The uprising number of applications that involve very large images with resolutions greater than 30\,000$\times$30\,000 raises major memory management issues. Firstly, the amount of data usually prevents such images from being processed globally and therefore, designing a global image partition raises several issues. Secondly, a multi-resolution approach is necessary since an analysis only based on the highest resolution may miss global features revealed at lower resolutions. This paper introduces the tiled top-down pyramidal framework which addresses these two main constraints. Our model provides a full representation of multi-resolution images with both geometrical and topological relationships. The advantage of a top-down construction scheme is twofold: the focus of attention only refines regions of interest which results in a reduction of the amount of required memory and in a refinement process that may take into account hierarchical features from previous segmentations. Moreover, the top-down model is combined with a decomposition in tiles to provide an accurate memory bounding while allowing global analysis of large images.