Color image segmentation is an important topic in the image processing field. MRF-MAP is often adopted in the unsupervised segmentation methods, but their performance are far behind recent interactive segmentation tools supervised by user inputs. Furthermore, the existing related unsupervised methods also suffer from the low efficiency, and high risk of being tra pped in the local optima, because MRF-MAP is currently solved by iterative frameworks with inaccurate initial color distribution models. To address these problems, the letter designs an efficient method to cal culate the energy functions approximately in the non-iteration style, and proposes a new binary segmentation algorithm based on the slightly tuned Lanczos eigensolver. The experiments demonstrate that the new algorithm achieves competitive performance compared with two state-of-art segmentation methods.