In this paper, we present a general guideline to establish the relation of noise distribution model and its corresponding error metric. By designing error metrics, we obtain a much richer set of distance measures besides the conventional Euclidean distance or SSD (sum of the squared difference) and the Manhattan distance or SAD (sum of the absolute difference). The corresponding nonlinear estimations such as harmonic mean, geometric mean, as well as their generalized nonlinear operations are derived. It not only offers more flexibility than the conventional metrics but also discloses the coherent relation between the noise model and its corresponding error metric. We experiment with different error metrics for similarity noise estimation and compute the accuracy of different methods in three kinds of applications: content-based image retrieval from a large database, stereo matching, and motion tracking in video sequences. In all the experiments, robust results are obtained for noise estimation based on the proposed error metric analysis.