This paper presents an efficient approximate inference algorithm for fully connected conditional random fields (CRFs) with Gaussian edge potentials, which are defined over the complete set of pixels in an image. Traditional CRFs, especially pixel-level models, suffer from high computational complexity due to their dense pairwise connectivity. The proposed algorithm leverages a mean field approximation to reduce the complexity of message passing from quadratic to linear in the number of variables, making it feasible to process images with billions of edges. The pairwise edge potentials are defined using a linear combination of Gaussian kernels, allowing for dense pixel-level connectivity. Experiments on the MSRC-21 and PASCAL VOC 2010 datasets demonstrate that this approach significantly improves segmentation and labeling accuracy compared to existing methods. The algorithm is highly efficient, with a single-threaded implementation processing benchmark images in just 0.2 seconds.This paper presents an efficient approximate inference algorithm for fully connected conditional random fields (CRFs) with Gaussian edge potentials, which are defined over the complete set of pixels in an image. Traditional CRFs, especially pixel-level models, suffer from high computational complexity due to their dense pairwise connectivity. The proposed algorithm leverages a mean field approximation to reduce the complexity of message passing from quadratic to linear in the number of variables, making it feasible to process images with billions of edges. The pairwise edge potentials are defined using a linear combination of Gaussian kernels, allowing for dense pixel-level connectivity. Experiments on the MSRC-21 and PASCAL VOC 2010 datasets demonstrate that this approach significantly improves segmentation and labeling accuracy compared to existing methods. The algorithm is highly efficient, with a single-threaded implementation processing benchmark images in just 0.2 seconds.