histeq (Image Processing Toolbox User's Guide)

Image Processing Toolbox User's Guide

Enhance contrast using histogram equalization

Syntax

J = histeq(I,hgram)
J = histeq(I,n)
[J,T] = histeq(I,...)

newmap = histeq(X,map,hgram)
newmap = histeq(X,map)
[newmap,T] = histeq(X,...)

Description

histeq enhances the contrast of images by transforming the values in an intensity image, or the values in the colormap of an indexed image, so that the histogram of the output image approximately matches a specified histogram.

J = histeq(I,hgram) transforms the intensity image I so that the histogram of the output intensity image J with length(hgram) bins approximately matches hgram. The vector hgram should contain integer counts for equally spaced bins with intensity values in the appropriate range: [0, 1] for images of class double, [0, 255] for images of class uint8, and [0, 65535] for images of class uint16. histeq automatically scales hgram so that sum(hgram) = prod(size(I)). The histogram of J will better match hgram when length(hgram) is much smaller than the number of discrete levels in I.

J = histeq(I,n) transforms the intensity image I, returning in J an intensity image with n discrete gray levels. A roughly equal number of pixels is mapped to each of the n levels in J, so that the histogram of J is approximately flat. (The histogram of J is flatter when n is much smaller than the number of discrete levels in I.) The default value for n is 64.

[J,T] = histeq(I,...) returns the grayscale transformation that maps gray levels in the intensity image I to gray levels in J.

newmap = 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,newmap) approximately matches hgram. The histeq function returns the transformed colormap in newmap. length(hgram) must be the same as size(map,1).

newmap = 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. It returns the transformed colormap in newmap.

[newmap,T] = histeq(X,...) returns the grayscale transformation T that maps the gray component of map to the gray component of newmap.

Class Support

For syntaxes that include an intensity image I as input, I can be of class uint8, uint16, int16, single, or double. The output image J has the same class as I.

For syntaxes that include an indexed image X as input, X can be of class uint8, single, or double; the output colormap is always of class double. The optional output T (the gray-level transform) is always of class double..

Example

Enhance the contrast of an intensity image using histogram equalization.

I = imread('tire.tif');
J = histeq(I);
imshow(I)
figure, imshow(J)

Display the resulting histograms.

```
imhist(I,64)
figure; imhist(J,64)
```

Algorithm

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

where c₀ is the cumulative histogram of A, c₁ is the cumulative sum of hgram for all intensities k. This minimization is subject to the constraints that T must be monotonic and c₁(T(a)) cannot overshoot c₀(a) by more than half the distance between the histogram counts at a. histeq uses this transformation to map the gray levels in X (or the colormap) to their new values.

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

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

and then applies the previous algorithm.

See Also

brighten, imadjust, imhist

graythresh hough