We present a simple cascading algorithm for rapid hierarchical image segmentation based on perceptually driven contour completion and scene statistics. We start with an initial fine-scale segmentation of an image obtained by perceptual completion of partial contours into polygonal regions using region-contour correspondences established by Delaunay triangulation of edge pixels. The resulting polygon size distribution is analyzed for a dominant mode of granularity of the image. Polygons whose sizes are less than or equal to this granularity are merged with their spectrally closest neighbors to obtain the next level of polygonal segments in the hierarchy. The iterative application of this process precipitates textured regions as polygons with highly convolved boundaries and helps distinguish them from objects which typically have more regular boundaries.