High-Boost Filtering and High-Frequency Emphasis Filtering:
All the filtered images have one thing in common: Their average background intensity has been reduced to near black. This is due to the fact that the highpass filters we applied to those images eliminate the zero-frequency component of their Fourier transforms. In fact, enhancement using the Laplacian does precisely this, by adding back the entire image to the filtered result. Sometimes it is advantageous to increase the contribution made by the original image to the overall filtered result. This approach, called high-boost filtering, is a generalization of unsharp masking. Unsharp masking consists simply of generating a sharp image by subtracting from an image a blurred version of itself. Using frequency domain terminology, this means obtaining a highpass-filtered image by subtracting from the image a lowpass-filtered version of itself. That is
High-boost filtering generalizes this by multiplying f (x, y) by a constant A > 1:
Thus, high-boost filtering gives us the flexibility to increase the contribution made by the image to the overall enhanced result. This equation may be written as
Then, using above Eq. we obtain
This result is based on a highpass rather than a lowpass image. When A = 1, high-boost filtering reduces to regular highpass filtering. As A increases past 1, the contribution made by the image itself becomes more dominant.
We have Fhp (u,v) = F (u,v) – Flp (u,v). But Flp (u,v) = Hlp (u,v)F(u,v), where Hlp is the transfer function of a lowpass filter. Therefore, unsharp masking can be implemented directly in the frequency domain by using the composite filter
Similarly, high-boost filtering can be implemented with the composite filter
with A > 1. The process consists of multiplying this filter by the (centered) transform of the input image and then taking the inverse transform of the product. Multiplication of the real part of this result by (-l) x+y gives us the high-boost filtered image fhb (x, y) in the spatial domain.