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The paper argues for the use of quadrature filters for local structure tensor and motion estimation. The question of which properties of a local motion estimator are important is discussed. Answers are provided via the introduction of a number of fundamental invariances that are required in object motion estimation. A combination of statistical and deterministic modeling leads to mathematical formulations corresponding to the required invariances. The discussion leads up to the introduction of a new class of filter sets loglets. A number of experiments support the claim that loglets are preferable to other designs. In particular it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness to variations in object illumination.