Histogram Adjustments in MATLAB

8/12/2019 Histogram Adjustments in MATLAB

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Histogram Adjustments in MATLAB Part I StretchingNick Loomis July 12, 2013 Image Enhancement,Recent Posts 6 Comments

Obtaining an image with the right contrast for your application is never easy. Whether it is for art,

detection, recognition, or improving your own photographs, contrast adjustment is a common

task. Industrial setups can adjust the lighting and camera parameters before image capturebut

what about after the image has been captured? Histogram processing is one answer for

computationally adjusting the contrast, and can also be applied to a number of problems

involving color balance or tone transfer.

This three-part post focuses on different methods for post-processing an image to modify itsunderlying histogram, affecting contrast and color balance in some amazing ways. The first part

introduces basic pixel operations and how they affect histograms, and then shows several

schemes for how to stretch a histogram to cover the full range of available pixel values.The

second partdiscusses how to spread out the pixel values evenly over some range, a process

known as histogram equalization.The third partextends the idea of controllably modifying the

pixel values so that the resulting histogram matches any arbitrary distribution.

To begin, well look at the basics of working with image histograms using MATLAB and how to

perform histogram stretching to modify contrast and color.

Histogram math

A histogram is the probability distribution of pixel values in an image. (For RGB images, the

histogram is usually broken into three histograms of the three component channels.) Like any

other distribution, histograms have simple mathematical rules. Two operations that affect the

pixel values, and thus the histograms, will be used extensively through these posts:

1) Adding a value to all the pixels adds that amount to the histogram; visually, this shifts the

histogram

2) Multiplying all the pixel values by a certain amount scales where the histogram data appears;

visually, this stretches the histogram
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To plot the histogram of an image, there are several options. If you have the Image Processing

Toolbox, the imhistfunction is the easiest to use, but only works on single color channels. For

example, to plot the green channel of an image,

img = imread('Flowers.jpg');

imhist(img(:,:,2))

If you dont have the Toolbox or want to have greater control over the histogram data, you can

compute the values directly using the hist function and plot using your desired methods:
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img = imread('Flowers.jpg');

g = img(:,:,2);

bins = 0:1:255;

H = hist(g(:), bins);plot(bins, H, 'linewidth',2, 'color', 'g');

This second example assumes that the image uses eight bits per color channel, or a maximum

value of 2^8-1 = 255. The remainder of the examples in these posts will use the assumption that

pixel values range from 0 to 255.

Histogram stretching

Contrastis a measure of how much the pixel brightness changes relative to the average

brightness. A technique known as histogram stretchingcan be used to shift the pixel values to fill

the entire brightness range, resulting in high contrast.

The first step is to find the pixel values that should get mapped to 0% and 100% brightness. Any

real-world image has noise, however. To keep the noise from unduly influencing the stretching,

an assumption is made: a small percentage of the brightest and darkest pixels are ignored, writing

them off to sensor noise. If you have the Image Processing Toolbox (well cover what you can do

if you dont have the toolbox in a moment), you can use
https://en.wikipedia.org/wiki/Contrast_(vision)https://en.wikipedia.org/wiki/Contrast_(vision)http://imageprocessingblog.com/wp-content/uploads/2013/07/flower-green-hist-direct.jpghttps://en.wikipedia.org/wiki/Contrast_(vision)


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There are several assumptions here. The first is that the image, img, is assumed to have pixels

which could range in value from 0 to 255. The second is that the histogram, H, could have bins

with 0 counts. Theproblem is that, in the next step, well be doing an inverse look-up, which

means that we need an invertible function. If H has zeros, then cumsum(H) will have at least two

identical values and will not be invertible. Setting the zero-count values in H

to eps(sum(H))ensures that H does not have non-zero values but only has a trivial effect on the

CDF. Using the CDF for the inverse look-up can be as simple as this:

h_low = interp1(cdf, [0,bins], pct);

h_high = interp1(cdf, [0,bins], 1-pct);

where pct is the percent of pixels to ignore. This will give similar limits as stretchlim.

Figure: Interpolating the CDF at pct = 0.05 to find the corresponding h_low and h_high pixelvalues.
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The next step is to adjust the image values so that the h_low and h_high values are remapped to

the 0% and 100% brightness levels. Using simple histogram math,

img_adjusted2 = uint8((double(img)h_low)/(h_high-h_low)* 255);

Note that this includes both a shift, double(img)h_low, and a stretch, 1/(h_high-h_low) of the

original histogram.

In general, histogram stretching tends to work well on images that have a poor image contrast to

start with and which should have full contrast. You can limit the amount of stretching that occurs

by not mapping h_low and h_high to the 0% and 100% brightness levels, but instead by only

scaling them a certain amount.

Multi-channel Histogram Stretching

The histogram stretching that weve looked at so far has focused on single-channel images.

Whats useful is that the same functions can be applied tomulti-channel images, like RGB

images, by applying the codes to each channel independently.

MATLABsstretchlimand imadjustfunctions are both written to be able to take in RGB images

in addition to single-channel images using the exact same code as we used earlier.

Again, if you dont have the Image Processing Toolbox or want to use multi-channel images that

dont have three channels (for example, some microscopy or satellite imagery), youll need to

take a few extra steps. For example, say you have a multi-channel image, img, and you plan to

adjust each channel. Then you could consider using something like this:

img_adjusted = zeros(size(img), 'uint8');

forch = 1:size(img,3)

img_channel = img(:,:,ch);

limits = stretchlim(img_channel, 0.01);

img_adjusted(:,:,ch)= imadjust(img_channel, limits, []);

end

Variations on Histogram Stretching

The RGB color space is the de-facto standard for images. It doesnt always result in the best

processing, however, especially when the image is intended for human viewing. A color space

that better represents the human visual system, likeL*a*b* orLuvcan provide more natural

stretching in some cases. In both of these color spaces, the L channel represents the brightness,while the (a*, b*) or (u, v) channels represent the color. (This is conceptually similar toYCbCr,
https://en.wikipedia.org/wiki/Lab_color_spacehttps://en.wikipedia.org/wiki/Lab_color_spacehttps://en.wikipedia.org/wiki/CIE_Luv_color_spacehttps://en.wikipedia.org/wiki/CIE_Luv_color_spacehttps://en.wikipedia.org/wiki/CIE_Luv_color_spacehttps://en.wikipedia.org/wiki/YCbCrhttps://en.wikipedia.org/wiki/YCbCrhttps://en.wikipedia.org/wiki/YCbCrhttps://en.wikipedia.org/wiki/YCbCrhttps://en.wikipedia.org/wiki/CIE_Luv_color_spacehttps://en.wikipedia.org/wiki/Lab_color_space


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used in JPEG encoding.) The stretching is performed on the L channel after converting the colors.

Using the functions in the Image Processing Toolbox,

img = imread('lion.png');

c_rgb2lab = makecform('srgb2lab');labimg = applycform(img, c_rgb2lab);

labimg(:,:,1)= imadjust(labimg(:,:,1), ...

stretchlim(labimg(:,:,1), 0.01));

c_lab2rgb = makecform('lab2srgb');

img_adjusted = applycform(labimg, c_lab2rgb);

Figure: Histogram stretching within a L*a*b* color space and in an RGB color space. Note that

the RGB stretching changes the colors slightly, emphasizing reds and yellows in this particular

case.

Since only the L channel was adjusted, the colors remain the same, but the brightness is re-

mapped. This adjusts the contrast in a way that sometimes can be more visually pleasing without

significantly affecting the color balance.

If you dont have the Image Processing Toolbox, Mark Ruzon wrote simple functions to convert

between RGB and L*a*b*:Lab2RGB andRGB2Lab.
http://www.mathworks.com/matlabcentral/fileexchange/24010http://www.mathworks.com/matlabcentral/fileexchange/24010http://www.mathworks.com/matlabcentral/fileexchange/24010http://www.mathworks.com/matlabcentral/fileexchange/24009http://www.mathworks.com/matlabcentral/fileexchange/24009http://www.mathworks.com/matlabcentral/fileexchange/24009http://imageprocessingblog.com/wp-content/uploads/2013/07/hist-stretching-w-lab-lion.jpghttp://www.mathworks.com/matlabcentral/fileexchange/24009http://www.mathworks.com/matlabcentral/fileexchange/24010


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Another variation is to apply histogram stretching in the hue-saturation-value (HSV)color space.

The histogram stretching is only applied to the S and V channels, but not the hue channel. This

tends to result in reasonable contrast and fuller colors without significantly affecting the color

balance.

img = imread('bopFlower.png');

hsvimg = rgb2hsv(img);

forch=2:3

hsvimg(:,:,ch)= imadjust(hsvimg(:,:,ch), ...

stretchlim(hsvimg(:,:,ch), 0.01));

end

img_adjusted = hsv2rgb(hsvimg);

Stretching on HSV is also sometimes done after stretching in the RGB color space to ensure full

color saturation. One example is this underwater image, which required significant stretching in

RGB, but then benefits from an additional HSV stretch to gain full contrast:
https://en.wikipedia.org/wiki/HSL_and_HSVhttps://en.wikipedia.org/wiki/HSL_and_HSVhttps://en.wikipedia.org/wiki/HSL_and_HSVhttp://imageprocessingblog.com/wp-content/uploads/2013/07/bopFlower-hsv-stretched.jpghttps://en.wikipedia.org/wiki/HSL_and_HSV


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This is a good point to try out histogram stretching on your own images and get familiar with thedifferent color transforms. In thenext post,well explore histogram equalization, primarily used

for modifying the contrast in an image, and some of its extensions.

Nick Loomis writes forloomsci.wordpress.comand uses the methods from this series ofposts for various projects: histogram stretching tocorrect the colors of underwater

photosand histogram matching toreplicate the effect of color filters.
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Histogram Adjustments in MATLAB