Figure 8.

Effect of Sobel filtering on the accuracy of angle measurements when using the Radon transform. (A) Radon transforms on a simulated image of 45° orderly streaks after subtracting the mean luminance from the image. Resulting angle of 44.88° (dashed green lines) represents a 0.12° deviation from the actual angle. (B) Vertical demeaning leads to the same angle measurement as shown in (A). The orderly vertical bands (highlighted by white arrows) are the result of different mean luminance across columns of the original image. (C) Vertical Sobel filtering of the image shown in (A) gives 44.98° (dashed black lines) on the Radon transform, an error of 0.02°. Thirteen iterations of the Radon transforms (52 Radon transforms) resulted in an angle step-size of ~0.002° (see Equation 19). (D) Sobel filtered images offer more accurate angle measurements when compared with vertically demeaned images. Mean ± SD of absolute difference in measured angles on simulated images are shown. Each angle value consists of results from n = 36 images with streaks at different spatial locations. Statistically significant differences are represented by a red asterisk for a given angle (p < 0.05, two-sample t-test).