The increasing availability of texture+depth (RGBD) content has recently motivated research towards the design of image features able to employ the additional geometrical information provided by depth. Indeed, such features are supposed to provide higher robustness than conventional 2D features in presence of large changes of camera viewpoint. In this paper we consider the first stage of RGBD image matching, i.e., keypoint detection. In order to obtain viewpoint-covariant keypoints, we design a filtering process, which approximates a diffusion process along the surfaces of the scene, by means of the information provided by depth. Next, we employ this multiscale representation to find keypoints through a multiscale keypoint detector. The keypoints obtained by the proposed detector provide substantially higher stability to viewpoint changes than alternative 2D and RGBD feature extraction approaches, both in terms of repeatability and image classification accuracy. Furthermore, the proposed detector can be efficiently implemented on a GPU.