3.2. Douglas-Peucker algorithm

In the first step, the aim is to compress data by using the Douglas-Peucker method to calculate the data-reduction rate (DR). We use the following equation:

$$\mathbf{D}\_{\rm R} = \frac{(\mathbf{P}\_{\rm O} - \mathbf{P}\_{\rm R})}{\mathbf{P}\_{\rm O}} \tag{6}$$

where PO is the number of the original data points and PR is the number of the reduced data points.

Table 2 summarizes the results obtained by the Douglas-Peucker algorithm. The simplification tolerance is given in line "ε." We also show the simplification rate in % for each value of ε.

The results in Table 2 show that the rate of simplification exceeds 71% and can reach up to 95%. This simplification rate increases proportionally with the tolerance value "ε." For example, for tolerance values between 0.5 and 2, the simplification rate for the image "02\_h.tif" is between 72 and 95%. For the same values of ε and for the image "im0139.vk.jpg," the rate of simplification is between 71.43 and 93.35%. It could be noted that the first image simplification rate is slightly higher than that of the second image. This is due to the complexity of their geometry of the blood vessel curves.

Figure 10 shows a result of control point test for a tolerance ε = 0.5. This figure shows clearly that the number of original points (blue points) is larger than the number of control points (red points).


#### Table 2.

Simplification rate for different tolerance values ε.

Figure 10. Determination of the control points (blue point, 3D original model; red point, control points).
