A Gaussian blur approximation is applied to an image by repeated down-sampling operations followed by an up-sample operation. By using a truncated Gaussian filter as the down-sample filter, the frequency spectrum removed during down-sampling operations closely approximates the frequency spectrum lost during a true Gaussian blur operation. While any "good" up-sample filter may be used, up-sampling via linear interpolation may be especially beneficial in systems having a dedicated graphics processing unit. One benefit of the described technique is that it is computationally less costly to implement than a Gaussian blur. Another benefit is that this computational benefit increases as the size of the blur increases--becoming significant even for small blurs. Yet another benefit of the invention is that a judicious selection of pixel address to convolve with the filter leads to substantially reduced number of texture lookups required to effect a convolution.