True AHE is intrinsically an expensive operation to perform, as it requires computing a different histogram per pixel. One efficient (although still costly) way to accomplish this, originally proposed by Pizer et al. (1987), reduces the redundancy in intermediate computations and is known as the sliding-tile variant of AHE. Here's how to use it in ahe

image_eq = ahe.equalize_histogram(
    image,
    adaptive_strategy={
        'kind': 'sliding-tile',
        'tile-size': 15,
    },
)

Note

This strategy requires odd-sized tile shapes, but supports image shapes with any parity.

While an exact implementation of AHE, this option remains resource-demanding and is not recommended for production.

Prioritizing performance: tile-interpolation

Alternatively, very similar results can be obtained at a fraction of the cost using an approximative method known as the tile-interpolation variant of AHE, also introduced by Pizer et al. (1987). In this method, an image is split into equal-sized sub domains (tiles), which may be specified either from a tile size

image_eq = ahe.equalize_histogram(
    image,
    adaptive_strategy={
        'kind': 'tile-interpolation',
        'tile-size': 16,
    },
)

or as a number of tiles to split the domain into (in each direction)

image_eq = equalize_histogram(
    image,
    adaptive_strategy={
        'kind': 'tile-interpolation',
        'tile-into': 8,
    },
)

Note

This strategy requires even-sized tile and image shapes.

General rules for tiling schemes

In all AHE strategies, all tiles created will be the exact same size, regardless of the pixel's relative position in the image. The whole domain is generally padded internally in order to respect this rule. The exact method used for padding is controlled by the boundaries keyword argument.

Both 'tile-size' and 'tile-into' will accept either a shape as a pair of integers (n, m), or a single integer n, which is a shorthand for (n, n), as illustrated above.

Migrating from scikit-image

TL;DR

Put simply, if all your project needs from scikit-image is skimage.exposure.equalize_(adapt)hist, ahe provides a faster, more lightweight and portable replacement. The following contains a much more detailed explanation of the differences. You can also jump to the final Migration Guide.

Disclaimer: missing features

The following features from skimage.exposure.equalize_(adapt)hist are currently missing from ahe:

• masking
• multi-channel images objects (from PIL) or arrays. The expectation is that this should be easy to re-implement on the user side.
• higher dimensionality: ahe currently only supports 2D input and outputs. The algorithms can be generalized to work in any dimensionality. Please open an issue

Some, though not all of the above are already planned. Don't hesitate to request the others (or anything else that could be in scope) by opening an issue.

Dependency Minimalism

ahe has no runtime dependencies beyond numpy. Additionally, its binaries are orders of magnitude lighter than scikit-image's, as well as future-compatible with yet-unreleased versions of Python.

(*: numpy itself, as the common dependency to ahe and scikit-image, is excluded from this graph)

Better performance

Interface Consistency

scikit-image's implementation of histogram equalization methods are exposed as two different functions: skimage.exposure.equalize_hist and skimage.exposure.equalize_adapthist. Only the former supports masking, and only the latter supports clipping. ahe.equalize_histogram provides a consistent feature set, independent of the adaptive strategy (or lack thereof) selected.

Furthermore, implicit, default behavior can be hard to reproduce explicitly. For instance, equalize_adapthist will, by default, create tiles by dividing the image in 8 along each direction, but only exposes a tile_size argument to override this; as a result, one needs to re-implement division logic if they need something very similar to the default, but with any other value than 8. In stark contrast, ahe.equalize_histogram's adaptive_strategy argument supports all these applications:

• adaptive_strategy=None corresponds to skimage.exposure.equalize_hist
• adaptive_strategy={'kind': 'tile-interpolation', 'tile-into': 8} corresponds to skimage.exposure.equalize_adapthist's default, but the exact divisor(s) used can easily be adjusted
• adaptive_strategy={'kind': 'tile-interpolation', 'tile-size': 64} is akin to using skimage.exposure.equalize_adapthist's tile_size argument.

Last but not least, equalize_hist does not support contrast limitation, while equalize_adapthist enables it by default (clip_limit defaults to 0.01), and things get messy when you actually want to disable it:

• clip_limit's name is not descriptive and only makes sense if you already know what it does under the hood. ahe's equivalent parameter is named max_normalized_bincount, which is more verbose, but also more explicit about what the number represents.

• clip_limit (a.k.a max_normalized_bincount) is effectively a fraction; only values within the open interval ]0.0, 1.0] are meaningful, but clip_limit=0.0 is allowed, and effectivaly disable all clipping, which means it's equivalent to 1.0, further mystifying the underlying behavior and meaning of the parameter. Another way to phrase this is that the results change discontinuously at 0.0, which is very close to the default value and should be easy to reason about.

• results for clip_limit=1.0 (or 0.0, as we just saw), are actually incorrect at a level that is visible to the naked eye (aliasing may be prominent). In comparison, ahe does not enable contrast limitation by default: such flagrant defects would be immediately visible in tests.

Conservation of transformation invariants

ahe.equalize_histogram also provides stricter guarantees regarding the transformation's geometric invariants. Outputs are guaranteed to be invariant (to machine precision) to left/right and top/ bottom symmetries. In contrast, skimage.exposure.equalize_adapthist's outputs are subject to biases on, because it does not enforce symmetry in its internal tiling scheme (as of scikit-image v0.26.0). This improved tiling scheme comes at the cost of stricter requirements in ahe.equalize_histogram: the tile-interpolation strategy only supports tiles and images with even sizes in both directions.

Additional features

ahe.equalize_histogram supports more tiling scheme than skimage.exposure.equalize_hist and skimage.exposure.equalize_adapthist combined, within a consistent interface and a unified feature set. In particular, it offers an exact implementation of Adaptive Histogram Equalization implemented as a sliding-tile, while skimage.exposure.equalize_adapthist only supports tile-interpolation (also available in ahe), which is generally faster, but also a less accurate approximation of a true AHE.

ahe.equalize_histogram also supports periodic boundary conditions, which can be specified as boundaries='periodic'.

Migration Guide

This section provides some practical examples of scikit-image applications and their equivalent in ahe.

Notes

• in ahe, the default nbins is generally aligned with scikit-image's (256), except for kernels (or tiles) spanning less than 256 pixels. For maximu compatibility, specifying an explicit value is recommended.
• ahe.equalize_histogram's max_normalized_bincount represents the same parameter as skimage.exposure.equalize_adapthist's clip_limit, but their default values differ: max_normalized_bincount defaults to 1.0 (no contrast limitation), while scikit-image's clip_limit default to 0.01
• "kernel", "tile" and "contextual region" are different names for the same concept.

HE

from skimage.exposure import equalize_hist

result = equalize_hist(array)

# becomes
import ahe

result = ahe.equalize_histogram(array, nbins=256)

AHE with implicit kernel size

from skimage.exposure import equalize_adapthist

result = equalize_adapthist(array, clip_limit=1.0)

# becomes
import ahe

result = ahe.equalize_histogram(
    array,
    nbins=256,
    adaptive_strategy={
      "kind": "tile-interpolation",
      "tile-into": 8, # or (8, 8)
    },
)

CLAHE with explicit kernel size

from skimage.exposure import equalize_adapthist

result = equalize_adapthist(array, kernel_size=64)

# becomes
import ahe

result = ahe.equalize_histogram(
    array,
    nbins=256,
    adaptive_strategy={
      "kind": "tile-interpolation",
      "tile-size": 64, # or (64, 64)
    },
    max_normalized_bincount=0.01,
)

References

1. Pizer, Stephen M. et al. (1987). Adaptive Histogram Equalization and Its Variations. Compute Vizion, Graphics, and Image Processing, 39, 355-368