Signed distance field

Overview

A signed distance field (SDF) assigns each point of a volume the distance to the closest surface. The sign separates the free side from the occupied side. The distance is the quantity planners and collision checks read; the sign tells them which side of a surface a query is on. The paper uses two stages. A truncated SDF (TSDF) is fused from depth images and only keeps values near the observed surfaces. An ESDF is then generated from the TSDF, at a resolution the task chooses, and holds distances over the whole grid 2603.05493 §5.

The shared invariant is that the magnitude comes from an exact nearest-surface assignment, while the sign is recovered from a sample on the query side of the surface. Unobserved cells need an explicit rule, and the paper treats them as free space 2603.05493 §5.4.

Variants

Depth-fused TSDF with on-demand ESDF

Space is stored as 8x8x8-voxel blocks, and memory is reserved only for blocks near observed geometry. A hash table finds each block's slot, and two float16 channels hold the depth average and an SDF for analytic primitives. The paper quotes about 350 MB for 100k active blocks, roughly 11 times less than a dense grid 2603.05493 §5.1. Integration projects every voxel into the depth image, so no atomic writes are needed. Each observation is weighted by the projected voxel area 2603.05493 §5.2. Each step multiplies block weights by a time factor, and blocks in view get an extra frustum factor, which removes stale observations 2603.05493 §5.3. The ESDF is seeded from cells that sit near a surface, propagated with an exact nearest-site method, and given a sign from an adjacent static sample 2603.05493 §5.4. Card: cuRoboV2.

Other variants

None in the wiki yet. The paper's comparison baseline for ESDF generation is nvblox, whose results are reported in 2603.05493 §7.6.

When to use which

The rows below rest on the author-reported benchmarks in one paper and one scene. They are not independent replications.

Implementation sketch

The sketch follows the three stages in the paper. It is not the paper's code. Pseudocode is in our own words, and values come from the cited section.

# Stage 1: seed ESDF cells that contain a surface  [arxiv:2603.05493 §5.4]
# tsdf(p): TSDF value at point p, or None if unobserved
# band: 0.9 * tsdf_voxel_size (paper's threshold)
def seed_sites(esdf_cells, tsdf, cell_size, band):
    sites = []
    for c in esdf_cells:
        # Centre plus six face probes at half a cell from the centre
        for p in probe_points(c, cell_size):
            d = tsdf(p)
            if d is not None and abs(d) < band:
                sites.append(c)
                break
    return sites

# Stage 2: exact nearest site per cell, then unsigned distance  [§5.4]
# nearest_site[c]: nearest seeded site, from a separable propagation
def unsigned_distance(c, nearest_site, cell_size):
    return dist(c, nearest_site[c]) * cell_size

# Stage 3: sign from a sample on the query side of the surface  [§5.4]
# geom_sdf(p): static-geometry SDF at p, or None if unobserved
def signed_distance(c, site, d, geom_sdf, step):
    # Step from the site toward the query; the step length is not
    # stated in the paper and must be chosen by the implementer
    sample = geom_sdf(step_toward(site, c, step))
    if sample is None:
        return d            # unobserved: treated as exterior
    return d if sample >= 0 else -d

Notes on the sketch:

• The sign convention in stage 3 is one choice. The paper uses the sign of the static sample; the exterior default for unobserved cells follows the paper.
• The paper does not state the step length in stage 3 2603.05493 §5.4.
• The paper's propagation step is an exact method. Any method that gives exact nearest sites works; the paper names PBA+ and a fixed launch count §5.4.

Contradictions

None across papers; this page currently rests on one paper. Within that paper, the abstract gives up to 99% collision recall for the ESDF, while the text of §7.6 reports 97.0% as the highest recall it shows 2603.05493 §7.6. Treat the 99% figure as unverified until the paper's text supports it.

Papers

• cuRoboV2 (arXiv:2603.05493, CC BY-SA 4.0): depth fusion into a block-sparse TSDF, on-demand GPU ESDF with exact nearest sites and sign recovery, and torque-limited B-spline trajectory optimisation in the same stack.