Histogram Matching Pan Sharpened Images

Fused pan sharpened images are created by combining the three lower resolution RGB bands with the higher resolution panchromatic band. The process transforms the RGB bands to hue, saturation and intensity bands. The hue and saturation bands are expanded to match the size of the panchromatic band. The intensity band is discarded and the panchromatic band is substituted instead. Although this often yields good results, some pan sharpened images may not look very pleasing and may need a lot of pre and post processing work to create an acceptable image.

One of the reasons that the pan sharpened image does not look the same as the corresponding RGB image results from differences between the panchromatic image and the computed intensity image. There is no reason that the grayscale color levels of the panchromatic image should exactly match those of the intensity image, as one is computed from the low resolution band files while the panchromatic image is acquired with a completely different sensor. The intensity image is not accurately named as it affects both the brightness of the image and its tonal quality. The differences between the panchromatic band and the intensity band cannot be completely corrected by simple linear transformations. A technique called histogram mapping is much more capable of addressing the problem of non-linear differences between the two images.

In order to histogram map one image to another, a discrete transformation function is computed that when applied to the panchromatic band, adjusts each pixel to a color level that results in a better match to the computed intensity band. When the transformed panchromatic band is fused in a pan sharpening algorithm, much better color tones may be achieved.

The transformation function, as its name implies is derived from the histograms of the panchromatic image and the intensity image. Since a grayscale image can have 256 discrete color levels ranging from 0x00 (black) to 0xff (completely white) it is possible to extract histogram distributions of color levels from each of the two images. A plot can be made of the 256 color levels on the abscissa by the frequency of occurrence of each of the levels on the ordinate. The histogram is represented on a computer as a one dimensional array. From the histograms the cumulative histograms are computed. The frequency of occurrence of a color level of a cumulative histogram is the frequency at that level plus the sum of all the frequencies of all lower color levels. The transformation function is derived from the two cumulative histograms.

If the transformation is successful, the relevant statistics of the transformed input (panchromatic) image (mean and standard deviation) should match those of the reference (intensity) image more closely than the unadjusted image.

An example is shown to the right of a Lansat image of northern Canada. The first image is the RGB color composite image. This image is nominally the target image as it results from substitution of the blue, green and red 30m bands into the image color model. (It is of course half the resolution of the pan sharpened images.)

The second image is the raw pan sharpened image. Although this image can be made quite presentable with some work, the raw image is characterized by blue foliage tones and a dark ocean. (However this image exhibits less haze than either the RGB or matched panchromatic.)

The third image is the result of histogram matching the panchromatic band with the computed intensity band. This particular image matches the reference RGB image much more closely (although it can still be considerably improved by additional processing.)

PANCROMA version 2.17 employs histogram mapping algorithms as its default condition when pan sharpening images. The normal settings will clip the first lowest color values from the histogram as many images are surrounded by black collars which can badly skew the transform. This can be turned off as well.

[Source, Reference and Computed Histograms. Click to enlarge.]

[10m Pan Sharpened Image. Click to enlarge.]

[20m RGB Natural Color Image. Click to enlarge.]

[10m Pan Sharpened Image. Click to enlarge.]

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