Fig. 1. Cross-scale data obtained by different measurement configures

Fig. 2. Multilevel wavelet transform space

Fig. 3. Process of two-dimensional discrete wavelet transform

Fig. 4. Flowchart of ICP algorithm

Fig. 5. Surface texture of cutting tool

Fig. 6. Three-dimensional topographical data at different magnifications. (a) 20×; (b) 50×; (c) 100×

Fig. 7. (a) Raw data; three-dimensional data after DWT at (b) level 3 and (c) level 5

Fig. 8. Two-dimensional contour of different levels at the same position of DWT data. (a) Level 0; (b) level 1; (c) level 2; (d) level 3; (e) level 4; (f) level 5

Fig. 9. Logarithmic graph of (a) raw data at magnification of 100× and data after DWT at (b) level 3 and (c) level 5

Fig. 10. Logarithmic graph of raw data at different magnifications. (a) 20×; (b) 50×; (c) 100×

Fig. 11. (a) Registration results of scale-approximated data of level 3 wavelet approximation of 100× small scale data and 20× data; (b) apply the transform matrix on raw data; (c)(d) corresponding local magnification diagram

Fig. 12. (a) Two-dimensional contour of registration result of scale-approximated data; (b) two-dimensional contour of raw data after applying transform matrix