A method of performing anisotropic texture filtering includes generating one or more parameters describing an elliptical footprint in texture space; performing isotropic filtering at each sampling point of a set of sampling points in an ellipse to be sampled to produce a plurality of isotropic filter results, the ellipse to be sampled based on the elliptical footprint; selecting, based on one or more parameters of the set of sampling points and one or more parameters of the ellipse to be sampled, weights of an anisotropic filter that minimize a cost function that penalises high frequencies in the filter response of the anisotropic filter under a constraint that the variance of the anisotropic filter is related to an anisotropic ratio squared, the anisotropic ratio being the ratio of a major radius of the ellipse to be sampled and a minor axis of the ellipse to be sampled; and combining the plurality of isotropic filter results using the selected weights of the anisotropic filter to generate at least a portion of a filter result.