More on the Fourier Transforms

Canvas Weave Removal

Lastly, Fourier Filtering can be useful in removing regular and periodic patterns in an image. An example of this is the thread used in canvas. The image below shows a zoomed in painting , wherein the canvas thread/bumps is prominent.

Zoomed-in painting showing the canvas threads/bumps, which shall be attempted to be removed through filtering.

Taking the Fourier Transform of the gray-scaled painting results in the image below. Note the bright spots in a diamond-like pattern. Filtering these spots results in the corrected image below. Notice that the regular bumps due to the canvas thread has been removed, resulting in a smooth painting.

Fourier Transform of the gray-scaled painting, shown in log-scale to emphasize the finer detail. Note the bright spots in a roughly diamond shape about the center.

Fourier Transform with the bright dots removed.

Corrected image after removing the bright spots

For the sake of confidence, we display the inverse Fourier transform of the “canvas” (i.e., the portion originally filtered out), just to see if it does resemble the canvas in the original image.

The inverse Fourier transform of the originally filtered portion. Luckily, it resembles the canvas weave in the original painting.

The inverse Fourier transform appear as regularly spaced dots/bumps, which correspond to the canvas weave in the original painting, thus boosting confidence in the efficiency of the technique.