histeq

Enhance contrast using histogram equalization

Syntax

J = histeq(I)

J = histeq(I,n)

J = histeq(I,hgram)

newcmap = histeq(X,map)

newcmap = histeq(X,map,hgram)

[___,T] = histeq(___)

Description

J = histeq(I) transforms the grayscale image I so that the histogram of the output grayscale image J has 64 bins and is approximately flat.

J = histeq(I,n) transforms the grayscale image I so that the histogram of the output grayscale image J with n bins is approximately flat. The histogram of J is flatter when n is much smaller than the number of discrete levels in I.

J = histeq(I,hgram) transforms the grayscale image I so that the histogram of the output grayscale image J approximately matches the target histogram hgram. The number of bins in the histogram of the output image is equal to length(hgram).

newcmap = histeq(X,map) transforms the values in the colormap so that the histogram of the gray component of the indexed image X is approximately flat. The transformed colormap is newcmap.

newcmap = histeq(X,map,hgram) transforms the colormap associated with the indexed image X so that the histogram of the gray component of the indexed image (X,newcmap) approximately matches the target histogram hgram. The histeq function returns the transformed colormap in newcmap. length(hgram) must be the same as size(map,1).

[___,T] = histeq(___) also returns the transformation T that maps the gray component of the input grayscale image or colormap to the gray component of the output grayscale image or colormap.

Examples

Enhance Contrast Using Histogram Equalization

Read an image into the workspace.

I = imread('tire.tif');

Enhance the contrast of an intensity image using histogram equalization.

J = histeq(I);

Display the original image and the adjusted image.

imshowpair(I,J,'montage')
axis off

Display a histogram of the original image.

figure
imhist(I,64)

Display a histogram of the processed image.

figure
imhist(J,64)

Enhance Contrast of Volumetric Image Using Histogram Equalization

Load a 3-D dataset.

load mristack

Perform histogram equalization.

enhanced = histeq(mristack);

Display the first slice of data for the original image and the contrast-enhanced image.

figure
subplot(1,2,1)
imshow(mristack(:,:,1))
title('Slice of Original Image')
subplot(1,2,2)
imshow(enhanced(:,:,1))
title('Slice of Enhanced Image')

Plot Transformation Curve for Histogram Equalization

This example shows how to plot the transformation curve for histogram equalization. histeq can return a 1-by-256 vector that shows, for each possible input value, the resulting output value. (The values in this vector are in the range [0,1], regardless of the class of the input image.) You can plot this data to get the transformation curve.

Read image into the workspace.

I = imread('pout.tif');

Adjust the contrast using histogram equalization, using the histeq function. Specify the gray scale transformation return value, T, which is a vector that maps graylevels in the intensity image I to gray levels in J.

[J,T] = histeq(I);

Plot the transformation curve. Notice how this curve reflects the histograms in the previous figure, with the input values mostly between 0.3 and 0.6, while the output values are distributed evenly between 0 and 1.

figure
plot((0:255)/255,T);

Input Arguments

I — Grayscale image

numeric array

Grayscale image, specified as a numeric array of any dimension.

Data Types: single | double | int16 | uint8 | uint16

hgram — Target histogram

numeric vector

Target histogram, specified as a numeric vector. The target histogram must have equally spaced bins spanning intensity values in the appropriate range. The intensity value range depends on the data type of the input image.

• single or double — [0, 1].

• uint8 — [0, 255].

• uint16 — [0, 65535].

• int16 — [–32768, 32767].

By default, the number of bins in the target histogram is equal to length(hgram).

For example:

hgram = 256:-4:4;
J = histeq(I,hgram);

specifies a target histogram with 64 bins as a non-flat, linearly decreasing function which emphasizes small pixel values.

histeq automatically scales hgram so that sum(hgram) == numel(I). The histogram J better matches hgram when length(hgram) is much smaller than the number of discrete levels in I.

Data Types: single | double

n — Number of discrete gray levels

64 (default) | positive integer

Number of discrete gray levels, specified as a positive integer.

Data Types: single | double

X — Indexed image

numeric array

Indexed image, specified as a numeric array of any dimension. The values in X are an index into the colormap map.

Data Types: single | double | uint8 | uint16

map — Colormap

c-by-3 numeric matrix

Colormap associated with indexed image X, specified as a c-by-3 numeric matrix with values in the range [0, 1]. Each row is a three-element RGB triplet that specifies the red, green, and blue components of a single color of the colormap.

Data Types: double

Output Arguments

J — Transformed grayscale image

numeric array

Transformed grayscale image, returned as a numeric array of the same size and class as the input image I.

T — Grayscale transformation

numeric vector

Grayscale transformation, returned as a numeric vector. The transformation T maps gray levels in the image I to gray levels in J.

Data Types: double

newcmap — Transformed colormap

n-by-3 numeric matrix

Transformed colormap, specified as an n-by-3 numeric matrix with values in the range [0, 1]. Each row is a three-element RGB triplet that specifies the red, green, and blue components of a single color of the colormap.

Data Types: double

Algorithms

When you supply a target histogram hgram, histeq chooses the grayscale transformation T to minimize

$$\left|c_1(T(k))-c_0(k)\right|,$$

c₀ is the cumulative histogram of the input image I, and c₁ is the cumulative sum of hgram for all intensities k. This minimization is subject to these constraints:

• T must be monotonic

• c₁(T(a)) cannot overshoot c₀(a) by more than half the distance between the histogram counts at a

histeq uses the transformation b = T(a) to map the gray levels in X (or the colormap) to their new values.

If you do not specify hgram, then histeq creates a flat hgram,

hgram = ones(1,n)*prod(size(A))/n;

and then applies the previous algorithm.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• histeq supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, histeq generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Types of Code Generation Support in Image Processing Toolbox.

• When generating code, histeq does not support indexed images.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

When generating code, histeq does not support indexed images.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.

Version History

Introduced before R2006a

R2022b: Generate CUDA code using GPU Coder

histeq now supports the generation of optimized CUDA^® code (requires GPU Coder™).

R2022b: Support for thread-based environments

histeq now supports thread-based environments.