First I apply the enhanced helix derivative filter to some familiar images and check the effects of adjustable parameters na and .
Figure 1 shows the views of the Sea of Galilee created by helix derivative filters with different na and .The top two plots (with ) indicate that as the half filter length na increases, the contrast of the image increases. This means the longer filter keeps less low frequency components, indicating a lower zero-frequency response. The vertical plots (with same na) indicate that as increases, the contrast increases also, as expected from the definition of the enhanced helix filter equation.
To compare the properties of the filters with different na other than the zero-frequency response, I set in the bottom two plots, so that they have the same zero-frequency response. The plots are very similar, and the difference between them is very weak.
As the examples above show, the zero-frequency response of the enhanced helix derivative filter decreases as na or increases. Thus filters with different na may create the same results by adjusting , which provides the possibility of using a short filter instead of a long filter in image processing and reduce the computational cost greatly. By adjusting , the enhanced short filter can reach a low level of zero-frequency response, which is done conventionally by using a long filter.
Since the short filter is equivalent to the long filter when adjusting , now plays the key role in image processing for the enhanced helix derivative filter, and na is not an important parameter. When the high frequency component is too weak compared with the low frequency, a large should be chosen in order resolve details in the image. Otherwise, a small would be suitable. Based on the balance of the computation cost and response symmetry, I recommend the use of .
From the quantitative analysis of spectra of the enhanced helix derivative filter (see the appendix A), I can find according to empirical formula
For the view of the Sea of Galilee, the high frequency component is very weak, so I chose I0=0.002, na=8, and . Figure 2 shows the preferred and gradient roughened results.