The morphing for continuous generalization of linear features based on Dynamic Time Warping distance

Figures & data

Figure 1. Flow chart of matching two linear features in different scales by DTW algorithm.

Figure 2. The simulated data with different levels of detail. (a) Large-scale representation. (b) Small-scale representation. (c) Overlapping representation.

Figure 3. The corresponding relationship of vertices between line a and line b.

Figure 4. The morphing effect of DTW distance-based morphing method.

Table 1. Similarity distance of shapes between intermediate scales and initial scales by the proposed method for simulated data.

T	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
$S_1$	0	0.027	0.050	0.071	0.091	0.11	0.13	0.15	0.17	0.19	0.16
${ S}_2$	0.16	0.21	0.19	0.17	0.14	0.12	0.10	0.081	0.054	0.027	0

Figure 5. Overlaps of the morphing results through the (a). linear interpolation method; (b). Fourier transformation-based morphing method and (c). proposed DTW distance-based morphing method; (d)-(f). close-up of region G.

Figure 6. Similarity distance of shapes between intermediate scales and initial scales by linear interpolation method, Fourier transformation-based morphing method, and DTW distance-based morphing method.

Figure 7. Continuous generalization of river networks by DTW distance-based morphing method.

Figure 8. Continuous generalization of contour lines by DTW distance-based morphing method.

Table 2. Similarity distance of shapes between intermediate scales and initial scales for rivers and contours.

T		0	0.2	0.4	0.6	0.8	1
1/$Rs$		10000	18000	26000	34000	42000	50000
Rivers	$S_1$	0	29.038	55.659	82.106	107.962	116.332
	${ S}_2$	116.332	109.179	83.854	59.481	34.58	0
Contours	$S_1$	0	2.725	4.723	6.859	9.191	9.861
	${ S}_2$	9.861	8.982	6.746	4.497	2.355	0

Code availability

The python code for the DTW algorithm to measure the similarity distance of linear features is available at the link: https://github.com/mao2023/mao_paper