A scale space for texture+depth images based on a discrete laplacian operator

In this paper we design a smoothing filter for texture+depth images based on anisotropic diffusion. Our proposed filter enables to generate a scale space on the texture image guided by depth information, and is linear and numerically stable. We show experimentally that using scene geometry preserves the internal structure of 3D surfaces (e.g., it avoids smoothing across object boundaries). As a consequence, the result of smoothing is more independent to changes in the camera position. To illustrate the practical utility of a scale space with such properties, we integrate our filter into the SIFT keypoint detector, getting a substantial improvement of the repeatability of detected keypoints under significant viewpoint position changes.