Master Thesis - Hochschule Bonn-Rhein-Sieg

5. Algorithms Master Thesis Björn Ostermann page 63 of 126
To redistribute the values a probability distribution function (PDiF) is calculated. The PDiF, as shown
in Figure 39c, is created by adding the amount of all pixels with lower intensity to each amounts of
pixels (see formula in Equation 4).
PDiF
pixels
n
�
i�0
�n�� Number _ of _ pixels�i�
Equation 4: Formula to calculate the PDiF
PDiFpixels �n��Amount of all pixels with an intensity value equal or lower than n
��� i
Number _ of _ pixels Amount of pixels with the intensity value i
Based on this PDiF the intensity value of each pixel is changed by a mapping function, shown in
Equation 5. This function changes the width of the intensity values, to match their respective heights.
This results in the values being centred on a straight line (Figure 39d).
newIllumVa lue
� PDiFpixels
� IllumRange �
�
�
� Number
�IllumValue�� �
�
Values
Equation 5: Intensity value redistribution function
newIllumVa lue � New intensity value of all pixels that have the old value
IllumRange � Size of the complete range of intensity values
PDiFpixels �IllumValue��see Equation 4
IllumValue � Old intensity Value of a pixel
Number � Number of different intensity values
Values
In the resulting intensity distribution, shown in Figure 39e, the intensity values are spaced evenly
throughout the image. As can be seen from the result, due to the missing information behind the
decimal point some previously separated values are compressed in a single value. This loss of
information is not important to the normal observer, who is not trained to distinguish 65536 different
greyscale values. In this project the reflection image was only used for depicting the information to the
user.
The visual improvement of the resulting image can be observed in Figure 40, which shows a sample
office environment with different materials present, including metallic objects with high reflectivity
and dully lacquered materials with low reflectivity.
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