An analysis of single image defogging methods using a color ellipsoid framework

The goal of this article is to explain how several single image defogging methods work using a color ellipsoid framework. The foundation of the framework is the atmospheric dichromatic model which is analogous to the reflectance dichromatic model. A key step in single image defogging is the ability to estimate relative depth. Therefore, properties of the color ellipsoids are tied to depth cues within an image. This framework is then extended using a Gaussian mixture model to account for multiple mixtures which gives intuition in more complex observation windows, such as observations at depth discontinuities which is a common problem in single image defogging. A few single image defogging methods are analyzed within this framework and surprisingly tied together with a common approach in using a dark prior. A new single image defogging method based on the color ellipsoid framework is introduced and compared to existing methods.