The logarithmic image processing model (LIP) is a robust mathematical framework, which, among other benefits, behaves invariantly to illumination changes. This paper presents, for the first time, two general formulations of the 2-D convolution of separable kernels under the LIP paradigm. Although both formulations are mathematically equivalent, one of them has been designed avoiding the operations which are computationally expensive in current computers. Therefore, this fast LIP convolution method allows to obtain significant speedups and is more adequate for real-time processing. In order to support these statements, some experimental results are shown in Section V.