In this paper, we address the problem of multi-view 3D shape reconstruction. While recent differentiable rendering approaches associated to implicit shape representations have provided breakthrough performance, they are still computationally heavy and often lack precision on the estimated geometries. To overcome these limitations we investigate a new computational approach that builds on a novel shape representation that is volumetric, as in recent differentiable rendering approaches, but parameterized with depth maps to better materialize the shape surface. The shape energy associated to this representation evaluates 3D geometry given color images and does not need appearance prediction but still benefits from volumetric integration when optimized. In practice we propose an implicit shape representation, the SRDF, based on signed distances which we parameterize by depths along camera rays. The associated shape energy considers the agreement between depth prediction consistency and photometric consistency, this at 3D locations within the volumetric representation. Various photo-consistency priors can be accounted for such as a median based baseline, or a more elaborated criterion as with a learned function. The approach retains pixel-accuracy with depth maps and is parallelizable. Our experiments over standard datasets shows that it provides state-of-the-art results with respect to recent approaches with implicit shape representations as well as with respect to traditional multi-view stereo methods.