From Box Filtering to Fast Explicit Diffusion

Abstract. There are two popular ways to implement anisotropic diffusion filters with a diffusion tensor: Explicit finite difference schemes are simple but become inefficient due to severe time step size restrictions, while semi-implicit schemes are more efficient but require to solve large linear systems of equations. In our paper we present a novel class of algorithms that combine the advantages of both worlds: They are based on simple explicit schemes, while being more efficient than semi-implicit approaches. These so-called fast explicit diffusion (FED) schemes perform cycles of explicit schemes with varying time step sizes that may violate the stability restriction in up to 50 percent of all cases. FED schemes can be motivated from a decomposition of box filters in terms of explicit schemes for linear diffusion problems. Experiments demonstrate the advantages of the FED approach for time-dependent (parabolic) image enhancement problems as well as for steady state (elliptic) image compression tasks. In the latter case FED schemes are speeded up substantially by embedding them in a cascadic coarse-to-fine approach.

Anisotropic range image integration

Abstract. Obtaining high-quality 3D models of real world objects is an important task in computer vision. A very promising approach to achieve this is given by variational range image integration methods: They are able to deal with a substantial amount of noise and outliers, while regularising and thus creating smooth surfaces at the same time. Our paper extends the state-of-the-art approach of Zach et al. (2007) in several ways: (i) We replace the isotropic space-variant smoothing behaviour by an anisotropic (direction-dependent) one. Due to the directional adaptation, a better control of the smoothing with respect to the local structure of the signed distance field can be achieved. (ii) In order to keep data and smoothness term in balance, a normalisation factor is introduced. As a result, oversmoothing of locations that are seen seldom is prevented. This allows high quality reconstructions in uncontrolled capture setups, where the camera positions are unevenly distributed around an object. (iii) Finally, we use the more accurate closest signed distances instead of directional signed distances when converting range images into 3D signed distance fields. Experiments demonstrate that each of our three contributions leads to clearly visible improvements in the reconstruction quality.