Many computer vision applications involve algorithms that can be decomposed in two main steps. In a first step,  events or objects are detected and, in a subsequent stage, detections are assigned to various classes. Examples of such ``detection plus classification'' problems can be found in human pose classification, object recognition or action classification among others. In this paper, we focus on a special case: depth ordering on single images. In this  problem, the detection step consists of the image segmentation, and the classification stage assigns a depth gradient to each contour or a depth order to each region.


In this paper, we discuss the limitations of the classical Precision-Recall evaluation framework for these kind of problems and define an extended framework called ``Precision-Recall-Classfication'' (PRC). Then, we apply this framework to depth ordering problems and design two specific PRC

measures to evaluate both the local and the global depth consistencies. We use these measures to evaluate precisely state of the art depth ordering systems for monocular images. Based on this evaluation, we also propose an extension to the method of [Cal13] applying an optimal graph cut on a hierarchical segmentation structure such as ultrametric contour maps. The resulting system is proven to provide better results than state of the art algorithms.