Table 1.
Classification of subjects with arch high ratio.
Fig 1.
Overall scheme of the texture analysis of lateral foot bone.
The x-ray radiographs were leveled, and then regions of interest were set up with the upper surface of the talus pulley as the upper edge, the bottom from the calcaneus base to the metatarsal head base, and the right and left edges to the calcaneal prominence and metatarsal head. The 2D-FFT and Inv-FFT [see Refs. 22 and 23] in these regions of interest were processed using ImageJ2 image processing software (Ver. 2.9.0/1.53t, National Institutes of Health, Washington, D.C., USA, https://imagej.nih.gov/ij/).
Fig 2.
The texture analysis of lateral foot bone.
The analysis process for a normal arch foot (a-c), a low arch foot (d-f), and a high arch foot (g-i) in each example is shown below. The original x-ray radiographs (a, d, and g) were leveled. Then ROIs were set up with the upper surface of the talus pulley as the upper edge, the bottom from the calcaneus base to the metatarsal head base, and the right and left edges to the calcaneal prominence and metatarsal head (b, e, and h). The 2D-FFTs in these ROIs were processed using ImageJ2 (c, f, and i). Roman numerals I, II, III, and IV indicate the respective quadrants.
Fig 3.
Angular measurement of the power spectrum of the normal arch group, low arch group, and high arch group.
(a and b) Normal arches, (c and d) low arches, and (e and f) high arches. All insets of a, c, and e were high-power views of the first quadrant. All power spectrum images obtained from 38 cases in the normal arch group (a), 11 cases in the low arch group (c), and 11 cases in the high arch group (e) were superimposed within each group to obtain an average power spectrum image. The angles (θ) in the low-frequency region for the high-intensity regions seen in this power spectrum were 68.73° (b) in the normal arch group, 70.43° and (d) in the low arch group, and 64.53° (f) in the high arch group. (u = ±256, v = ±256).
Fig 4.
Inv-FFT images of the high-frequency and low-frequency regions.
The images were reproduced using a high-pass or low-pass filter on a No.36 subject with a normal arch. (a) A whole 2D-FFT image of the subject. Inset, high-power views of the first quadrant with θ = 69.79° of power spectrum angle. (b) Inv-FFT image obtained from (a). (c) A high pass filter (arrow) and (d) Inv-FFT image from (c). (e) A low pass filter and (f) Inv-FFT image from (e). The unfiltered area is indicated by an arrowhead. (g) Inv-FFT image in the low-frequency domain superimposed with the original x-ray radiographic image. The inv-FFT image in the low-frequency domain was overlaid on the original image as a binarized image with adjusted threshold, and was found to be consistent with the metatarsal with a tilt angle of 20.07°.
Table 2.
Comparison of arch height ratios, lateral metatarsal tilt angles and orthogonal angles of power spectral populations derived from 2D-FFT.