The studies on Fourier Analysis of images is being continued. For the following studies in this field – and other tasks relying on matrix math – I switched to using the Parallel colt library by Piotr Wendykrier.

The following series shows part of an image taken from an online photo stock with the typical watermark across it. The second image shows the fast fourier transform of it. The grayscale is logarithmic in order to show more details. From the center [0,0] towards the bottom right corner, there is a bright area representing the main wavelengths and phase angles. This area is masked (frequency filter) with the orange area. The third image then shows the inverse fourier transform of only the masked part and the fourth image of all but the masked part. With this procedure, the main image features (sand dune pattern) can be separated from the watermark.

dunes

[1] original image / [2] fft with the main features masked in orange / [3] inverse fourier transform of only the masked part in 3 / [4] inverse fourier transform of the rest, unmasked part of 3

The same was then made on a more architectural input, the floorplan of Villa Savoye by LeCorbusier.

savoye

fft of floorplan of villa savoye. 0/90 phase angles masked out to separate orthogonal from other features

In the second image, a quick mask was sketched on the 0 and 90 degree phases. The third and fourth image then show the orthogonal features on the one hand and all the others like hemicircular staircases and furniture on the other hand.