Optimized algorithm for Gaussian second order derivative filters in fast Hessian detector

When, constructing the scale space of fast Hessian detector in SURF, using integral image and box filters to approximate the Gaussian second order derivative filters is the most pivotal step. The common algorithm for this is firstly calculating the pixels´ sums in each sub-rectangle region of a mask, then multiplying the coefficients and adding them together. This way may cause some repeatable calculations, so the fast Hessian detector´s speed is influenced. In order to make the filter process much faster, an optimized algorithm for Gaussian second order derivative filters was proposed. Firstly, the multiplication operators was all replaced by additions. Then, use variants instead of repeatable steps. At last, complexity of the whole convolution process was decreased. Verified by the experimental results, fast Hessian detector based on the optimized filter algorithm was much faster than that on the common method.