In many computer vision algorithms, the well known Euclidean or SSD (sum of the squared differences) metric is prevalent and justified from a maximum likelihood perspective when the additive noise is Gaussian. However, Gaussian noise distribution assumption is often invalid. Previous research has found that other metrics such as double exponential metric or Cauchy metric provide better results, in accordance with the maximum likelihood approach. In this paper, we examine different error metrics and provide a theoretical approach to derive a rich set of nonlinear estimations. Our results on image databases show more robust results are obtained for noise estimation based on the proposed error metric analysis.