Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these weights suitably has been a painstaking, empirical process. Even if such ideal weights are found for a novel image, most current approaches fix the weight across the whole image domain, ignoring the spatially-varying properties of object shape and image appearance. We propose a novel technique that autonomously balances these terms in a spatially-adaptive manner through the incorporation of image reliability in a graph-based segmentation framework. We validate on synthetic data achieving a reduction in mean error of 47% (p-value << 0.05) when compared to the best fixed parameter segmentation. We also present results on medical images (including segmentations of the corpus callosum and brain tissue in MRI data) and on natural images.