Illustration of the convolution algorithm. To smooth a specific ring of the input map (upper left), we first interpolate the kernel on the grid, centered on this particular ring (upper right). After a ringwise Fourier transformation of both map and kernel, we multiply the two components (lower left, transformed to pixel space for illustrative purposes). Finally, we perform the summation alongside the longitudinal direction and write the inverse Fourier transformed result to the output (lower right image).
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