Event-Based Single Integration

• Event-Based Single Integration is an event-only intensity reconstruction method that incrementally updates a per-pixel log-intensity accumulator with each incoming event.
• It employs an enhanced, adaptive decay algorithm that reduces noise and stale information while preserving critical contrast and edge details in low-light UAV applications.
• This lightweight, real-time approach avoids complex optimization, achieving 100 FPS on low-power CPUs for dynamic event-camera perception.

Searching arXiv for the primary ESI paper and closely related/disambiguation papers. Event-Based Single Integration (ESI) is an event-only intensity reconstruction scheme for event cameras that reconstructs grayscale images from asynchronous event streams by maintaining a single per-pixel accumulator of log-intensity change, applying one integration step per event, and combining that update with an enhanced decay algorithm (Dong et al., 4 Aug 2025). In the event-vision literature represented here, ESI is presented as a model-based, extremely lightweight method designed for real-time onboard UAV perception, with the explicit goals of preserving the intrinsic advantages of event cameras, enabling the portability of conventional frame-based vision methods to event-based scenarios, and sustaining a reconstruction rate of typically 100 FPS under challenging conditions such as extremely low illumination (Dong et al., 4 Aug 2025). The acronym is not uniform across recent arXiv usage: in "Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability" ESI denotes "Exhaustive Symbolic Integration" (Desmond, 6 May 2026), while in "Single-Image HDR Reconstruction Assisted Ghost Suppression and Detail Preservation Network for Multi-Exposure HDR Imaging" it denotes "Enhancement Stop Image" (Li et al., 2024). In the present sense, however, ESI refers specifically to event-based single integration for event-camera intensity reconstruction (Dong et al., 4 Aug 2025).

1. Terminology, scope, and problem setting

Event-Based Single Integration was introduced as a streamlined event-based intensity reconstruction scheme for UAV real-time perception, motivated by the need to extract and utilize effective information from asynchronous event streams under onboard computational constraints (Dong et al., 4 Aug 2025). The method is explicitly event-only: it reconstructs intensity images from pure event streams in real time and does not depend on conventional frames, thereby avoiding the exposure bottleneck that limits frame-based sensing in low light (Dong et al., 4 Aug 2025).

The target operating regime is defined by several constraints stated in the source material. ESI is intended for onboard computation on a low-power CPU without GPU, high-frame-rate reconstruction at 100 FPS from a DAVIS346 operating at up to 12 million events/s, and visually adverse environments including 2–10 lux illumination, high dynamic range, motion blur, event noise, hot pixels, and ghost structures from long-term accumulation (Dong et al., 4 Aug 2025). The method is structured around three implementation commitments: maintain a single per-pixel accumulator of log-intensity change, update this accumulator on each event with one integration step, and apply a specially designed time decay directly on the accumulator (Dong et al., 4 Aug 2025).

The phrase "single integration" is used in opposition to prior model-based approaches that rely on double or multiple integrations and explicit optimization. The paper contrasts ESI with methods using double integral with threshold optimization or sharpness-based cost functions, as well as with learning-based approaches such as E2VID and FireNet, which provide excellent quality but are computation-heavy and require GPU (Dong et al., 4 Aug 2025). ESI therefore occupies a deliberately narrow design space: it abandons complex optimization and multi-stage integration, treats each event as a small increment in log intensity, and relies on decay to counteract noise and stale information (Dong et al., 4 Aug 2025).

A common source of ambiguity is terminological rather than technical. The same acronym appears in unrelated contexts on arXiv. "Exhaustive Symbolic Integration" studies symbolic integrability by exhaustive differentiation (Desmond, 6 May 2026), and "Enhancement Stop Image" is a frame-based auxiliary image in HDR reconstruction (Li et al., 2024). Neither corresponds to event-camera single-pass integration. This distinction matters because "ESI" alone is insufficient to identify the method family without domain context.

2. Event generation model and reconstruction formulation

The mathematical formulation of ESI begins with the event generation model for an event camera pixel. For a pixel $(x,y)$ with log intensity $L(x,y,t)$, an event is represented as

$e = (x, y, t, p),\quad p \in \{+1,-1\},$

where $p=+1$ denotes a brightness increase and $p=-1$ a decrease (Dong et al., 4 Aug 2025). The triggering condition is

$\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$

with $t_k$ the time of the last event at $(x,y)$ and $c$ the contrast threshold (Dong et al., 4 Aug 2025).

Under the idealized impulse view of events, the relationship between log intensity at two times $t_1$ and $L(x,y,t)$0 is written as

$L(x,y,t)$1

for the signed event stream $L(x,y,t)$2 at that pixel (Dong et al., 4 Aug 2025). ESI then makes its defining simplification: absolute log intensity at the baseline time is unknown, and baseline intensity differences across pixels are assumed negligible relative to motion-induced changes. Under that assumption, reconstruction proceeds from the integrated event increments alone:

$L(x,y,t)$3

In implementation, this estimated log-intensity change is maintained per pixel as an accumulator $L(x,y,t)$4 up to scaling (Dong et al., 4 Aug 2025).

The paper states the consequences of this approximation directly. Moving objects produce strong event activity and therefore clear structures in $L(x,y,t)$5. Static background baseline is unknown, which leads to reverse intensity artifacts at past positions. Without forgetting, noise accumulates rapidly (Dong et al., 4 Aug 2025). These limitations motivate the decay mechanism added to the raw single integration. With decay, the model becomes

$L(x,y,t)$6

where $L(x,y,t)$7 is decreasing in time so that older events contribute less (Dong et al., 4 Aug 2025).

The resulting reconstruction is relative rather than absolute. The source explicitly states that absolute photometric fidelity is not available and that baseline intensity differences between areas are ignored (Dong et al., 4 Aug 2025). This makes ESI best understood as a dynamic contrast reconstruction method that outputs frame-compatible intensity-like images rather than a calibrated radiometric estimator. A plausible implication is that its operational value lies less in photometry than in preserving the geometric and contrast information required by downstream vision modules.

3. Accumulator dynamics, enhanced decay, and clamping

The core technical contribution of ESI is the enhanced decay mechanism applied directly to the accumulated state rather than to stored event history. A naive implementation of the decayed accumulation in Eq. (3) would require storing all undecayed events, which the paper identifies as impossible at millions of events/s on board (Dong et al., 4 Aug 2025). ESI avoids that requirement by maintaining only two per-pixel scalars: the accumulator $L(x,y,t)$8 and the last decay timestamp $L(x,y,t)$9 (Dong et al., 4 Aug 2025).

The decay function is defined as an exponentially weighted polynomial with finite support:

$e = (x, y, t, p),\quad p \in \{+1,-1\},$0

The exact accumulator at a given pixel, for event times $e = (x, y, t, p),\quad p \in \{+1,-1\},$1, is expressed as

$e = (x, y, t, p),\quad p \in \{+1,-1\},$2

with a suitable convention for $e = (x, y, t, p),\quad p \in \{+1,-1\},$3 (Dong et al., 4 Aug 2025). In practice, the history is not stored; the update is incremental.

For each incoming event $e = (x, y, t, p),\quad p \in \{+1,-1\},$4, ESI performs the following update sequence (Dong et al., 4 Aug 2025):

1. Compute $e = (x, y, t, p),\quad p \in \{+1,-1\},$5.
2. Compute the decay factor

$e = (x, y, t, p),\quad p \in \{+1,-1\},$6

1. Apply decay:

$e = (x, y, t, p),\quad p \in \{+1,-1\},$7

2. Integrate the new event:

$e = (x, y, t, p),\quad p \in \{+1,-1\},$8

3. Update the timestamp:

$e = (x, y, t, p),\quad p \in \{+1,-1\},$9

4. Clamp the accumulator:

$p=+1$0

Here $p=+1$1 is a tunable constant proportional to the log-intensity threshold $p=+1$2 (Dong et al., 4 Aug 2025). The assumptions listed in the paper are that the physical contrast threshold $p=+1$3 is approximately constant or absorbed into $p=+1$4, baseline intensity differences are negligible compared to motion-induced changes, event noise exists and is mitigated by decay and clamping rather than explicitly modeled, and timestamps arrive at microsecond resolution (Dong et al., 4 Aug 2025).

The enhanced decay is contrasted with a simple exponential decay model $p=+1$5 (Dong et al., 4 Aug 2025). Two properties are emphasized. First, finite support: for $p=+1$6, $p=+1$7, so old events vanish completely in finite time, which strongly limits long-term noise accumulation (Dong et al., 4 Aug 2025). Second, event-rate adaptivity: when $p=+1$8 is small, decay per interval is small; when $p=+1$9 is large, decay is strong (Dong et al., 4 Aug 2025). The paper proves the inequality

$p=-1$0

meaning that many short intervals produce less total decay than one long gap of equal total duration (Dong et al., 4 Aug 2025). High-rate regions therefore retain more intensity, while low-rate regions decay faster.

Clamping serves two stated roles. It suppresses hot pixels that would otherwise accumulate very large $p=-1$1 and dominate the contrast range, and it improves robustness to illumination changes that would otherwise shift or saturate the dynamic range of $p=-1$2 (Dong et al., 4 Aug 2025). The output grayscale image is then obtained by linear mapping:

$p=-1$3

Because $p=-1$4 is treated as proportional to log-intensity change, the paper states that a linear mapping suffices (Dong et al., 4 Aug 2025).

4. Algorithmic pipeline and computational profile

The processing pipeline is asynchronous at the event level and periodic at the frame readout level. Initialization sets $p=-1$5 and $p=-1$6 for all pixels and chooses the global parameters $p=-1$7, $p=-1$8, $p=-1$9, $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$0, and $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$1 (Dong et al., 4 Aug 2025). Event processing follows the per-event update rule described above. Frame readout occurs periodically, for example at 100 Hz, and maps the current accumulator state to an 8-bit grayscale image (Dong et al., 4 Aug 2025). The paper notes that the pseudocode decays only on events; in practice this is often sufficient, although an optional final decay step at frame time may also be applied (Dong et al., 4 Aug 2025).

Frame-rate control is tied to the event packetization behavior of the DAVIS346. The camera emits events asynchronously at up to approximately $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$2M events/s and packages them for output at a maximum frequency of $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$3 Hz (Dong et al., 4 Aug 2025). ESI therefore processes events as they arrive and outputs one reconstructed frame at each packet time, yielding a reconstruction frame rate set to $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$4 FPS and synchronized to the packet rate (Dong et al., 4 Aug 2025). Reconstruction is thus purely time-driven rather than event-count-driven.

The computational structure is explicitly constant-time per event. Complexity per event is $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$5, consisting of scalar subtraction, multiplication, power, addition, and clamping, while memory is $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$6 because only $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$7 and $\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$8 are stored (Dong et al., 4 Aug 2025). This low-memory, low-state design is central to the paper's claim of onboard suitability.

The reported runtime benchmark on an Intel i7-1185G7E @ 1.8 GHz is summarized below (Dong et al., 4 Aug 2025).

Method	Throughput
ESI	$\bigl| L(x,y,t) - L(x,y,t_k) \bigr| \ge c,$9 ev/s
FEDI	$t_k$0 ev/s
Camera plugin	$t_k$1 ev/s
Complementary filter	$t_k$2 ev/s
E2VID	$t_k$3 ev/s
FireNet	$t_k$4 ev/s

These figures support several bounded conclusions stated in the source. ESI is slightly slower than the barebones camera plugin because its decay is more complex, faster than FEDI and the complementary filter on CPU, and orders of magnitude faster than the learning-based methods even when those are run on RTX4070 hardware (Dong et al., 4 Aug 2025). Since the DAVIS346 maximum rate is approximately $t_k$5M events/s and ESI handles approximately $t_k$6M events/s, the paper concludes that ESI comfortably runs in real time at $t_k$7 FPS even under extreme dynamic scenes (Dong et al., 4 Aug 2025).

The implementation details reinforce the same profile. The method is implemented as C++/ROS nodes on Ubuntu 20.04, using a DAVIS346 event camera and a TGU8 onboard computer with an Intel Core i7-1185G7E @ 1.8 GHz (Dong et al., 4 Aug 2025). Per-pixel storage is just the float accumulator and the last timestamp; exact numeric hyperparameter values are not listed, but the required parameters are $t_k$8, $t_k$9, $(x,y)$0, $(x,y)$1, and $(x,y)$2 (Dong et al., 4 Aug 2025).

5. Empirical evaluation against model-based and learning-based baselines

The paper evaluates ESI against five named baselines: FEDI, the DAVIS camera plugin, complementary filter, E2VID, and FireNet (Dong et al., 4 Aug 2025). These methods span frame-plus-event fusion, simple decayed accumulation, event-frame complementary estimation, and learning-based event reconstruction. The comparison is not limited to image quality; it also includes temporal resolution and runtime.

Under AprilTag detection in 2–6 lux with a moving camera, the total number of reconstructed frames is 6200 at 100 FPS for event-only methods (Dong et al., 4 Aug 2025). Detection counts and rates are reported as follows (Dong et al., 4 Aug 2025):

Method	Detection count	Detection rate
ESI	5046	81.39%
Camera plugin	2871	46.31%
Complementary filter	2693	43.44%
FEDI	18	14.52%
E2VID	5495	88.63%
FireNet	5748	92.71%

The paper interprets these results in a specific way. Learning-based methods achieve the best image quality and detection, but are not real-time onboard. ESI's detection rate is close to E2VID and FireNet and much higher than the other model-based schemes. Camera plugin and complementary filter exhibit strong trailing artifacts and low contrast, while ESI's improved decay better preserves edges and reduces shadows (Dong et al., 4 Aug 2025). FEDI is limited by motion-blurred base frames in low light because exposure reaches $(x,y)$3 s, yielding $(x,y)$4 FPS and large blur and delay (Dong et al., 4 Aug 2025).

Temporal resolution is a decisive differentiator in the reported experiments. ESI, camera plugin, complementary filter, E2VID, and FireNet operate at 100 FPS when run on events only, whereas FEDI is limited to 2 FPS by conventional exposure time (Dong et al., 4 Aug 2025). The paper states that 2 FPS is inadequate for UAV real-time perception and tracking (Dong et al., 4 Aug 2025).

Computational-cost comparisons further separate the methods by deployment regime. ESI is CPU-only and real-time on both TGU8 and Intel i7, with low memory consumption; E2VID and FireNet require an RTX4070-class GPU and remain non-real-time even on desktop hardware for the tested 62-second sequence, taking 428.79 s and 255.73 s respectively (Dong et al., 4 Aug 2025). This establishes a recurring tradeoff in the article: deep models yield cleaner reconstructions, but ESI offers a more favorable compute-quality operating point for small airborne platforms.

The qualitative notes supplied in the paper are consistent with these metrics. ESI images still exhibit some noise and trailing and are less clean than E2VID or FireNet, but they remain clearly sufficient for AprilTag detection. The camera plugin often shows dark ghost shadows from previous positions due to its decay behavior (Dong et al., 4 Aug 2025). This suggests that the main empirical advantage of ESI is not maximally faithful reconstruction, but a better balance among contrast retention, trail suppression, and deployable throughput.

6. UAV tracking deployment and practical significance

The paper embeds ESI in a complete UAV tracking pipeline rather than evaluating it only as an isolated reconstruction module (Dong et al., 4 Aug 2025). The hardware stack consists of a 250 mm wheelbase UAV carrying a DAVIS346 event camera with $(x,y)$5 resolution, $(x,y)$6 resolution, and $(x,y)$7 dB dynamic range, a TGU8 onboard computer, and a Pixhawk 6cmini flight controller (Dong et al., 4 Aug 2025). The tracked target is a $(x,y)$8 AprilTag board mounted on a UGV, with OptiTrack used for ground-truth UAV and UGV positions, and an IR cut filter on the DAVIS to avoid motion-capture IR interference (Dong et al., 4 Aug 2025).

The software stack uses Ubuntu 20.04, ROS, the DAVIS ROS driver, a C++/ROS node implementing ESI at 100 FPS, an AprilTag detector operating on the reconstructed frames, an Extended Kalman Filter estimating UGV motion state, and a controller commanding the UAV to track the UGV (Dong et al., 4 Aug 2025). This is important because it demonstrates the intended notion of "portability of conventional frame-based vision methods": ESI reconstructs a standard intensity image, after which established frame-based perception can proceed unchanged (Dong et al., 4 Aug 2025).

The principal flight experiment takes place under 2–10 lux illumination. The UGV moves randomly through straight motion, an obstacle zone with frequent turns, and a final straight motion while the UAV lands on the UGV platform, over a duration of 62 s (Dong et al., 4 Aug 2025). ESI reconstructs 6540 frames at 100 FPS and the AprilTag is detected 4589 times, yielding a 74% success rate (Dong et al., 4 Aug 2025). The same recorded events are then processed offline with comparison methods. Detection counts by motion phase are (Dong et al., 4 Aug 2025):

Scheme	Straight	Turning	Landing	Total
ESI	2626	1252	711	4589
FEDI	51	14	8	73
Camera plugin	444	493	154	1091
Complementary filter	2208	706	659	3573

The phase-by-phase interpretation is explicit. In straight motion, where relative motion and event rate are low, the camera plugin decays too fast and loses contrast, while ESI's polynomial decay and event-rate adaptivity preserve texture and improve detection reliability (Dong et al., 4 Aug 2025). In turning, where event rate is high, camera plugin and complementary filter exhibit pronounced trailing or shadows, whereas ESI retains sharper edges with less trailing (Dong et al., 4 Aug 2025). In landing, FEDI remains ineffective because the conventional frames are blurred, while ESI maintains sufficient contrast and geometry for detection until touchdown (Dong et al., 4 Aug 2025).

The paper therefore concludes that only ESI simultaneously achieves real-time onboard operation on TGU8, high frame rate at 100 FPS, and high detection rates across all motion phases under 2–10 lux (Dong et al., 4 Aug 2025). The failure modes of alternatives are categorized as insufficient frame rate for FEDI, poor image quality and trail artifacts for the camera plugin, moderate but insufficient quality for the complementary filter, and excessive computational demand for E2VID and FireNet (Dong et al., 4 Aug 2025). This framing situates ESI less as a universal best reconstructor than as a method optimized for the specific system constraints of small UAV perception.

7. Strengths, limitations, and relation to adjacent meanings of ESI

The strengths claimed for ESI are tightly coupled to its design choices. It delivers real-time, high-FPS operation on a small CPU, supports event-only reconstruction without dependency on conventional frames, produces standard intensity images compatible with existing frame-based detectors and trackers, preserves event-camera advantages such as high dynamic range and motion-blur immunity, and uses adaptive decay plus clamping for robustness to sparse noise, hot pixels, and illumination flicker (Dong et al., 4 Aug 2025). The paper additionally argues that no per-scenario tuning is needed for the adaptive decay behavior itself, because the inequality $(x,y)$9 produces the desired event-rate dependence intrinsically (Dong et al., 4 Aug 2025).

The stated limitations are equally specific. ESI reconstructs relative intensity only and ignores baseline intensity differences between areas, so absolute photometric fidelity is unavailable (Dong et al., 4 Aug 2025). Artifacts remain compared with deep learning approaches, including residual noise, trailing, and brief reverse-contrast effects in low-motion or highly noisy regions (Dong et al., 4 Aug 2025). The choice of $c$0, $c$1, $c$2, $c$3, and $c$4 affects smoothing, sharpness, and forgetting speed, and the paper does not provide a detailed ablation over $c$5 and $c$6 (Dong et al., 4 Aug 2025). Noise suppression is purely implicit through decay and clamping; there is no explicit denoiser or probabilistic noise model (Dong et al., 4 Aug 2025).

In broader context, the paper places ESI between physically motivated model-based methods and learning-based methods (Dong et al., 4 Aug 2025). Formation-model-based approaches such as double integral, complementary filtering, and FEDI aim for physical correctness but may require conventional frames or optimization loops. Learning-based approaches achieve state-of-the-art image quality and better denoising but are heavily GPU-dependent and not yet practical for small UAVs (Dong et al., 4 Aug 2025). ESI is described as a pragmatic middle ground: model-based, training-free, event-only, almost as fast as the simplest accumulators, but significantly better in quality because of its improved decay algorithm (Dong et al., 4 Aug 2025).

The acronym overlap with unrelated literatures is noteworthy because it can produce bibliographic confusion. In symbolic mathematics, ESI means "Exhaustive Symbolic Integration" and refers to exhaustive enumeration of symbolic function spaces for integration by differentiation (Desmond, 6 May 2026). In a multi-exposure HDR pipeline, ESI means "Enhancement Stop Image" and denotes a single-channel auxiliary image derived from an LDR reference frame in IPT space (Li et al., 2024). Neither is connected to event-camera reconstruction. For event vision, "Event-Based Single Integration" should therefore be understood as the specific per-pixel, single-pass accumulation-and-decay method defined above (Dong et al., 4 Aug 2025).

The future directions listed in the source include learning-enhanced ESI, noise-aware variants, integration with SLAM and depth, adaptive parameter tuning based on event statistics, and hardware-specific optimization using SIMD, GPU, or FPGA back ends (Dong et al., 4 Aug 2025). These proposals are not yet results. They indicate, however, that the method is intended as an efficient substrate that may be extended rather than as a terminal reconstruction architecture. A plausible implication is that ESI's main lasting contribution may be architectural: it identifies a minimal state representation and decay law that preserve enough scene structure to make event-only, frame-compatible perception practical on embedded platforms.