In image segmentation and in general in image processing, noise and outliers distort contained information posing in this way a great challenge for accurate image segmentation results. To ensure a correct image segmentation in presence of noise and outliers, it is necessary to identify the outliers and isolate them during a denoising pre-processing or impose suitable constraints into a segmentation framework. In this paper, we impose suitable removing outliers constraints supported by a well-designed theory in a variational framework for accurate image segmentation. We investigate a novel approach based on the power mean function equipped with a well established theoretical base. The power mean function has the capability to distinguishes between true image pixels and outliers and, therefore, is robust against outliers. To deploy the novel image data term and to guaranteed unique segmentation results, a fuzzy-membership function is employed in the proposed energy functional. Based on qualitative and quantitative extensive analysis on various standard data sets, it has been observed that the proposed model works well in images having multi-objects with high noise and in images with intensity inhomogeneity in contrast with the latest and state of the art models.