HelixTrack: Event-Based Tracking and RPM Estimation of Propeller-like Objects

Radim Spetlik; Michal Pliska; Vojtěch Vrba; Jiri Matas

cs.CVMar 10, 2026

HelixTrack: Event-Based Tracking and RPM Estimation of Propeller-like Objects

Authors: Radim Spetlik, Michal Pliska, Vojtěch Vrba, Jiri Matas

Organizations: Faculty of Electrical Engineering, Czech Technical University in Prague

Abstract

Safety-critical perception for unmanned aerial vehicles and rotating machinery requires microsecond-latency tracking of fast, periodic motion under egomotion and strong distractors. Frame-based and event-based trackers drift or break on propellers because periodic signatures violate their smooth-motion assumptions. We tackle this gap with HelixTrack, a fully event-driven method that jointly tracks propeller-like objects and estimates their rotations per minute (RPM). Incoming events are back-warped from the image plane into the rotor plane via a homography estimated on the fly. A Kalman Filter maintains instantaneous estimates of phase. Batched iterative updates refine the object pose by coupling phase residuals to geometry. To our knowledge, no public dataset targets joint tracking and RPM estimation of propeller-like objects. We therefore introduce the Timestamped Quadcopter with Egomotion (TQE) dataset with 13 high-resolution event sequences, containing 52 rotating objects in total, captured at distances of 2 m / 4 m, with increasing egomotion and microsecond RPM ground truth. On TQE, HelixTrack processes full-rate events (approx. 11.8x real time) faster than real time and microsecond latency. It consistently outperforms per-event and aggregation-based baselines adapted for RPM estimation.

Figures & tables

Panel of Figure 1 — Figure 1: HelixTrack – tracking and instantaneous rotations per minute estimation of propeller-like objects from asynchronous events. Incoming events are back‑warped from the image plane “ $\mathbf{z}$ ” into the rotor plane “ $\mathbf{u}$ ” by a homography. Rotor‑plane coordinates are gated with $r_{\text{in}}$ and $r_{\text{out}}$ to a ring‑shaped band and used for: (i) per-event phase update via Kalman filter, and (ii) batched pose refinement via iterative homography update.

Panel of Figure 2 — Figure 2: Aggregated events from two sequences in the Timestamped Quadcopter with Egomotion dataset. Top row: smallest egomotion ( $M_{\text{ego}}=1$ ); bottom row: largest egomotion ( $M_{\text{ego}}=7$ ). Events are aggregated from the first 10 ms of five 1-second intervals.

$d$	$M_{\text{ego}}$	$l$ (s)	propeller		ours	AEB [ 15 ]	DeepEv [ 4 ]	ours	AEB [ 15 ]	DeepEv [ 4 ]	ours	AEB [ 15 ]	DeepEv [ 4 ]
					MArE ( $\%$ ) $\downarrow$			MAE (RPM) $\downarrow$			RMSE (RPM) $\downarrow$
$2$ m	1	28.7	rear	right	1.3	61.4	8564.8	93.7	5980.8	652423.7	215.9	7186.8	785896.2
			rear	left	1.3	0.9	402.4	81.4	73.0	32090.3	241.4	241.2	46466.0
			front	left	1.5	35.3	4132.0	118.4	2487.0	303141.3	194.1	3302.9	359054.3
			front	right	1.2	65.5	94.6	77.8	5650.8	8759.2	186.3	7673.3	9700.4
	3	27.7	rear	right	1.2	1198.7	5013.6	85.1	102482.5	386360.6	223.2	192935.8	437954.9

Table 1: Benchmark on selected recordings of Timestamped Quadcopter with Egomotion (TQE). For each presented method and setting (camera-target distance

d

, egomotion level

M_{\text{ego}}

), the average shaft-RPM mean absolute relative error (MArE), mean absolute error (MAE), and root mean squared error (RMSE) are reported over 4‑fold cross‑validation across the four propellers (one training propeller per fold). Both AEB-Tracker [ 15 ] and DeepEv [ 4 ] methods were modified to allow RPM estimation (see Sec. 4.3 ). TQE ground-truth RPM has

\mu\pm\sigma\!=\!11193\pm 3540

\min

917

\max

15768

. Duration

l

of recording reported in seconds.

M_{\text{ego}}=1

roughly means “slow camera movement”, while

M_{\text{ego}}=5

means “fast camera movement” (see Fig. 2 ). As

M_{\text{ego}}

increases, the camera experiences stronger egomotion, leading to increase of the number of events generated in the background. Complete results are provided in supplementary Table S3 .

Event
Stride	MAE (RPM) $\downarrow$		$\text{RTF}_{\text{est}}$ $\uparrow$		$U_{\text{evt}}/U_{\text{GN}}$
1	${105.6}$ $\pm$	${48.8}$	${13.6}$ $\pm$	${3.6}$	${775.00}$ $\pm$	${249.17}$
2	${1382.2}$ $\pm$	${3277.8}$	${30.3}$ $\pm$	${12.5}$	${1520.84}$ $\pm$	${1477.22}$
3	${1339.7}$ $\pm$	${2933.5}$	${42.8}$ $\pm$	${12.2}$	${1081.24}$ $\pm$	${854.28}$
4	${2492.1}$ $\pm$	${3520.2}$	${53.1}$ $\pm$	${22.8}$	${559.09}$ $\pm$	${645.35}$

Table 2: Runtime-accuracy trade‑off for event subsampling. We report mean

\pm

standard deviation across 4-fold cross-validation on the 23 successfully tracked propellers (MAE

\leq

300 RPM) from Timestamped Quadcopter with Egomotion dataset. Metrics: Mean Absolute Error (MAE, RPM; lower is better), the estimated real‑time factor

\text{RTF}_{\text{est}}

(higher is better) computed as sequence duration divided by the total compute time (per‑event EKF updates plus batched Gauss-Newton (GN) solves), and the mean per‑update costs

U_{\text{evt}}/U_{\text{GN}}

for a single event update and a single GN pose solve, respectively. “Event stride = k” means only every k-th event is processed. See Sec. 4.5 for the details and definitions.

Panel of Figure 3 — Figure 3: Projection of per‑propeller unit circles under the final homography estimate, overlaid with HelixTrack trajectories on selected Timestamped Quadcopter with Egomotion sequences. Propellers are color‑coded: rear left green, rear right orange, front left red, front right cyan. Markers encode time: size increases and opacity decreases backward in time, so older states appear larger and more transparent.

Figure 4: Robustness to initialization errors. We perturb the initial tracker position, in‑plane scale, and initial RPM by

\pm\{1,2,\dots,100\}\%

around the nominal initialization and run HelixTrack end‑to‑end. For position, we average shifts “toward” and “away from” the nearest distractor (propeller). The plot reports shaft‑RPM Mean Absolute Error (MAE) across propellers with MAE

\leq 300

(lower is better); red line marks 10,000 RPM.

Panel of Figure 7 — Figure S1 : Aggregated events from all sequences in the Timestamped Quadcopter with Egomotion dataset with camera-to-quadcopter distance of 2 m, from the smallest (top row, $M_{\text{ego}}$ =1), to the largest (bottom row, $M_{\text{ego}}$ =7) egomotion intensity. Events from the first 10 ms of five 1-second intervals are shown. Positive events displayed in black, negative in gray.

Panel of Figure 8 — Figure S2 : Aggregated events from all sequences in the Timestamped Quadcopter with Egomotion dataset with camera-to-quadcopter distance of 4 m, from the smallest (top row, $M_{\text{ego}}$ =1), to the largest (bottom row, $M_{\text{ego}}$ =7) egomotion intensity. Events from the first 10 ms of five 1-second intervals are shown. Positive events displayed in black, negative in gray.

$\mathrm{r_{out}}$	MAE (RPM) $\downarrow$		median
1.4	25897.838 $\pm$	64560.838	6837.504
1.5	31173.431 $\pm$	89359.956	6623.163
1.6	21958.240 $\pm$	62330.271	7017.397
1.7	33919.799 $\pm$	133795.000	7763.656
1.8	17984.723 $\pm$	43510.488	6545.428
1.9	15783.097 $\pm$	43241.885	7078.281

Table S1 : Grid search over

r_{\mathrm{in}}

and

r_{\mathrm{out}}

with

q_{\mathrm{jerk}}{=}400

\lambda_{\phi}{=}1.0

\lambda_{\mathrm{r}}{=}1.0

\lambda_{\mathrm{pol}}{=}0.25

\lambda_{\mathrm{band}}{=}5.0

\lambda_{\mathrm{BTO}}{=}1.0

\gamma_{x}{=}\gamma_{y}{=}6.0

\gamma_{\mathrm{persp}}{=}1.0

. The best setting (lowest MAE mean) is highlighted in bold. See Sec. S4

$d$	$M_{\text{ego}}$	all		$\lambda_{\phi}=0$		$\lambda_{r}=0$		$\lambda_{\text{pol}}=0$		$\lambda_{\text{band}}=0$		$\lambda_{\text{BTO}}=0$
$2$ m	1	92.8 $\pm$	18.4	98.8 $\pm$	21.5	$F$		5701.9 $\pm$	3786.9	92.8 $\pm$	18.4	92.8 $\pm$	18.4
$2$ m	2	90.1 $\pm$	16.9	2347.5 $\pm$	2766.6	9327.1 $\pm$	175.7	2103.3 $\pm$	4024.6	89.7 $\pm$	16.6	90.1 $\pm$	16.9
$2$ m	3	680.2 $\pm$	974.9	3883.1 $\pm$	7372.4	8430.9 $\pm$	1589.7	7438.6 $\pm$	1700.5	1319.7 $\pm$	1522.6	612.5 $\pm$	841.1
$2$ m	4	7212.5 $\pm$	332.2	7807.8 $\pm$	3357.2	8720.0 $\pm$	1068.0	7427.7 $\pm$	950.7	$F$		6821.1 $\pm$	475.0
$2$ m	5	7488.4 $\pm$	2162.5	6718.4 $\pm$	2246.1	$F$		7142.7 $\pm$	1866.7	7452.8 $\pm$	1056.6	8434.2 $\pm$	974.4
$2$ m	6	7981.4 $\pm$	1705.1	8902.2 $\pm$	307.7	8210.8 $\pm$	2099.4	8182.7 $\pm$	1695.0	7997.8 $\pm$	1939.9	7868.9 $\pm$	899.4

Table S2 : Loss term ablation. Mean Absolute Error (MAE) of RPM (lower is better) under 4‑fold cross‑validation on the Timestamped Quadcopter with Egomotion (TQE) dataset, reported for two camera–target distances (2 m / 4 m) and seven egomotion levels

M_{\text{ego}}

. “All” uses the full batch objective in Eq. ( 4 ) with: phase–geometry alignment

r_{\phi}

, radial centering

r_{r}

, polarity alignment

r_{\text{pol}}

, soft annulus barriers

r_{\text{in}},r_{\text{out}}

, and Balanced Tip Occupancy

\ell_{\text{BTO}}

. Each ablation zeroes the indicated coefficient

(\lambda_{\phi},\lambda_{r},\lambda_{\text{pol}},\lambda_{\text{band}},\lambda_{\text{BTO}})

. TQE ground-truth RPM has

\mu\pm\sigma=11193.5\pm 3540.2

. Values are mean

\pm

std.

				MArE (%) $\downarrow$			MAE (RPM) $\downarrow$			RMSE (RPM) $\downarrow$
$d$	$M_{\text{ego}}$	propeller		ours	AEB [ 15 ]	DeepEv [ 4 ]	ours	AEB [ 15 ]	DeepEv [ 4 ]	ours	AEB [ 15 ]	DeepEv [ 4 ]
$2$ m	1	rear	right	1.3	61.4	8564.8	93.7 ✓	5980.8	652423.7	215.9	7186.8	785896.2
		rear	left	1.3	0.9	402.4	81.4 ✓	73.0	32090.3	241.4	241.2	46466.0
		front	left	1.5	35.3	4132.0	118.4 ✓	2487.0	303141.3	194.1	3302.9	359054.3
		front	right	1.2	65.5	94.6	77.8 ✓	5650.8	8759.2	186.3	7673.3	9700.4
	2	rear	right	1.2	52.1	9523.5	85.0 ✓	4637.6	749060.3	178.9	5549.9	904654.7

Table S3 : Benchmark, Timestamped Quadcopter with Egomotion (TQE). For each presented method and setting (camera-target distance

d

, egomotion level

M_{\text{ego}}

\mu\pm\sigma\!=\!11193\pm 3540

\min

917

\max

15768

M_{\text{ego}}=1

roughly means “slow camera movement”, while

M_{\text{ego}}=5

means “fast camera movement” (see Fig. 2 ). As

M_{\text{ego}}

increases, the camera experiences stronger egomotion, leading to increase of the number of events generated in the background.

$rb$	$\Delta t$	$q_{xy}$	$q_{q}$	MArE (%) $\downarrow$		median	MAE (RPM) $\downarrow$		median
22	2	0.2	0.25	496.419 $\pm$	402.402	428.662	39026.775 $\pm$	35704.452	27149.123
22	2	0.2	0.5	538.978 $\pm$	532.238	335.813	41383.706 $\pm$	40575.234	24252.682
22	2	0.2	1	650.760 $\pm$	610.255	580.914	49669.433 $\pm$	45197.183	44281.303
22	2	0.2	2	697.412 $\pm$	668.144	537.904	53110.765 $\pm$	50873.870	39796.295
22	2	1	0.25	587.555 $\pm$	478.454	411.100	39086.051 $\pm$	29527.280	26570.284
22	2	1	0.5	544.618 $\pm$	510.582	401.498	41860.949 $\pm$	39341.854	30303.074

Table S4 : AEB-Tracker grid search results. MAE and MArE reported as

\mu\pm\sigma

. See Sec. S3 for description.

Visual Object Tracking

Visual object tracking follows objects across video frames, maintaining their locations and identities despite motion, occlusion, and changing appearance.

See all 175 papers

CoHelix: Event-Based Multi-Propeller Rotation-Rate Tracking with Shared Projective Geometry
Oct 22, 2026Radim Spetlik, Tobiáš Vinklárek, Jan Klivan +3Event-Based Vision
Czech Technical University in Prague, Faculty of Electrical Engineering
Relative State Estimation using Event-Based Propeller Sensing
Apr 20, 2026Ravi Kumar Thakur, Luis Granados Segura, Jan Klivan +4Event-Based Vision Multi-Robot Systems
Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo Namesti 13, 121 35 Prague 2, Czechia
Event-Only Drone Trajectory Forecasting with RPM-Modulated Kalman Filtering
Mar 2, 2026Hari Prasanth S. M., Pejman Habibiroudkenar, Eerik Alamikkotervo +2Trajectory Prediction Kalman Filtering
Department of Energy and Mechanical Engineering, Aalto University, 02150 Espoo, Finland

Oct 22, 2026J/K move · Enter open · S save

CoHelix: Event-Based Multi-Propeller Rotation-Rate Tracking with Shared Projective Geometry

Radim Spetlik, Tobiáš Vinklárek, Jan Klivan, Tomáš Kestřánek+2

Czech Technical University in Prague, Faculty of Electrical Engineering

Event-Based Vision

Open paper AskPDF arXiv

Estimating propeller rates from a moving event camera requires separating blade rotation from the changing image geometry. Background activity mixes with blade events, while repeated blade appearances admit half- and double-rate ambiguities. We propose CoHelix, a recursive filter that estimates one shared homography and separate rotation states for four rigidly mounted, coplanar propellers. Each admitted event updates its assigned rotation state, and its accepted geometry measurements correct the shared homography used to interpret later events from every propeller. We report lock, the fraction of evaluated time for which an estimate remains within 2% of synchronized ground truth, because mean error alone does not show how long a tracker follows the true rate. With fixed-rate initialization, leave-one-recording-out evaluation on moving-camera data gives CoHelix 62.9% lock, compared with 39.8% for HelixTrack and 22.2% for EventPro. With other settings fixed, allowing four geometry contributors instead of one raises lock from 3.4% to 62.9%. On a private target-follower dataset with a different target quadcopter, CoHelix retains the measurement settings selected on moving-camera data and uses a fixed initial rate. It reaches 95.9% lock, compared with 56.2% for HelixTrack and 61.1% for EventPro.

Abstract

Visual Object Tracking

Explore similar work

CoHelix: Event-Based Multi-Propeller Rotation-Rate Tracking with Shared Projective Geometry

Relative State Estimation using Event-Based Propeller Sensing

Event-Only Drone Trajectory Forecasting with RPM-Modulated Kalman Filtering