Fig 2. Effect of spatial domain image filters on the power spectrum.

Images in the spatial domain are shown in greyscale (A-C), whereas the respective power spectra are shown in false colors as well as in logarithmic scale for a better visibility (D-H). Power spectrum values are shifted, such that low frequencies are located in the center. (A) shows the original image boat [46]. (B) shows the periodic component of the periodic plus smooth decomposition of Moisan et. al [45]. Apart from small areas near the image boundary, the entire image information of the original image is conserved. However, as shown in (C), the Hamming window reduces the image information gradually towards the image boundary. (D), the discrete Fourier transform of images causes cross-like artifacts (black arrows) to appear in the power spectrum as the image is assumed to be periodical. (E-F), these artifacts disappear in the power spectra if firstly either the periodic decomposition or the Hamming window are applied. Note that the artifacts reappear in (G) and (H) where the absolute difference of the power spectra of the filtered images with respect to the power spectrum of the original image are shown. (G) also reveals that mostly non-directional information is removed from the power spectrum of the original image as only cross-like shapes are pronounced. Other than in (F), where the reduction of image information by the Hamming window also affects the power spectrum, which appears less sharp (white arrows) compared to (D) and (E).