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

Radim Spetlik; Tobiáš Vinklárek; Jan Klivan; Tomáš Kestřánek; Matouš Vrba; Jiří Matas

cs.ROOct 22, 2026

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

Authors: Radim Spetlik, Tobiáš Vinklárek, Jan Klivan, Tomáš Kestřánek, Matouš Vrba, Jiří Matas

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

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Coupled geometry and rotation estimation. The shared homography $\mathbf{H}$ maps the rotor plane to the image. The filter maps event $e_{i}$ by $\mathbf{H}^{-1}$ , assigns it to a propeller and applies spatial checks. An admitted event updates its assigned rotation state $\mathbf{x}_{k}$ , and its accepted geometry measurements correct $\mathbf{H}$ for later events from every propeller. Each state $\mathbf{x}_{1},\ldots,\mathbf{x}_{4}$ contains phase, rate and acceleration and supplies its own shaft-rate estimate $\widehat{\mathrm{RPM}}_{1},\ldots,\widehat{\mathrm{RPM}}_{4}$ . Insets integrate $10$ ms from the highest-motion $4$ m recording; color denotes polarity. Green curves show equal rotor-plane rings and their different image projections under the same homography; grey lines join their centres.

	HelixTrack [ 26 ]	CoHelix
Geometry	one map per propeller	one map for all propellers
Geometry update	batched Gauss–Newton	per-event Kalman
Rotation states	separate per propeller	separate per propeller

Table 1: Geometry and rotation updates. Both methods update phase per event. CoHelix also uses accumulated centre measurements and an ellipse-based drift observer.

Figure 2: Event streams and tracked propellers. Each panel integrates $10$ ms of events; warm and cool colors show the two polarities. Columns begin about $0.5$ s after the fixed evaluation cut of each recording and continue every $0.4$ s. These times were chosen without examining tracker output. The first two rows show the highest camera-motion levels at $2$ and $4$ m. The third row shows the target–follower recording in which the camera travels farthest. Green circles are the propeller rings tracked by CoHelix, and grey lines connect their centres under the shared geometry. Sec. S4.2 gives the exact timestamps.

		CoHelix				HelixTrack [ 26 ]				EventPro [ 4 ]
$d$	$M_{\text{ego}}$	$T_{\text{lock}}$	%	MAE	cov%	$T_{\text{lock}}$	%	MAE	cov%	$T_{\text{lock}}$	%	MAE	cov%
$2$ m	1	94.6	82	43	100	93.6	81	47	100	51.2	45	1000	100
	2	89.3	81	44	100	88.7	80	45	100	38.2	34	1348	100
	3	90.3	81	56	100	75.2	68	33661	100	34.2	31	1256	99
	5	53.4	46	1565	100	5.9	5	3825	92	6.5	6	2119	45
	6	43.8	39	7653	100	2.7	2	4347	100	2.1	2	2330	31

Table 2: Timestamped Quadcopter with Egomotion benchmark : 12 recordings

\times

4 propellers,

1356.9

propeller-seconds. Every tuned setting was selected without the recording it scores. CoHelix and HelixTrack [ 26 ] start every propeller at

4\,750

shaft RPM. Every method is scored at every timestamp. % is the lock percentage (Eq. 3 ),

T_{\text{lock}}

is its duration in propeller-seconds, MAE is the mean absolute shaft-RPM error and cov % is coverage, the percentage of evaluation timestamps with an estimate. Higher is better except for MAE. Bold marks the best lock and error values in each row; coverage is descriptive. The damaged

2

M_{\text{ego}}\!=\!4

recording is reported separately in Sec. S4.1 .

Method	$T_{\text{lock}}$	%	MAE	cov%
CoHelix	770.4	95.9	68.4	100.0
EventPro [ 4 ]	490.9	61.1	115.0	100.0
HelixTrack [ 26 ]	451.7	56.2	1767.1	98.0

Table 3: Private target–follower dataset : 3 recordings

\times

4 propellers,

803.6

propeller-seconds. CoHelix and HelixTrack [ 26 ] are initialized at

9\,500

shaft RPM. The CoHelix and EventPro [ 4 ] configurations were selected on the TQE recordings and applied unchanged. Lock is the percentage of evaluated propeller-time;

T_{\text{lock}}

is the corresponding duration. MAE is mean absolute shaft-RPM error; cov % is coverage, the percentage of evaluation timestamps with an estimate.

Figure 3: Shaft rate over time for one propeller in four recordings spanning the camera-motion range. Rows show CoHelix, HelixTrack [ 26 ] and EventPro [ 4 ] together with the same dashed ground-truth reference, filtered by a centred $55$ ms median for display only; scoring uses the synchronized trace without filtering. The vertical axis ends at $1.25\times$ the largest filtered reference rate, so larger estimates are clipped. Gaps in the EventPro row are samples for which that method does not report.

Comparison	Change [points]	95 % interval
four contributors vs. one	$+59.6$	$[47.8,70.1]$
per-event Kalman vs. selected Gauss–Newton window	$+23.1$	$[3.7,43.5]$
correlations retained vs. cleared	$-2.1$	$[-13.8,6.8]$
restricted vs. full homography	$+3.9$	$[-6.5,13.4]$

Table 4: Effects of four design choices on the 12 TQE recordings. Each row compares the two named versions under the same evaluation conditions. Change is the lock percentage of the first version minus that of the second; positive values favour the first. Intervals resample complete recordings. Sec. S6 gives the absolute results.

Measurement	Weight	Used
R1 helical phase-dynamics (phase)	$\mathcal{I}=\max\{10^{-3},\kappa w_{\text{ring}}\}$	✓
R2 geometry helical-phase	$\lambda_{\phi}=1$	$\times$
R3 radial $(r-1)$ , symmetric window	$\lambda_{r}=2.000$	✓
R4 band barriers, gate-following	$\lambda_{\text{band}}=4.000$	✓
R5 polarity	$\lambda_{\text{pol}}=0.500$	✓
R6 propeller centre, two measurements per $2\,000$ events	none	✓

Table S1 : Measurements considered in this study. A check mark indicates that the measurement is used in the reported configuration. The radial, annulus and polarity weights were selected together; rotating silhouette and signed crossing use separately selected weights. The propeller-centre update requires

N_{\text{eff}}\geq 50

and uses variance inflation

\iota=3.0

Parameter	Value	Role
Measurement weights in the fixed ablation configuration
$\lambda_{r}$ (radial) / $\lambda_{\text{band}}$ / $\lambda_{\text{pol}}$	$2.000$ / $4.000$ / $0.500$	weights of R3 / R4 / R5
$\lambda_{\text{sc}}$ (signed crossing) / $\lambda_{\text{sil}}$ (silhouette)	$0.200$ / $0.400$	weights of R7e / R7c
$\lambda_{\phi}$ (helical phase $\to$ geometry)	$1.0$ , measurement omitted	R2 not used
radial symmetric window / band gate-following	on / on	measurement support
$b_{\text{in}}$ , $b_{\text{out}}$ , $\tau$ (band)	$0.3$ , $1.3$ , $0.05$	softplus barriers

Table S2 : Fixed configuration used for the mechanism ablations. The primary benchmark instead selects the measurement weights inside each recording-level outer fold. Radii and annulus boundaries use propeller-local units; translations use pixels;

h_{31}

and

h_{32}

use inverse propeller-radius units; and angular rates use rad s -1 unless an internal limit is stated in blade-pass RPM. Reported rates use shaft RPM.

Dataset	Method	$1$ %	$2$ %	$5$ %
Moving camera	CoHelix	45.62	62.94	76.79
	HelixTrack [ 26 ]	26.32	39.75	48.86
	EventPro [ 4 ]	15.22	22.22	28.84
Target–follower	CoHelix	32.63	95.87	99.35
	HelixTrack [ 26 ]	28.53	56.21	61.01
	EventPro [ 4 ]	30.49	61.09	90.98

Table S3 : Lock percentage at three relative-error thresholds. No method is retuned between columns.

Evaluation recording	Crossing, silhouette	Radial, annulus, polarity	$T_{\text{lock}}$	Lock	MAE	Coverage
			[s]	[%]	[RPM]	[%]
$2$ m, $M_{\text{ego}}=1$	$(.250,.250)$	$(2,8,.5)$	94.565	82.3	42.5	99.9
$2$ m, $M_{\text{ego}}=2$	$(.250,.250)$	$(2,8,.5)$	89.305	80.6	43.7	99.9
$2$ m, $M_{\text{ego}}=3$	$(.250,.250)$	$(0,4,.5)$	90.335	81.4	55.6	99.9
$2$ m, $M_{\text{ego}}=5$	$(.250,.250)$	$(2,8,.5)$	53.440	46.3	1565.3	99.8
$2$ m, $M_{\text{ego}}=6$	$(.200,.450)$	$(1,4,.25)$	43.835	39.1	7652.8	99.9

Table S4 : Two-stage configuration selection with fixed-rate initialization. Each moving-camera row names the configuration selected without that recording. The target–follower rows use one configuration selected on all 12 moving-camera recordings. MAE is in shaft RPM. The damaged

2

M_{\text{ego}}=4

stream is not an outer fold and is reported separately in Sec. S4.1 .

Crossing	Silhouette	Lock [%]	$\Delta$ [points]
off	off	76.0	0.0
on	off	77.0	+1.0
off	on	73.1	-2.8
on	on	82.3	+6.3

Table S5 : Fixed-configuration factorial for the signed-crossing and rotating-silhouette measurements on the 12 moving-camera and three target–follower recordings. The interaction is

+8.2

percentage points. These values are not outer-fold scores.

Radial	Band	Polarity	Lock [%]	$\Delta$ [points]
off	off	off	65.5	-13.7
off	off	on	78.7	-0.6
off	on	off	67.2	-12.0
off	on	on	68.6	-10.6
on	off	off	72.8	-6.4
on	off	on	79.8	+0.6

Table S6 : Fixed-configuration factorial for the radial, annulus and polarity measurements on the 15 intact recordings. Deltas use

(1,4,0.25)

as the reference. These values are not outer-fold scores.

Training	Test	Crossing, silhouette	Weights $(r,b,p)$	MAE	MArE	$T_{\text{lock}}$	Lock
propeller	propellers			[RPM]	[%]	[s]	[%]
0	1, 2, 3	$(0.20,0.30)$	$(0.25,2,0.30)$	435.8	9.83	790.215	71.66
1	0, 2, 3	$(0.20,0.30)$	$(0.50,2,0.25)$	667.8	14.28	744.750	67.50
2	0, 1, 3	$(0.125,0.35)$	$(0.25,1,0.40)$	980.6	23.99	793.770	71.94
3	0, 1, 2	$(0.20,0.30)$	$(0,4,0.40)$	633.9	13.86	759.300	68.82
All four folds				679.5	15.49	3088.035	69.98

Table S7 : Complete propeller-wise four-fold result on the 13 moving-camera recordings. Each fold selects both configuration stages using one propeller identity and tests the other three, giving 39 test tracks per fold and 156 track-fold predictions in total. MAE is in shaft RPM, and coverage is

100

% in every fold. Lock normalizes the summed duration over these predictions; each physical propeller track appears in three test folds.

Dataset	Initialization	$T_{\text{lock}}$ [s]	Lock [%]	MAE [RPM]
Moving camera	reference rate	857.9	63.2	834.5
	fixed $4\,750$ RPM	854.0	62.9	1383.1
Target–follower	reference rate	770.44	95.874	64.2
	fixed $9\,500$ RPM	770.40	95.869	68.4

Table S8 : Rate initialization for CoHelix. For each moving-camera recording, both rows use the configuration selected on the other 11 recordings and differ only in their initial rate. The target–follower rows use the configuration selected on all 12 moving-camera recordings. The fixed-rate rows are the reported setting; the reference-rate rows are a diagnostic comparison, not a main result. The fixed values are

4\,750

shaft RPM for moving camera and

9\,500

shaft RPM for target–follower.

Setting	$T_{\text{lock}}$	Lock %	MAE
Propellers contributing to shared geometry
one	45.5	3.4	10070
two	240.8	17.7	6954
three	680.5	50.2	1812
four	854.0	62.9	1383
Kalman and windowed Gauss–Newton geometry

Table S9 : Complete results for the controlled comparisons summarized in Table 4 . Each block has its own control, and only the named choice changes within that block.

T_{\text{lock}}

is in propeller-seconds, and MAE is in shaft RPM.

Recording	CoHelix	HelixTrack [ 26 ]	Speed ratio
$2$ m, $M_{\text{ego}}=1$	.0210	.0237	.88
$2$ m, $M_{\text{ego}}=2$	.0183	.0196	.93
$2$ m, $M_{\text{ego}}=3$	.0195	.0176	1.11
$2$ m, $M_{\text{ego}}=5$	.0241	.0122	1.98
$2$ m, $M_{\text{ego}}=6$	.0215	.0138	1.56
$2$ m, $M_{\text{ego}}=7$	.0268	.0107	2.50

Table S10 : End-to-end real-time factor for four rates. Higher is faster. Speed ratio is HelixTrack [ 26 ] wall time divided by CoHelix wall time, so values above one favour CoHelix. Each comparison uses one node, one CPU thread and two balanced repeats.

Annotation change	TQE lock [%]	Change [points]	Target lock [%]	Change [points]
Nominal	62.9	—	95.9	—
Centre displacement 1 %	66.4	+3.4 $[-1.0,8.3]$	95.9	+0.0 $[-0.0,0.1]$
Centre displacement 2 %	63.5	+0.6 $[-4.8,6.5]$	95.9	-0.0 $[-0.1,0.1]$
Centre displacement 5 %	61.0	-1.9 $[-11.7,5.9]$	88.4	-7.5 $[-23.9,0.0]$
Centre displacement 10 %	60.9	-2.0 $[-7.4,3.0]$	95.9	-0.0 $[-0.1,0.1]$
Radius multiplier $0.80$	55.4	-7.6 $[-17.2,0.4]$	94.9	-1.0 $[-1.9,-0.4]$

Table S11 : Sensitivity to supplied ring calibration on 12 TQE and three target–follower recordings, with selected measurement settings fixed. Lock scores all four rates at

2

% relative tolerance on the complete

5

ms grid; missing estimates are unlocked. Centre displacements are fractions of the nominal mean ring radius. Scores average four direction realizations within each recording. Radius multipliers apply to all four supplied rings. Changes are percentage points from the nominal row; brackets give 95 % intervals from

100\,000

paired recording resamples, with time denominators recomputed in each draw. Both perturbations change the assumed fixed layout.

Slots/s	Lock [%]		Change [points]	Filled slots [%]		Max. count gap [%]
	Single	Four		Single	Four	Mean	Individual
2000	1.2	2.9	+1.7 $[0.3,3.5]$	99.8	99.6	1.3	1.6
10000	1.1	1.4	+0.3 $[-0.3,1.3]$	93.6	83.7	34.7	39.1
100000	1.3	1.5	+0.2 $[-0.4,1.1]$	60.8	40.5	74.5	76.5
1000000	1.7	1.6	-0.1 $[-1.0,1.1]$	36.1	23.7	87.1	91.5

Table S12 : Contributor comparison under four equal geometry-event caps on all 12 TQE recordings, with the ellipse observer disabled. All four rate states enter the

2

% lock score; missing estimates are unlocked. Single averages the four single-contributor scores within each recording. Change is Four minus Single in percentage points, with 95 % intervals from

100\,000

paired recording resamples. Filled slots are selected events divided by scheduled opportunities. Count gaps are absolute selected-count differences divided by the larger count. Mean gives the maximum gap against the mean single count over recordings; Individual also maximizes over single masks. Equal caps do not imply equal realized measurements.

Slots/s	Contributor(s)	Lock [%]	Selected events [ $10^{3}$ ]	Accepted rows [ $10^{3}$ ]
2000	0	1.3	677.1	2166.8
2000	1	1.3	677.1	2000.0
2000	2	1.0	677.0	2115.2
2000	3	1.2	676.5	2176.8
2000	all four	2.9	675.4	2238.1
10000	0	0.9	3089.1	9359.1

Table S13 : Realized geometry input for each contributor condition in Table S12 . Single propellers use annotation indices

0

–

3

. Lock scores all four rates, including those that supply no geometry input. Selected events and accepted scalar geometry rows are totals over the 12 TQE recordings, in thousands. One selected event produces one or more scalar rows, and measurement rejection remains active. These counts exclude phase updates, which use every admitted event.

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Mar 10, 2026J/K move · Enter open · S save

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

Radim Spetlik, Michal Pliska, Vojtěch Vrba, Jiri Matas

Faculty of Electrical Engineering, Czech Technical University in Prague

Visual Object Tracking Event-Based Vision

Open paper AskPDF arXiv

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.

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