Visual attention can be deployed to stimuli based on our willful, top-down goal (endogenous attention) or on their intrinsic saliency against the background (exogenous attention). Flexibility is thought to be a hallmark of endogenous attention, whereas decades of research show that exogenous attention is attracted to the retinotopic locations of the salient stimuli. However, to the extent that salient stimuli in the natural environment usually form specific spatial relations with the surrounding context and are dynamic, exogenous attention, to be adaptive, should embrace these structural regularities. Here we test a non-retinotopic, object-centered mechanism in exogenous attention, in which exogenous attention is dynamically attracted to a relative, object-centered location. Using a moving frame configuration, we presented two frames in succession, forming either apparent translational motion or in mirror reflection, with a completely uninformative, transient cue presented at one of the item locations in the first frame. Despite that the cue is presented in a spatially separate frame, in both translation and mirror reflection, human performance in visual search is enhanced when the target in the second frame appears at the same relative location as the cue location than at other locations. These results provide unambiguous evidence for non-retinotopic exogenous attention and further reveal an object-centered mechanism supporting flexible exogenous attention. Moreover, attentional generalization across mirror reflection may constitute an attentional correlate of perceptual generalization across lateral mirror images, supporting an adaptive, functional account of mirror images confusion.