This paper is aimed at obtaining the statistics as a probabilistic model pertaining to the geometric, topological and photometric structure of natural images. The image structure is represented by its segmentation graph derived from the low-level hierarchical multiscale image segmentation. We first estimate the statistics of a number of segmentation graph properties from a large number of images. Our estimates confirm some findings reported in the past work, as well as provide some new ones. We then obtain a Markov random field based model of the segmentation graph which subsumes the observed statistics. To demonstrate the value of the model and the statistics, we show how its use as a prior impacts three applications: image classification, semantic image segmentation and object detection.