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Building Spatial Databases – Theory / Intensity transformation

Learners guide


The histogram equalization is an important group of functionalities of the image processing. In this chapter some of them will be shown.


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Intensity transformation

Histogram equalization

All images contain different photometric values on each pixel. These pixel photometric values are varying from black to white, although this never occurs in real life. Due to the environmental and digital projection methods, the dynamic range of intensity values are much narrower than expected.

Figure 52. On the left is a histogram of Band A, which is the frequency of intensity values on pixels. On the right is Band A and Band B with crossplotted intensity space, describing their relationship.

However all images contain a darkest and a brightest pixel, the brightest and darkest points are not equal to the theoretical white and black points in the RGB colour model. By representing the light emission values and their occurrence frequency in a coordinate system we will receive a histogram, which is the basis of image processing methods.

Figure 53. Process of histogram equalization: histogram of the original image (upper left figure), histogram after transformation (upper right figure) and transformation function (lower figure).

Histogram is the probability (P) representing the occurrence of intensity values on pixels by calculating the occurrence of an intensity value (i) on every point:

Minimum and maximum intensity values of an image can be determined by a histogram. During histogram transformation, the transformation function will transform the intensity of pixels into the minimum and maximum range, so the histogram has been stretched by increasing the difference between intensity values, which is the contrast.

Many histogram transformation methods exist along with the linear transformation. Any function can be applied for intensity transformation as described in Figure 54. The intensity value of point i can be given with the following formula:

which if applied for on an image matrix with a 24-bit RGB colour model, we get the following:

where f(x,y) represents the original image on (x,y) position, min and max are the minimum and maximum intensity values on the original image, and (x,y) transformation function will transform the image into an intensity range between 0 and 255. We have increased the intensity difference on pixels, hence we are increasing the contrast of the image. This transformation method is called histogram equalization.

Figure 54. Intensity transformation can be given by any T function.

Figure 55. Original SPOT image. Let us take a closer look at Figure 55, which is a black-and-white image representing a remote sensed image. Let us create a histogram for it by representing the probability density function of intensity values varying from 0 to 255. As you can see, the darkest and brightest points of the image are not 0 and 255. Usually the distribution function, which is the integral of histogram, is represented instead of the histogram.

Let us transform the original image. After icreasing the dynamic range of the image, namely the darkest point of the image is 0, and the brightest point is 255; The result is shown in Figure 57.

Figure 56. Histogram and distribution function of the remote sensed image. The indication of the possible dynamic range is quite narrow, because the darkest point is starting somewhere at 60, while the brightest point is around 120.

Figure 57. Remote sensed image transformed by histogram. Contrast has been significantly increased, as the brightest area on the image is almost white (255), whereas the darkest areas are almost black (0).

Let us take a coloured image and apply the same histogram equalization transformation method on each RGB band.

Figure 58. LANDSAT image.

Figure 59. LANDSAT image after histogram equalization.

If histogram equalization is applied on each colour, it may result changes in the aspect, colour characteristics, rations, appearance of the image. However, these changes are not relevant in remote sensed images. Its crucial to keep the colour characteristics of a normal image. Figure 59 shows the LANDSAT image after histogram equalization.

The role of base colours is emphasized by increasing their intensity between 0 and 255 with transformation; therefore, the colours of a raw image may gain some artificial characteristics, namely we may break up the colour balance of the image. By the above mentioned examples, the authors’ intention is to raise your attention: changing the characteristics of colours and colour balance should be taken with care. We must know the consequences of our modifications, for example by increasing the contrast we have broken up the colour balance of the image. It is possible to increase the contrast without breaking up the colour balance by not using the whole range of dynamic intensity range for all the three colour channels.

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A special case of intensity transformation is binarization, where the transformation degree is determined by a k threshold value (Figure 60). A special binarization transformation is the slicing filter, where resetting is performed on the intensity band or within a range of an intensity band (Figure 61).

Figure 60. Binarization resets the intensity value under the threshold k, and sets the value to 1 for those having intensity value over the threshold k. T describes the intensity transformation function, which in our case is a step-function.

Figure 61. Slicing filters are working inside a band by resetting its value (in other words, they subtract the intensity band from the image), or keep it.

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