In many applications of imaging, we would like to know whether we have an image of a single-component object or an image of an object that consists of several components. Many algorithms have been designed to solve this problem; however, these algorithms are all heuristic. Often, according to some reasonable methods, we have a single component, while according to some other equally reasonable methods, the same image have multiple components. It is desirable to produce reliable methods, so that if a method claims that there are multiple components, then it should mean that the observed data is incompatible with the assumption that there is only one component. At present, there exist reliable methods for separating components in a (interval-valued) 1D source. In this paper, we develop an efficient algorithm for separating components in a general (interval-valued) 2D source.