Robotics
Truncated signed distance field
Definition
A truncated signed distance field stores the signed distance to the nearest observed surface only within a limited band around that surface, usually on a voxel grid. Robots use weighted TSDF fusion to combine depth images into a dense three-dimensional surface model.
Also known as: TSDF, Truncated signed distance function
Updated
A narrow distance band around surfaces
A signed distance is positive on one side of a surface, negative on the other, and zero on the surface. A truncated signed distance field clips or ignores values beyond a chosen distance. The truncation concentrates storage and updates near the surface instead of representing accurate distance everywhere.
For each registered depth image, a fusion system projects voxels into the camera, compares their predicted depth with the measurement, and updates distance and confidence values. Curless and Levoy introduced a cumulative weighted signed-distance volume for integrating aligned range images, followed by extraction of an isosurface from the grid.
Dense maps from depth cameras
An RGB-D robot can fuse successive frames into a TSDF while simultaneous localization and mapping estimates camera poses. The zero crossing can be converted to a mesh or ray-cast into a synthetic view. Manipulation and navigation systems can use the resulting surface for scene reconstruction, visibility, or collision queries. Open3D provides an official voxel-block TSDF integration implementation.
A TSDF is one representation of a signed distance field, not a synonym for every SDF. The truncation band and observed-space update rule are defining parts of the map. An occupancy grid instead represents whether cells are occupied, free, or unknown rather than storing a local surface distance.
It also differs from a raw point cloud. A point cloud keeps samples, while TSDF fusion accumulates them in a structured field and can average repeated noisy depth observations.
Resolution, pose error, and motion
Voxel size limits the smallest recoverable geometry. A dense fine grid consumes substantial memory, so implementations use sparse blocks, hashing, or bounded local volumes. A narrow truncation distance can lose corrections under noisy depth; a wide one smooths across more space and costs more updates.
Fusion assumes the input poses align observations of the same surface. Pose drift can create duplicated or blurred geometry, and a later loop closure is difficult to apply if raw observations or a deformable map were not retained. Moving people and objects violate the static-scene assumption and can leave trails. The field also does not automatically encode object identity, material, uncertainty correlations, or whether an unobserved region is safe to enter.
Sources
Related terms
Signed distance field
A signed distance field represents a surface by assigning spatial locations a distance value whose sign distinguishes the two sides of the surface. Its zero level marks the surface, while the sign convention depends on the representation.
Point cloud
A point cloud is a collection of points representing sampled locations in space, usually with three-dimensional coordinates. Individual points may also carry attributes such as color or return intensity.
Simultaneous localization and mapping
Simultaneous localization and mapping is the joint estimation of a robot's state and a map of its environment from sensor observations. It is commonly abbreviated SLAM.
Occupancy grid
An occupancy grid divides space into cells and records occupancy information for each cell. A two-dimensional robot map commonly distinguishes occupied, free, and unknown regions.