Fig. 1. Translation and rotation characteristics of 2D Fourier transformation. (a) f1; (b) f2; (c) M1; (d) M2

Fig. 2. Fan-shaped area used to evaluate relationship between energy and angle in magnitude spectrum

Fig. 3. Schematic of polar transformation. (a) Cartesian coordinate; (b) polar coordinate

Fig. 4. Ring-shaped area used for polar transformation

Fig. 5. Polar transformation of magnitude spectra shown in Fig. 1. (a) M1; (b) M2

Fig. 6. Energy as a function of angle

Fig. 7. Schematic of directional projection

Fig. 8. Projection curves along normal direction of images shown in Fig.1. (a) f1; (b) f2

Fig. 9. Experimental detecting results of local bending of laser stripe images. (a) (b) laser stripe images recorded in experiment; (c) (d) h(?) obtained after Fourier-polar transformation; (e) (f) projection curves of laser stripe images along normal direction

Fig. 10. Experimental results of laser stripe images with local contamination and Gaussian noises. (a) Laser stripe image; (b) Fourier-polar transformation result and h(?); (c) projection curve of laser stripe image along normal direction

Fig. 11. Extracting result of center-line in Fig. 10(a) by gray level gravity algorithm