**4.1 Quality assessment**

The best method to assess output of polygonal approximation is visual perception. Thus, we include extensive qualitative results. Moreover, we include quantitative performance measures as well for comparison of the performance of the tested methods, including the proposed technique. This chapter considers the following metrics to measure the goodness of the results: (i) compression ratio (CR), (ii) integral square error (ISE), (iii) figure of merit (FOM), (iv) weighted sum of square errors (WE), (v) modified version of WE (WE2). Details of these metrics are provided in **Table 1**. These metrics are taken from [9–11, 15, 19, 33, 36]. The readers interested in them are encouraged to read these articles and the references therein.

### **4.2 Experimental set 1**

The quantitative performance measure for the synthetic curves chromosome, leaf, semicircle and infinity in experiment set 1 is given in **Table 2**. The visual shots are shown in **Figures 4–6**. The methods in [16–19, 34, 36, 37] present optimal solutions for the polygonal approximation. The proposed method output is close to optimal solution for all the curves and further supports reduction of the number of dominant points while retaining the shape information of the curve. **Table 2** summarizes the results from various articles [9, 11, 15–19, 23, 24, 26, 31–38] for the given input synthetic curves. For the chromosome curve display using 15 amount of dominant points, the proposed technique produces a low value for ISE than the method in [32–34]. The snapshot of chromosome curve at 6 number of points using the proposed method as well as by the methods [9, 23, 24] snapshots can be found in **Figure 4**. For the leaf curve, where the output curve at 21 number of dominant points, the proposed method produces the low value for ISE than [11, 24, 34] (in turn FOM value is high, which is appreciable) and high value than [19]. The snapshot for leaf output curve produced by the proposed method along with some of the state-of-the-art methods results is displayed in **Figure 5**. The final synthetic curve for this experiment set is a curve that intersects itself, that is, infinity-shaped curve. In the attempt of producing the output curve using 10 number of points, the proposed produce the minimal possible error than [11, 26]. And also the summarized results reveal that the proposed method output is better than [9, 11, 19, 24, 26, 33] in terms of ISE, WE and FOM. The graphic shots for the same can be found in **Figure 6**. According to human visual perception, four points are sufficient


#### **Table 1.**

*Quality assessment metrics for comparing polygonal approximation methods.*


*Polygonal Approximation of Digital Planar Curve Using Novel Significant Measure DOI: http://dx.doi.org/10.5772/intechopen.92145*


**Table 2.**

*Comparative results of synthetic contour (chromosome, leaf, semicircle, infinity).*

enough to represent the infinity curve; please see **Figure 6(g)**. On the outset, it is perceived that the proposed technique gives the best or second best ISE values for all the cases. This indicates competitiveness of the proposed technique.
