Histogram Matching

The Histogram Matching (also called Histogram Specification) algorithm generates an output image based upon a specified histogram.

Background

The process of Histogram Matching takes in an input image and produces an output image that is based upon a specified histogram. The required parameters for this algorithm are the input image and the specified image, from which the specified histogram can be obtained.

The algorithm works as follows:

The histograms for the input image p(f) and the specified image pd(g) are generated. Here, the desired histogram of the specified image is denoted as pd(g). Cumulative histograms - P(f) and Pd(g) are then generated using the following equations:

Equation 1
<math> P(f) = \sum_{k=0}^fp(k) </math>

Equation 2
<math> P_d(g) = \sum_{k=0}^gP_d(k) </math>

where f and g are the pixel intensity levels.

The transformation function is obtained by choosing g for each f, such that if g > f, then Pd(g) > P(f). The transformation function is then applied to the input image to produce an output image by remapping the pixel intensities. The objective is to find a transformed digital picture of a given picture, such that the sum of absolute errors between the intensity level histogram of the transformed picture and that of a reference picture is minimized. Refer to Figure 1.

Figure 1. Histograms and cumulative histograms: (A) histogram of 8x8 pixel image; (B) cumulative histogram derived from (A); (C) desired histogram of the same 8x8 pixel image; (D) cumulative histogram derived from (C); (E) gray scale transformation function that approximately transforms the histogram (A) to desired histogram (C); (F) histogram of gray-scale-transformed image obtained by applying the transformation function in (E) to the image with the histogram shown in (A).

Figure 2. The input image and its histogram p(f)

Figure 3. The specified image and its histogram pd(g)

Figure 4. The result image and its histogram

References

Rafael C. Gonzalez and Richard E. Woods. Digital Image Processing. Addison-Wesley Publishing Company, 1992, pp. 173-182

Jae S. Lim. Two-Dimensional Signal and Image Processing. Prentice-Hall, Inc., 1990, pp. 453-459

Image types

You can apply this algorithm to both color and black-and-white images, as well as 2D and 3D images.

Applying the Histogram Matching algorithm

To use this algorithm, do the following:

1. Select Algorithms > Histogram Tools > Histogram Matching in the main MIPAV window. The Histogram Matching dialog box (Figure 5) appears.
2. Complete the information in the dialog box.
3. Click OK. The algorithm begins to run, and a progress bar appears momentarily with the status. When the algorithm finishes running, the progress bar disappears, and the results appear in a separate image window.

Figure 5. Histogram Matching dialog box

Histogram match <File name> to	Select the specified image pd(g) from the list box
New image	Shows the results of the algorithm in a new image window
Replace image	Shows the results of the algorithm in the same image window
OK	Applies the algorithm according to the specifications in this dialog box.
Cancel	Disregards any changes that you made in the dialog box and closes this dialog box.
Help	Displays online help for this dialog box.