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This article presents improvements to the efficient approximation of Gaussian filters by sequentially applying uniform box filters. For 1-D filters, a simple and nearly optimal fit criterion for the length S of the box filters to the approximated Gaussian is given. For 2-D filters, a new method is introduced to improve the circular symmetry and the lowpass properties of the approximation without increasing the computational complexity. Finally, a multirate implementation for large Gaussian filters is presented that requires significantly fewer floating-point operations than the standard technique