Fast Hierarchical 3D Distance Transforms on the GPU

This paper describes a novel approach for the GPU-based computation of approximate 3D Euclidean distance transforms, i.e. distance fields with associated vector information to the closest object point. Our hierarchical method works on discrete voxel grids and uses a propagation technique, both on a single hierarchy level and between the levels. We assume a closed object, so that a signed distance of a voxel w.r.t. the object boundary is defined. The object’s boundary is given by means of the grid voxel classification as interior or exterior and the preinitialization of voxels lying directly next to the boundary. The propagation method can be seen as a filtering process, where the voxel’s distance transform is updated by computing alternative distances according to the distance transforms for neighbor voxels. Using our hierarchical approach, the effort to compute the distance transform is significantly reduced. Our technique is purely GPU-based. We build upon a specific approach to work on a 3D distance transform using Multiple Render Targets (MRT). All hierarchical operations are performed on the GPU. ACM Categories: I.3.5 Computer Graphics (Computational Geometry and Object Modeling Curve, surface, solid, and object representations)