It is well established that the units of attention on human vision are not merely spatial but closely related to perceptual objects. This implies a strong relationship between segmentation and attention processes. This interaction is bi-directional: if the segmentation process constraints attention, the way an image is segmented may depend on the specific question asked to an observer, i.e. what she 'attend' in this sense. When the focus of attention is deployed from one visual unit to another, the rest of the scene is perceived but at a lower resolution that the focused object. The result is a multi-resolution visual perception in which the fovea, a dimple on the central retina, provides the highest resolution vision. While much work has recently been focused on computational models for object-based attention, the design and development of multi-resolution structures that can segment the input image according to the focused perceptual unit is largely unexplored. This paper proposes a novel structure for multi-resolution image segmentation that extends the encoding provided by the Bounded Irregular Pyramid. Bottom-up attention is enclosed in the same structure, allowing to set the fovea over the most salient image region. Preliminary results obtained from the segmentation of natural images show that the performance of the approach is good in terms of speed and accuracy.