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Logarithmic transformations

Having discussed linear transformations in the last section, we step into logarithmic transforms now. You will notice that they are mathematically more involved than their linear counterparts. Again, we'll be discussing two different types of enhancement techniques under logarithmic transforms:

• The log transform
• The exponential (or inverse log) transformation

Log transformation

Simply put, the log transform takes the (scaled) logarithm of every input pixel intensity value. Let's put it down in terms of a mathematical equation:

First, note that the input intensity values have all been incremented by 1 (r+1). This is because ...

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