Interactive image segmentation traditionally involves the use of algorithms such as graph cuts or random walker. Common concerns with using graph cuts are metrication artifacts (blockiness) and the shrinking bias (bias towards shorter boundaries). The random walker avoids these problems, but suffers from the proximity bias (sensitivity to location of pixels labeled by the user). In this work, we introduce a new family of segmentation algorithms that includes graph cuts and random walker as special cases. We explore image segmentation using continuous-valued Markov random fields (MRFs) with probability distributions following the p-norm of the difference between configurations of neighboring sites. For p=1 these MRFs may be interpreted as the standard binary MRF used by graph cuts, while for p=2 these MRFs may be viewed as Gaussian MRFs employed by the random walker algorithm. By allowing the probability distribution for neighboring sites to take any arbitrary p-norm (p ges 1), we pave the path for hybrid extensions of these algorithms. Experiments show that the use of a fractional p (1 < p < 2) can be used to resolve the aforementioned drawbacks of these algorithms.