This paper introduces a new model for logarithmic image processing, called Symmetric Logarithmic Image Processing (SLIP), that provides an algebraic framework for the processing of transmitted light images and intensity images. The SLIP model is inspired by the previously developed Logarithmic Image processing (LIP) model and has been built to exhibit a symmetric structure that allows to deal with negative values during logarithmic processing. Structured with a combination law and an amplification law, the SLIP model defines a vector space structure on a symmetric bounded set instead of the positive cone structure that was characteristic of the LIP model. Furthermore, in the continuation of the LIP model, the SLIP model is physically consistent with transmitted light formation and human vision's brightness perception laws, but also allows to unify the two physical entities. This article introduces mathematical notions and operations defining the SLIP model, then explains why it is physically and psychophysically well justified, and finally the SLIP model specificity is illustrated with a real application example.