In this paper, the well-known SIFT detector is extended with a bivariate feature localization. This is done by using function models that assume a Gaussian feature shape for the detected features. As function models we propose (a) a bivariate Gaussian and (b) a Difference of Gaussians. The proposed detector has all properties of SIFT, but provides invariance to affine transformations and blurring. It shows superior performance for strong viewpoint changes compared to the original SIFT. Compared to the most accurate affine invariant detectors, it provides competitive results for the standard test scenarios while performing superior in case of motion blur in video sequences.