Ambient obscurance (AO) is an effective approximation of global illumination, and its screen-space (SSAO) versions that operate on depth buffers only are widely used in real-time applications. We present an SSAO method that allows the obscurance effect to be determined from the entire depth buffer for each pixel. Our contribution is two-fold: Firstly, we build an obscurance estimator that accurately converges to ray traced reference results on the same screen-space geometry. Secondly, we generate an intermediate representation of the depth field which, when sampled, gives local peaks of the geometry from the point of view of the receiver. Only a small number of such samples are required to capture AO effects without undersampling artefacts that plague previous methods. Our method is unaffected by the radius of the AO effect or by the complexity of the falloff function and produces results within a few percent of a ray traced screen-space reference at constant real-time frame rates.