Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps

Sensor fusion by diffusion maps

Data fusion and the analysis of high-dimensional multisensor data, are fundamental tasks in many research diciplines. In this work we propose a unified embedding scheme for multi sensory data, which is based on the recently introduced diffusion framework. Our scheme is purely data-driven and assumes no a-priory knowledge of the underlying statistical or deterministic models of the different dat...

Space-Optimized Texture Maps

Texture mapping is a common operation to increase the realism of three-dimensional meshes at low cost. We propose a new texture optimization algorithm based on the reduction of the physical space allotted to the texture image. Our algorithm optimizes the use of texture space by computing a warping function for the image and new texture coordinates. Neither the mesh geometry nor its connectivity...

Improving Depth Maps by Nonlinear Diffusion

Dense depth maps, typically produced by stereo algorithms, are essential for various computer vision applications. For general configurations in which the cameras are not necessarily parallel or close together, it often proves difficult to obtain reasonable results for complex scenes, in particular in occluded or textureless regions. To improve the depth map in such regions, we propose a post-p...

Diffusion-Controlled Reaction Kinetics

Diffusion maps Ronald

In this paper, we provide a framework based upon diffusion processes for finding meaningful geometric descriptions of data sets. We show that eigenfunctions of Markov matrices can be used to construct coordinates called diffusion maps that generate efficient representations of complex geometric structures. The associated family of diffusion distances, obtained by iterating the Markov matrix, de...