Event-Based Smoke Velocimetry

• Event-based smoke velocimetry is a method that employs high-speed event cameras to capture brightness changes in smoke for rapid flow estimation.
• It converts asynchronous event streams into pseudo-frames processed with GPU-parallel template matching and SSD-based estimators for velocity reconstruction.
• The technique achieves sub-millisecond latency and high update rates while addressing challenges such as soft smoke edges and out-of-plane motion.

Searching arXiv for papers on event-based smoke velocimetry and closely related EBIV work. Event-based smoke velocimetry is a class of flow-measurement methods that uses event cameras to observe smoke or smoke-borne tracers, typically under light-sheet or pulsed illumination, and estimates velocity from the resulting asynchronous stream of brightness-change events rather than from conventional frames. In the current literature, the term most explicitly denotes a method that observes smoke illuminated in a thin light sheet inside a pipe, converts the asynchronous event stream into low-latency event-frames, and applies GPU-parallel template matching to recover a sparse $2$D velocity slice at sub-millisecond latency; more broadly, it sits within event-based imaging velocimetry, where event streams are grouped into pseudo-snapshots or processed directly to infer fluid motion from particles, droplets, or smoke structures (Bauersfeld et al., 21 Jul 2025, Willert et al., 2022).

1. Definition, scope, and relation to classical velocimetry

Classical PIV uses particles, pulsed laser sheets, high-speed cameras, and cross-correlation, while smoke image velocimetry uses smoke rather than discrete particles and is usually frame-based, optical-flow-like, and typically offline or low frame rate. Event-based smoke velocimetry departs from both by replacing the frame camera with an event sensor that asynchronously records intensity changes at microsecond scale. In the narrow-pipe study, this design choice was motivated by unsteady, self-induced recirculating flows, by the need for sub-millisecond processing and $>500$ Hz updates, and by the impracticality of conventional high-speed imaging with pulsed lasers in a long PVC pipe (Bauersfeld et al., 21 Jul 2025).

Within the wider EBIV literature, two measurement paradigms coexist. One uses continuously illuminated tracers and processes the raw event cloud by motion compensation or correlation; the other uses pulsed illumination so that each pulse induces a burst of events, which can then be grouped into pseudo-images and processed with standard PIV pipelines. The latter was shown to enable flow-field measurements at light pulsing rates up to $10$ kHz in both water and air, with an upper bound on the frequency response on the order of $10$–$20$ kHz for the specific sensor tested (Willert, 2022).

A recurring conceptual distinction is between smoke as a passive scalar structure and smoke as a carrier of visible tracers. Some methods treat smoke edges, filaments, or light-sheet intensity structures as the observable signal; others remain particle-centered and are only smoke-adjacent. This distinction matters because brightness constancy, feature sharpness, and out-of-plane motion behave differently for diffuse smoke than for discrete particles, a point emphasized both by the narrow-pipe EBSV work and by frame-based dense smoke-motion estimation research (Bauersfeld et al., 21 Jul 2025, Chen et al., 2016).

2. Sensing principles and event representations

An event camera outputs events

$$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$

where each event records pixel location, timestamp, and polarity. In event-based imaging literature, events are generated when the logarithm of intensity changes by more than a contrast threshold; this is why static backgrounds produce few events while moving smoke edges or pulsed illumination produce bursts of activity (Willert et al., 2022, Tao et al., 26 Mar 2026).

For smoke velocimetry in a pipe, the sensing geometry is a light sheet perpendicular to the pipe axis, viewed by a Prophesee Gen4 event camera with a Zeiss Classic $25$ mm $f/2$ lens. Smoke is injected through $18$ nozzles, illuminated by an LED-based light sheet, and viewed as a $2$D cross-section of the $>500$0–$>500$1 plane, so the recovered field is a planar optical-flow slice that approximates the projection of a $>500$2D flow (Bauersfeld et al., 21 Jul 2025).

The narrow-pipe method converts events into fixed-interval event-frames after $>500$3 spatial binning: $>500$4 To increase robustness for sparse, low-contrast smoke, the frames are Gaussian-blurred with a $>500$5 kernel and $>500$6, then accumulated over an overlapping window of length $>500$7: $>500$8 This construction is explicitly motivated by the fact that smoke structures are soft and edgeless, brightness constancy is violated, and per-pixel flow is not meaningful; hence the method operates on interrogation patches rather than on individual pixels (Bauersfeld et al., 21 Jul 2025).

The pulsed-illumination EBIV literature uses a related but distinct representation. Events generated by each laser pulse are grouped into a pseudo-frame with timestamp equal to the pulse time, after which multi-frame, pyramid-based cross-correlation PIV is applied. In that setting, pulsed illumination both makes slow or stationary tracers visible and quantifies sensor latency, because pulse-locked event histograms expose the spread between optical excitation and recorded event times (Willert, 2022).

3. Velocity estimation algorithms

The core narrow-pipe EBSV estimator is a patch-wise normalized SSD matcher between two consecutive accumulated event-frames $>500$9 and $10$0. The image is divided into a $10$1 grid of interrogation windows of size $10$2, and for each patch a displacement $10$3 is sought within $10$4 pixels. The SSD cost is

$10$5

with a normalized score

$10$6

The optical-flow vector is the minimizer

$10$7

followed by quadratic $10$8 sub-pixel refinement and rejection by determinant and magnitude tests. The final field is stored as

$10$9

with channels $10$0, where the third channel is a confidence measure (Bauersfeld et al., 21 Jul 2025).

The implementation is intentionally simple and GPU-friendly. The reported parameters are $10$1 pixels, patch step $10$2 pixels, and $10$3, yielding an $10$4 sparse grid over the observed cross-section. At a downsampled spatial scale of about $10$5 px/mm and $10$6 ms, the measurable range is approximately $10$7 to $10$8 m/s, from the half-pixel lower limit and the $10$9-pixel upper displacement limit (Bauersfeld et al., 21 Jul 2025).

A related but earlier EBIV literature proposed two direct event-domain alternatives: motion compensation that maximizes local contrast after warping events by a candidate velocity, and a sum-of-correlations method that bins events into temporal slices and cross-correlates the slices across time-separated volumes. Those methods were demonstrated on particle-seeded flows in water and air rather than on smoke, but they established the basic event-domain analogy to PIV interrogation windows and motion-compensation warps (Willert et al., 2022).

The narrow-pipe EBSV paper compared its SSD matcher against contrast maximization, an unsupervised learning-based event optical flow network, and PIVLab as an offline reference:

Method	RMSE slow (~2 m/s) [m/s]	RMSE fast (~5 m/s) [m/s]	Real-time factor
PIVLab	– (reference)	–	0.0007
CM	0.81	0.52	–
UL	1.18	0.70	0.27
Ours	0.34	0.35	3.2

The same work reports $20$0 for event stacking and Gaussian blurring, $20$1 for SSD cost computation, and $20$2 for CPU-side post-processing, for a total latency of $20$3 on an RTX 3090, corresponding to about $20$4 kHz maximum processing rate, although experiments were run at $20$5 Hz (Bauersfeld et al., 21 Jul 2025).

4. From planar flow slices to reduced-order and volumetric reconstructions

Current event-based smoke velocimetry is primarily planar: the narrow-pipe method measures a thin illuminated slice and recovers a sparse $20$6D flow field. A separate event-based imaging velocimetry line addresses the inverse problem of lifting coarse real-time event-derived fields into higher-resolution, dynamically consistent representations. In that framework, a fast low-resolution EBIV pipeline produces coarse velocity snapshots online, while paired low-resolution and high-resolution fields from the same event data are used offline to learn a POD-based reduced model and a linear dynamical system. Online, the low-resolution snapshot is projected onto a POD basis, mapped into high-resolution coordinates, and temporally regularized by a Kalman filter or by LSE/LSE+VR estimators before reconstructing the high-resolution field (Franceschelli et al., 5 May 2026).

The high-resolution reconstruction is written in POD form as

$20$7

with the retained rank chosen by an elbow criterion. Three estimators were compared: a direct Kalman filter, LSE, and LSE+VR. On a submerged water jet, the normalized RMSE $20$8 decreased from $20$9 for cubic interpolation to $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$0 for KF, $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$1 for LSE, and $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$2 for LSE+VR; on channel flow over a square rib, the corresponding values were $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$3, $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$4, $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$5, and $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$6. The same work states that latent-coordinate estimation is negligible compared with low-resolution processing, and that projection plus state estimation plus full high-resolution reconstruction costs less than $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$7 ms per frame on average, with worst-case less than $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$8 ms for the jet case (Franceschelli et al., 5 May 2026).

A separate but related reconstruction line addresses dynamic smoke from a single RGB video rather than from events. SmokeSVD reconstructs time-varying $$\mathcal{E} = \left\{e_i = (x_i, y_i, t_i, p_i), \; p_i \in \{-1, 1\}, i = 1,\dots,N \right\},$$9D density and velocity by generating physically guided novel views with diffusion models, then enforcing consistency by differentiable advection and incompressibility. Its core transport model is

$25$0

with a differentiable advection operator

$25$1

The paper explicitly states that adapting these ideas to event-based smoke velocimetry suggests design directions, including modality-agnostic velocity representation on a $25$2D grid, incompressibility, smoothness penalties $25$3, differentiable advection, and multi-view consistency via a differentiable event-rendering model (Li et al., 16 Jul 2025).

This suggests a bifurcation in the field. One branch prioritizes very fast planar estimation for feedback; the other prioritizes physically constrained state reconstruction, reduced coordinates, or high-resolution fields from coarse event measurements. The literature does not yet present a unified event-based smoke system that simultaneously achieves low-latency control-grade sensing and full $25$4D volumetric smoke reconstruction.

5. Closed-loop robotics and disturbance-aware control

The most explicit application of event-based smoke velocimetry to control is autonomous quadrotor flight inside a narrow pipe. The flow field $25$5, together with quadrotor position $25$6 in the pipe cross-section, is fed into a disturbance estimator built from a ConvLSTM flow encoder and an MLP. The network outputs

$25$7

that is, horizontal and vertical disturbance forces and a roll torque disturbance. A separate bias MLP is used during training to remove per-experiment biases, after which the ConvLSTM learns a mapping from flow history and position to aerodynamic wrench (Bauersfeld et al., 21 Jul 2025).

Those disturbance estimates are then supplied to an LSTM-PPO reinforcement-learning controller. The observation vector includes position, attitude, target position, previous action, the estimated disturbances, and a validity flag $25$8 indicating whether disturbance measurements are currently valid. The paper reports that incorporating real-time flow information reduces RMSE in $25$9 and $f/2$0 by about $f/2$1–$f/2$2 overall relative to a position-only disturbance model, and that the policy using disturbance observations achieves about $f/2$3 reduction in hover position standard deviation in $f/2$4 and about $f/2$5 reduction in overshoot during lateral translations across the pipe (Bauersfeld et al., 21 Jul 2025).

The same study argues that the flow-based RCNN captures vortex-state hysteresis that a position-only model cannot. In a lateral translation sequence, the position-only model predicts the sign change of $f/2$6 and $f/2$7 as soon as the quadrotor crosses the pipe center, whereas the flow-based RCNN delays the sign flip until the vortex structure actually collapses and rebuilds. This is significant because the sensor is not merely measuring local motion vectors; it is being used as an estimator of the global flow state that mediates aerodynamic disturbance (Bauersfeld et al., 21 Jul 2025).

A broader EBIV assessment reaches a compatible conclusion from a reduced-order perspective. By comparing EBIV with synchronized PIV in a submerged jet and in airflow around a square rib, it finds that event-based pseudo-snapshots processed by standard PIV are sufficient to recover dominant POD modes, their energy, and their temporal dynamics, even though higher modes are more noise-contaminated. That result positions event-based velocimetry as a plausible sensing layer for real-time, imaging-based closed-loop flow control systems (Franceschelli et al., 2024).

6. Assumptions, failure modes, and recurring misconceptions

A central misconception is that event-based smoke velocimetry provides dense, direct, per-pixel flow. The narrow-pipe method explicitly avoids per-pixel dense flow because smoke structures are soft and edgeless, brightness constancy is not satisfied, and out-of-plane motion causes smoke to enter and leave the light sheet. The recovered field is therefore patch-based, sparse, and confidence-weighted, with only $f/2$8 interrogation windows in the reported implementation (Bauersfeld et al., 21 Jul 2025).

A second misconception is that the event modality removes the classical ambiguities of planar flow measurement. It does not. The illuminated sheet is still a thin slice of a $f/2$9D flow, instantaneous local $18$0 can be nonzero even when the mean longitudinal flow vanishes, and tracking is only meaningful over the residence time of structures in the sheet: $18$1 For $18$2 cm and $18$3 m/s, the paper gives $18$4 ms, which is why update rates much greater than $18$5 Hz are required (Bauersfeld et al., 21 Jul 2025).

Sensor-side limits also remain fundamental. Pulsed-illumination EBIV shows that latency is introduced both on the pixel level and during array read-out, and that arbiter saturation can smear event bursts over hundreds of microseconds at high event rates. Using pulsed illumination, the overall latency indicates an upper bound on the usable frequency response on the order of $18$6–$18$7 kHz for the specific sensor, with reliable operation at full sensor format more typically in the $18$8–$18$9 kHz range; reduced ROIs shorten the effective burst width to about $2$0–$2$1 (Willert, 2022).

The broader EBIV assessment adds peak locking and binary pseudo-snapshots to the list of caveats. In the air-channel case, the binary nature of event pseudo-images and single-pixel tracer activations produced strong peak locking, while high-frequency PSDs exhibited a higher noise floor than frame-based PIV. Dominant low-order dynamics were still recovered, but the literature is explicit that higher modes, fine turbulence content, and poorly seeded regions are more fragile (Franceschelli et al., 2024).

Finally, real deployments may require substantial infrastructure. The narrow-pipe system relies on an instrumented pipe with smoke injectors, a light sheet, external event cameras, and an external desktop GPU. The paper states that the flow estimator itself runs in under $2$2 ms on an RTX 3090, but not onboard; onboard deployment would require an embedded GPU and careful optimization (Bauersfeld et al., 21 Jul 2025).

7. Extensions, datasets, and emerging multimodal directions

The event-based smoke velocimetry literature is increasingly connected to multimodal and synthetic-data programs. FED-PV addresses what it calls a bottleneck in fusion measurement algorithms by generating synchronized grayscale particle frames, event streams, and dense ground-truth velocity fields for the same underlying flow. The dataset spans $2$3 flow subsets at $2$4 resolution, provides $2$5 grayscale frames per sample at $2$6 ms spacing, simulates events over $2$7 ms from intermediate images at $2$8 steps, and reports average event counts per sample ranging from about $2$9 to $>500$00. Although FED-PV is particle-based rather than smoke-specific, it is explicitly positioned as a training and benchmarking resource for event-only or frame-plus-event velocimetry, which is directly relevant to smoke systems that use aerosol droplets or tracer-like structures (Wu et al., 1 Jul 2025).

Another frontier is smoke-aware fusion under extreme dynamic range. A closed-loop Event–SVE system for propellant combustion combines a spatially variant exposure camera with a stereo pair of event cameras. It constructs a smoke-likelihood map

$>500$01

where $>500$02, $>500$03, $>500$04, and $>500$05 encode brightness deviation, Weber contrast, generalized contrast under an atmospheric scattering model, and normalized response variance. The resulting HDR maps provide the absolute-intensity reference missing in event cameras and are used to suppress smoke-driven event artifacts and improve particle-state discrimination; the stereo event pipeline then estimates $>500$06D separation height and equivalent particle size with maximum calibration error $>500$07 (Tao et al., 26 Mar 2026).

From the perspective of event-based smoke velocimetry proper, this multimodal branch matters because it treats smoke not merely as nuisance but as a measurable, classifiable medium. A plausible implication is that future systems will combine low-latency event flow sensing, smoke-aware HDR intensity references, and reduced-order or physics-guided reconstruction. The present literature already contains each ingredient separately: real-time smoke-slice velocimetry and control (Bauersfeld et al., 21 Jul 2025), pulsed EBIV with quantified latency (Willert, 2022), reduced-order high-resolution reconstruction from coarse event fields (Franceschelli et al., 5 May 2026), and smoke-aware event fusion under HDR and heavy smoke (Tao et al., 26 Mar 2026).