The volume of video and other image data is expanding at a rapid pace with the increasing use of surveillance systems, unmanned vehicles, and other collection systems. The sheer volume of images requires the use of automatic systems to select interesting image features for further analysis. These systems should have a low false alarm rate, e.g. satisfying a pre-determined constant false alarm rate (CFAR). Various filters may be applied to filter out non- target (background) parts of an image. The output of these filters is noise, plus possible target features. When the noise is Gaussian, CFAR thresholds may be based on t- distributions, with reduced degrees of freedom in the case of correlated noise. For the non-Gaussian case, the use of t distributions is inappropriate, and we suggest alternatives based on parametric families of distributions, with location, scale, and shape parameters. When shape parameters are known the thresholds can be determined using a Monte Carlo technique, using variance reduction techniques to improve the computational efficiency by a factor of 1800. We discuss methods for handling unknown shape parameters.