I check the effects of adjustable parameters k0, na and on roughened images. The quantitative analysis of the effects on the filter spectrum is provided in appendix A.
When comparing the effects of k0 and na, I set to make sure the filters have the same zero-frequency response. Figure 3 shows the Bay Area map created with different k0. As k0 increases, more low-frequency components were removed and the detailed structure turns out to be the main focus of the map. This indicates the cut-off frequency increases as k0 increases. In other words, k0 governs the cut-off frequency. When k0 remains the same, filters with different na can create very similar results if the zero-frequency response is the same by adjusting , as shown in the middle and bottom plots in Figure 4. As expected, controls the zero-frequency response. The larger leads to higher contrast, as shown in the top and middle plots in Figure 4.
Among the three adjustable parameters, na is the least important one because the long filter can be replaced with a short one by adjusting .k0 controls the cut-off frequency and controls the zero-frequency response. It is hard to tell which one is more important if I use only this information. From the quantitative analysis, I know k0 affects zero-frequency response significantly, but does not have such an influence on cut-off frequency. So k0 is the most important parameter.
For the enhanced helix low-cut filter, it is very reasonable to choose parameter k0 first, then and na.
When roughening the image with the helix low-cut filter, the key point is to choose the cut-off frequency f0 or the adjustable parameter k0. My suggestion is that if the lowest frequency component to be preserved is fL, k0 should be
Since the short filter is made equivalent to the long filter by adjusting , I suggest the use of based on the balance of computation costs and symmetric features.
With k0 and na determined, I can find according to Equation (13)
Figure 5 consists of three maps of the Bay Area. The top portion is a topographic map of the Bay Area. The bottom plot is the preferred result. From one slice of the Bay Area topographic map, I know one main low frequency component is about 0.4. So I chose k0 = 0.3 to remove the lower frequency. I chose na = 16. In order to obtain the highest contrast, I chose . The middle one is the reference plot with k0 = 0.1, na =16 and . I notice that the bottom plot removes more low frequency components than the middle one and has clearer details, as predicted by the theory.
Figure 6 consists of a normal mammogram and the roughened images. The main low frequency component of the mammogram slice is about 0.3, so I choose k0 = 0.2 in the right plot as the preferred result, and use k0 = 0.1 in the middle as reference. I use to achieve the highest contrast.