We propose to rely on the wave equation for the detection of repeatable keypoints invariant up to image scale and rotation and robust to viewpoint variations, blur, and lighting changes. The algorithm exploits the properties of local spatial–temporal extrema of the evolution of image intensities under the wave propagation to highlight salient symmetries at different scales. Although the image structures found by most state-of-the-art detectors, such as blobs and corners, occur typically on highly textured surfaces, salient symmetries are widespread in diverse kinds of images, including those related to poorly textured objects, which are hardly dealt with by current pipelines based on local invariant features. The impact on the overall algorithm of different numerical wave simulation schemes and their parameters is discussed, and a pyramidal approximation to speed-up the simulation is proposed and validated. Experiments on publicly available datasets show that the proposed algorithm offers state-of-the-art repeatability on a broad set of different images while detecting regions that can be distinctively described and robustly matched.