In this paper, we investigate image segmentation by region merging. Given any similarity measure between regions , satisfying some weak constraints, we give a general predicate for answering if two regions are to be merged or not during the segmentation process. Our predicate is generic and has six properties. The first one is its inde-pendance with respect to the similarity measure, that leads to a user-independant and adaptative predicate. Second, it is non-parametric, and does not rely on any assumption concerning the image. Third, due to its weak constraints, knowledge may be included in the predicate to fit better to the user's behaviour. Fourth, provided the similarity is well-chosen by the user, we are able to upperbound one type of error made during the image segmentation. Fifth, it does not rely on a particular segmentation algorithm and can be used with almost all region-merging algorithms in various application domains. Sixth, it is calculated quickly, and can lead with appropriated algorithms to very efficient segmentation.