This paper addresses an image labeling problem, in which it is assumed that there are multiple sensors available at each pixel with some of them possibly inactive. In addition to not being known which sensors are active or inactive, the sensor measurements are also obtained in random unknown order. Given these incomplete observations, we wish to identify which sensors are active at each site and which observations were produced by each sensor. This labeling problem extends classic image segmentation, since it allows multiple labels (i.e., region overlapping). The paper provides methods to solve this problem in two scenarios: known and unknown sensor models. A new minimization algorithm, inspired by hierarchical clustering, is introduced to minimize the energy function resulting from the proposed inference criterion.