Build a Gaussian. Put it in a radar beam. Watch a 3D scene become a range–azimuth image.
Scene parameters → differentiable rendering → measurement error → updated splats.
Preprocessing is out of scope. Poses and an occupancy reference are assumed available.
Drag a center to move it. Use the inspector for height and shape.
Click a row to inspect its range profile. The display scale stays fixed.
The Gaussian range kernel approximates spectral leakage after windowing. Increase its width in the Radar controls; the geometry has not changed.
The same scene, sliced along range.
Local range maxima above a fixed power threshold. This is not CFAR, object classification, or a RadarSplat component. Noise returns may also produce peaks.
The center μ places the splat. Three positive scales give its principal widths; a rotation q turns those axes. The editor exposes yaw and pitch, a two-angle subset of the quaternion rotation.
A splat is a smooth basis function, not one radar detection. Several splats can contribute to the same bin, and a single splat can spread into many bins.
First move the mean and covariance into the radar frame. Linearize the nonlinear spherical conversion around that mean. The upper-left 2 × 2 covariance block gives the range–azimuth footprint after marginalizing elevation.
Rows are r, θ, φ; columns are sensor-frame x, y, z. Large splats or near-axis geometry can make this first-order approximation inaccurate.
ρ controls view-dependent reflectivity; α and η distinguish occupancy and noise contributions. Set α low and η high: the return can stay bright without representing occupied space.
The total, target, noise, and occupancy selectors replace the return weight. The occupancy rendering is a weighted image, not a calibrated per-pixel probability.
Our explicit teaching discretization of the paper’s additive rendering equation:
No depth-sorted transparency product. This model sums power contributions; it does not solve full electromagnetic visibility or coherent interference.
Azimuth convolution mixes neighboring directions, with circular padding at ±180°. Range convolution mixes neighboring distances. Neither changes the underlying 3D geometry.
An elongated object and a broad antenna can both widen a return. Keeping the sensor kernel separate prevents assigning every blurred pixel to larger scene geometry.
The forward model predicts a signal; inverse rendering changes parameters to reduce the mismatch. This small, deterministic experiment fits a synthetic one-beam measurement, not Boreas data.
Ready. Every step computes a numerical gradient and checks the objective.
Initialize 20,000 random Gaussians (scale 0.5 m, α = η = 0.1); render from known poses; minimize image L1 + SSIM, occupancy L1, size, and probability regularization losses. The supplement reports 3,000 training iterations.
Gradients update the scene. A new radar pose uses the learned splats without fitting again. The input occupancy reference comes from preprocessing, which we do not implement here.
One radial Gaussian; five scalar parameters; fixed leakage; energy-normalized squared power and occupancy errors; a squared excess-probability penalty. Central finite differences and backtracking keep accepted steps non-increasing. No SSIM, CUDA training, density control, or full 3D reconstruction is claimed.
Positions, scale, reflectivity, α, and η really update. The orange curve and objective history are calculated from those current parameters, not pre-recorded animation.
Kung, Harisha, Vasudevan, Eid & Skinner. RadarSplat: Radar Gaussian Splatting for High-Fidelity Data Synthesis and 3D Reconstruction of Autonomous Driving Scenes. ICCV 2025; arXiv:2506.01379.
Four editable splats, 400 azimuth rows, 240 range bins over 2.5–50 m, and Q = 4. The paper uses 400 × 839, Q = 10, and a 0.17 m range-kernel standard deviation.
We use a symmetric analytic elevation gain and a normalized Gaussian azimuth kernel, not the manufacturer’s measured antenna pattern. Reflectivity uses a restricted first-order SH slice; the paper reports SH level 10. Power units and display thresholds are illustrative.
A small pixel-variance floor limits aliasing; range convolution uses zero padding. The separately estimated periodic multipath source map is omitted. η is not a replacement for that map. There is no Doppler, tracker, or semantic detector here.
The paper’s ReLU(α + η − 1) penalty discourages sums above one; it does not enforce equality. Target + noise equals total only where clipping is inactive.