SurfelWarp: Efficient Non-Volumetric Single View Dynamic Reconstruction

We contribute a dense SLAM system that takes a live stream of depth images as input and reconstructs non-rigid deforming scenes in real time, without templates or prior models. In contrast to existing approaches, we do not maintain any volumetric data structures, such as truncated signed distance function (TSDF) fields or deformation fields, which are performance and memory intensive. Our system works with a flat point (surfel) based representation of geometry, which can be directly acquired from commodity depth sensors. Standard graphics pipelines and general purpose GPU (GPGPU) computing are leveraged for all central operations: i.e., nearest neighbor maintenance, non-rigid deformation field estimation and fusion of depth measurements. Our pipeline inherently avoids expensive volumetric operations such as marching cubes, volumetric fusion and dense deformation field update, leading to significantly improved performance. Furthermore, the explicit and flexible surfel based geometry representation enables efficient tackling of topology changes and tracking failures, which makes our reconstructions consistent with updated depth observations. Our system allows robots to maintain a scene description with non-rigidly deformed objects that potentially enables interactions with dynamic working environments.Comment: RSS 2018. The video and source code are available on https://sites.google.com/view/surfelwarp/hom

Differential Chow Form for Projective Differential Variety

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective differential hyperplane is shown to be an irreducible projective differential variety of dimension d-1 and order h. Based on the generic intersection theorem, the Chow form for an irreducible projective differential variety is defined and most of the properties of the differential Chow form in affine differential case are established for its projective differential counterpart. Finally, we apply the differential Chow form to a result of linear dependence over projective varieties given by Kolchin.Comment: 17 page