Conclusions

The enhanced derivative and low-cut filters with adjustable parameters improve our ability to roughen an image for details. The introduction of adjustable parameter $\rho$ makes it possible to gain computational savings by using a short filter instead of a long one.

For the enhanced helix derivative filter, the filter length determines its spectral symmetry and controls the zero-frequency response with $\rho$. For the low-cut filter, the cut-off frequency is mainly determined by k₀, and the zero-frequency response is affected by all three parameters. n_a is an unimportant parameter for helix filters.

The enhanced helix derivative filter emphasizes the small-scale structures in the image, while the low-cut filter emphasizes the medium-scale structures and costs more than derivative filter.

Based on our analysis of the effects of the parameters on the roughened image and filter spectrum, I present guidelines for choosing the adjustable parameters for image processing application.