Optimized float Blur variations

Question

I am looking for optimized functions in c++ for calculating areal averages of floats. the function is passed a source float array, a destination float array (same size as source

Answer 1

What you are trying to implement are various sorts of digital filters for image processing. This is equivalent to convolving two signals where the 2nd one would be the filter's impulse response. So far, you regognized that a "rectangular average" is separable. By separable I mean, you can split the filter into two parts. One that operates along the X axis and one that operates along the Y axis -- in each case a 1D filter. This is nice and can save you lots of cycles. But not every filter is separable. Averaging along other shapres (S, O, +, X) is not separable. You need to actually compute a 2D convolution for these.

As for performance, you can speed up your 1D averages by properly implementing a "moving average". A proper "moving average" implementation only requires a fixed amount of little work per pixel regardless of the averaging "window". This can be done by recognizing that neighbouring pixels of the target image are computed by an average of almost the same pixels. You can reuse these sums for the neighbouring target pixel by adding one new pixel intensity and subtracting an older one (for the 1D case).

In case of arbitrary non-separable filters your best bet performance-wise is "fast convolution" which is FFT-based. Checkout www.dspguide.com. If I recall correctly, there is even a chapter on how to properly do "fast convolution" using the FFT algorithm. Although, they explain it for 1-dimensional signals, it also applies to 2-dimensional signals. For images you have to perform 2D-FFT/iFFT transforms.