Our analysis of event cameras under various outdoor lighting showed distinct performance patterns, most notably in bright sunlight. This gave us deeper insight into the technical issues faced under these conditions.

The first impact is pixel saturation: The sun's potent luminance had resulted in widespread pixel saturation across the event camera sensor. The graphical representation clearly demarcates regions where the pixels are overwhelmed by the influx of photons, quickly exceeding their electron storage limits and as a result generating a false positive. In fact, once this threshold is crossed, additional photons do not amplify the accumulated charge in these pixels. This persistent state essentially means that the pixel remains unresponsive, or blind, to subsequent brightness variations until the overall luminance recedes to less than the saturation limit. In typical scenarios, these saturated pixels would simply lead to overexposed regions in an image. However, the ramifications for event cameras are more nuanced. Referring back to Fig. 2A where areas directly exposed to the sun manifest a significant increase in event generation (all the pixels were triggered at the same time), the sudden burst of events breaks the steady stream of data, creating gaps in the recorded information. This unevenness can lead to a distorted or incomplete view of moving scenes, which could be problematic for applications that rely on constant and real-time event data.

The second effect caused by bright sunlight is the diminished pixel sensitivity. Under the influence of intense brightness, the operational efficacy of the pixels in event cameras becomes markedly compromised. In less extreme lighting scenarios, these cameras excel in discerning even the most subtle shifts in luminance, ensuring that every meaningful change is registered as an event. However, under overly bright conditions, the intrinsic sensitivity of the pixels deteriorates. The challenge that arises is rooted in the pixel's diminished capacity to distinguish between varying brightness levels when overwhelmed with light. As the ambient background brightness increases, the subtle variations in light intensity that would otherwise trigger events become nearly indistinguishable from the dominant light source. As a result, the camera may register and return false negatives as seen in Fig. 2C, resulting in situations where significant brightness variations occur but are overshadowed by the prevailing luminance, causing the camera to not detect and register them. These false negatives can be particularly problematic. Since events might not be generated when ideally they should be, crucial details of the environment, as captured under dim light conditions in Fig. 2D, can remain uncaptured under intense natural luminance. This means that in the presence of a strong light source, such as direct sunlight, the camera could fail to capture important nuances of the surroundings, creating gaps in the data and potentially compromising the overall fidelity and accuracy of the camera's output.

Our analyses extend to the event camera's functioning in dim and dark outdoor environments, specifically during evenings, after sunset, and night devoid of bright sunlight. The presence of artificial lighting during these periods presents unique challenges, affecting not only the event data but also postprocessing techniques such as denoising algorithms.

Artificial light sources, in dark outdoor scenarios, result in a pronounced spatial disparity in the distribution of event data. In other words, artificial light affects data clustering performance. This disparity is most evident as regions of high data density near the light source. Such variance is influenced by the nonuniform photon emission patterns of artificial lighting as their brightness varies across their emission spectrum and, combined with the asynchronous characteristic of event cameras' response of event cameras, often leads to significant and instantaneous changes in intensity. Such rapid changes, especially if a light source has a flickering behavior, can lead to a cascade of events within a relatively brief time frame. As seen in Fig. 2B, the artificial light (top left of the picture) has higher event density compared to the surroundings. The challenge arises when the algorithm HDBSCAN (hierarchical density-based spatial clustering of applications with noise), which is tailored for identifying and segregating data clusters, encounter this data landscape. The inherent logic of HDBSCAN is based on determining core samples of high density and extrapolating clusters from these high-density sample. In situations where there is an extreme contrast of data densities, dense event regions near artificial lights versus sparse ones elsewhere, the algorithm can falter. This high gradient between regions might cause the significantly less denser area to be perceived as an outlier or even be categorized as noise, especially if the dense regions lack substantial connectivity to the broader data structure. The feature space, which shows the event data's characteristics, gets noticeably altered near artificial lights. Elements such as event frequency, temporal consistency, and spatial coherence deviate drastically between dense and less dense regions. The pronounced difference produced by this contrast in light density further compounds the difficulty for HDBSCAN in making accurate classifications. Moreover, HDBSCAN's reliance on local density metrics for cluster formation is a source of weakness when applied to scenarios with such diverse lighting conditions. The sharp variations in event densities around artificial light sources can adversely affect the algorithm's assessment of the local region of influence, potentially leading to the derivation of inaccurate cluster boundaries.

As illustrated in Fig. 2E and F, which align with our preliminary calculations, environments with dim and dark lighting conditions inherently elevate the noise level within the captured event data. This augmentation in noise becomes even more apparent when visually assessing sequences recorded under varying light conditions ranging from bright to dim and dark. Considering our data acquisition process was closely controlled, whereby all sequences were recorded using the same camera within a consistent environment and at a steady velocity, it is therefore justifiably feasible to draw comparative insights. Despite the absence of a clear ground truth for direct validation, our comparative method offers a reliable way to identify and measure the noise increase in less favorable lighting conditions.

Moreover, the event data distinctly showcases concentric circular patterns encircling the light sources as seen in Fig. 3A. These concentric patterns, while often being imperceptible to the human eye, are genuine manifestations of light intensity variations. Their origin can be traced back to effect of diffraction when light interacts with the camera's lens system or from the spatial intensity gradients radiating from the light source. Such nuances are picked up by the event camera due to its acute sensitivity to change in the light intensity. However, the concentric circular patterns' presence creates challenges in data processing. Event-based algorithms, especially those tailored for tracking and recognition, rely heavily on distinguishing authentic features data from BA. The concentric circular patterns, being real intensity variations, can adversely impact these algorithms, potentially introducing inaccuracies or false positives. In essence, while these circular patterns are true indicators of brightness changes, they can inadvertently detract from the optimal performance of particular event-based algorithms.

Finally, artificial light sources, when interrogated through the lens of event cameras, present unique event distribution patterns in the temporal–spatial domain. The events generated by these light sources exhibit well-defined clustering behavior in 3D space. Such patterns arise because of the periodic nature of artificial light emissions, often caused by the AC powering. This periodicity leads to light intensity modulations at a frequency typically related to the AC frequency (e.g., 50 or 60 Hz in most regions). These periodic fluctuations culminate in the formation of compact, equidistant event clusters as seen in Fig. 3B, as the camera captures the rhythmic intensity variations of the light source. When we delve into the maximum power spectral density (PSD) map, these clusters translate into pronounced peaks as seen in Fig. 3C where the maximum frequencies are located at the center of the artificial light source (shown as yellow dots). This manifestation is consistent with the Fourier transform principles, where periodic signals lead to sharp spikes when presented in the frequency domain. The resultant peaks from artificial light sources, in this spectrum, appear more frequently than those corresponding to the broader environment. These higher frequencies are indicative of rapid changes in light intensity, typical of many artificial sources. Photodiodes in the event camera, sensitive to minute changes in photon influx, trigger events more frequently when faced with such rapid oscillations. While these sharp and periodic frequency components provide valuable insight into the nature of the light source, these components pose challenges. Any applied algorithms need to discern these high-frequency components, associated with artificial light, from other potential high-frequency noise or events in the scene, to help ensure accurate data interpretation without importing classification errors.

To assess the effectiveness of our denoising and data compression algorithm, we will undertake a detailed analysis of the frequency patterns in the data. This involves a comparison between the frequencies evident in the initial, unfiltered dataset and those present after filtering. By collecting data under a spectrum of lighting conditions, we aim to ascertain the algorithm's capability to adapt and maintain consistency across a range of external illumination scenarios. Thus, to analyze the frequency characteristics of the event data, a maximum PSD frequency map was generated. The PSD is a fundamental tool in signal processing that quantifies how the power of a signal is distributed over its frequency components and typically expressed in units of power per frequency interval. In other terms, it offers a profile of the signal's strength across different frequencies. For our event data, we generated a maximum PSD frequency map. This map effectively pinpoints where the majority of the signal's energy is concentrated in terms of frequency. By comparing the PSD of the raw event data to that of the filtered data, we can gauge the effectiveness of our denoising algorithm, specifically in its ability to attenuate or remove frequencies associated with noise, while preserving those pertinent to the actual event signal. The comparative analysis thus aids in ensuring that our filtering approach maintains data integrity, especially under varying light conditions. This map is constructed by first applying the FFT to each individual pixel's temporal event stream. The FFT is a widely used technique that transforms time-domain signals into frequency-domain representations, which allows for the isolation and examination of different frequency components of the data. After applying the FFT, PSD is computed for each pixel. For our study, we used the PSD to break down the signal's strength across its frequencies. We calculated the PSD by squaring the FFT results and then dividing by the signal's length. This method helps standardize the data, making it easier to compare between different pixels and scenes, even if they have varying amounts of information. Here, the term power is essentially the activity level at each pixel, indicated by the rate of events. In the maximum PSD frequency map, we pinpoint the highest frequency value for each pixel. Essentially, this shows us that frequency is most dominant for every individual pixel. By doing this for all pixels, we get a clear picture of the main frequency patterns across the whole scene. In our frequency analysis, we discerned a pronounced concentration of noise within the low-frequency domain, as delineated by the preponderance of purple markers in Fig. 4A, C, and E. The omnipresence of these purple indicators, particularly in sparse regions of the frequency map, corroborates the hypothesis that noise is predominantly confined to these lower frequencies. While a quantitative substantiation remains elusive because of the absence of an established ground truth, the visual manifestations serve as a potent heuristic. It is imperative to elucidate that not every manifestation in the low-frequency domain can be ubiquitously classified as noise. Nonetheless, our prior knowledge of the actual environment facilitates heuristic demarcation of probable noise-centric areas. This observed trend matches what we often see in many real-world systems, where random changes or slow shifts in the environment typically produce noise in the low-frequency parts of the signal. Interestingly, our data show that the important environmental outlines and features, crucial for efficient data compression, mainly appear in the mid to high-frequency range, as shown by the green–blue markers. Indeed, upon inspecting the maximum PSD frequency map of the filtered data, a notable outcome is that the denoising/data compression algorithm effectively attenuates these low-frequency components (shown as purple dots) while keeping the important features (green–blue dots) as seen in Fig. 4B, 4D, and 4F. In essence, the denoising process acts as a high-pass filter, allowing high-frequency components, which correspond to rapid intensity changes and genuine events, to pass through, while substantially reducing the power of low-frequency noise. This high-pass filtering property of the denoising and data compress algorithm is a critical feature. It ensures that the essential details captured by the camera, which are characterized by high-frequency components due to their transient nature, are preserved in the denoised data. Meanwhile, undesirable low-frequency noise, which does not contribute to the meaningful interpretation of the scene, is significantly minimized, enhancing the clarity and reliability of the event data for subsequent processing and analysis.

As mentioned above, it is important to note that not all components in the low-frequency range equate to noise; some genuinely represent gradual changes in scene intensity. These might be due to shifting shadows or clouds altering the lighting, and they might sometimes be mistakenly addressed as noise by the denoising algorithm. This nuance partly justifies viewing our denoising technique as a compression method. This approach selectively retains essential scene structures by reducing low frequencies, as illustrated in Fig. S4. The 3D clustering method we have used effectively preserves significant data clusters while filtering out BA, as evident in Fig. S4A and B. This effectiveness is further showcased in the accumulated images, where the filtered image Fig. S4D predominantly emphasizes edges and primary features, making it more defined than the original (Fig. S4C). By focusing on higher-frequency components, our algorithm ensures retention of pivotal scene changes vital for applications like motion analysis or object tracking.

By filtering out slower, possibly redundant variations, we not only refine the data's clarity but also reduce its volume, optimizing it for subsequent processing stages. In evaluating the performance of our data compression algorithm under various lighting conditions, we observed the following results:

As indicated above, we managed to cut down the dataset's size by approximately 37% across various lighting scenarios without sacrificing essential scene details. The core of our method is thus about preserving the dataset's key structural elements and crucial features, all while delivering a more concise representation that accentuates rapid scene changes over minor, slow ones.

In our study, we conducted a comprehensive quantitative evaluation of various denoising methods, including our own, as seen in Table. This analysis was crucial to assess the computational efficiency and effectiveness of our approach compared to the state of the art. We compared the peak memory use (PMU), computational time (CT), and percentage of data reduction (DR) across different denoising algorithms. Our algorithm demonstrated significant efficiency in data reduction, achieving the second-best performance with a 40% reduction rate, as underlined in TableA. It is important to note that the best and second-best performances in terms of data reduction were determined while also considering the tendency of other algorithms to overdenoise. Our algorithm strikes a balance between effective noise reduction and preserving essential data, avoiding the common pitfall of overdenoising and losing substantial information that was observed in other algorithms with higher data reduction percentages. In addition, EvFlow, another focal point of our analysis, while showing a comparable PMU to our method and others, had a significantly higher CT, being 145 times greater than that of our algorithm. This marked difference highlights the superior processing efficiency of our approach. In terms of PMU, all methods exhibited similar performance, indicating a general efficiency in memory usage across the board. However, the stark contrast in CT, particularly for EvFlow, underscores the need for balanced optimization between memory use and processing speed in denoising algorithms.

To finalize our comprehensive quantitative assessment, as presented in TableB, we meticulously compared the denoising performance of our 3D adaptive algorithm with that of EvFlow. This comparison was pivotal, given that both algorithms were specifically selected for their proficiency in effective denoising while avoiding the common issue of overdenoising. Indeed, the event structure ratio [19] is a sophisticated, nonreference metric for event denoising. It quantitatively measures the structural intensity of events, providing a robust assessment of denoising quality. This metric is particularly valuable as it is independent of the number of events and their projection direction, offering an unbiased comparison. In the context of denoising, a higher event structure ratio value is indicative of superior performance.

Our analysis, based on the event structure ratio values across different lighting conditions simulated with ND filters, revealed key insights. Both algorithms showed a decrease in denoising performance from daylight to darker conditions, correlating with increased noise levels in low-light environments. However, this degradation in performance was more pronounced for EvFlow compared to our algorithm, indicating our method's enhanced resilience to noise. Furthermore, the event structure ratio values during daytime conditions, under ND filters such as ND00, ND04, and ND16, illustrated that our algorithm either matched or exceeded the performance of EvFlow. In more challenging nighttime scenarios, our algorithm consistently registered higher event structure ratio values across all ND filter settings. This consistent superiority in event structure ratio values, particularly under low-light and noise-intensive conditions, highlights the robustness of our algorithm.

This detailed quantitative comparison underscores the effectiveness of our 3D adaptive denoising algorithm in maintaining the structural integrity of events, even in diverse and challenging lighting conditions. It confirms our algorithm's advanced capability in handling complex denoising tasks while preserving essential event details, thus establishing its superior performance in varied denoising scenarios.

Upon a detailed qualitative analysis of Fig. 5, we discern the performance characteristics of various denoising algorithms across different lighting conditions.

In Fig. 5A, under daytime lighting with no filter, it is observed that while all algorithms manage to reduce noise to a degree, there is a notable variance in their propensity to overdenoise. Algorithms such as TS and KNoise appear to excessively smooth the event data, resulting in a loss of critical structural detail within the bicycle image. Conversely, our adaptive 3D filter and EvFlow demonstrate a more conservative denoising approach, retaining more of the scene's inherent details and avoiding the pitfalls of overdenoising.

In Fig. 5B introduces an ND4 filter, simulating reduced light conditions. In this setting, the challenge of balancing noise suppression with detail preservation becomes more pronounced. Algorithms like RED and TS begin to exhibit clear signs of overdenoising, as evidenced by a substantial diminution of event density, suggesting an aggressive loss of information. Our adaptive 3D filter, however, maintains a superior level of detail retention, indicating its robust performance under suboptimal lighting conditions.

As we transition to nocturnal conditions in Fig. 5C, without a filter, the inherent noise levels in the data increase significantly. This increment in noise presents a heightened challenge for denoising algorithms. Here, we observe that algorithms like RED and TS tend to overdenoise, leading to an important loss of features. This is particularly problematic for capturing the nuances of nonrigid body motion under street lights. Our adaptive 3D filter continues to mitigate noise effectively while preserving the critical features necessary for accurate event interpretation.

Under the most challenging condition, Fig. 5D, under nighttime with an ND4 filter, the algorithms are subjected to increased noise levels. Many algorithms exhibit decreased performance, with some, such as TS and RED, completely overdenoising the scene, resulting in the obliteration of essential event information. Moreover, DWF and YNoise display pronounced tendencies toward excessive denoising. In contrast, our adaptive 3D filter adeptly preserves the structural integrity of fast-moving objects, demonstrating its capacity to maintain high-quality event data without succumbing to overdenoising.

Throughout these analyses, it is evident that our adaptive 3D filter and EvFlow maintain a consistently higher standard of denoising across both daytime and nighttime conditions. They effectively reduce noise while safeguarding the detail integrity of the event data, showcasing their advanced capabilities in event denoising without overdenoising, which is critical for retaining essential information within dynamic environments. However, the quantitative analysis reveals that EvFlow's CT exceeds that of our algorithm by a factor of 145, underscoring the superior efficiency of our approach.

Temporal noise, also referred to as shot noise, is a form of noise that originates from the unpredictable arrival times of charge carriers, such as photons or electrons [24]. Shot noise in event cameras is attributed to the intrinsic randomness of photon arrival times at the photodetector, which results in the fluctuation of signal amplitude. Thus, when light is incident on a pixel's photoreceptor as seen in Fig. 1B, photons are absorbed, generating electron-hole pairs that contribute to the photocurrent. Since the arrival times of photons follow a Poisson distribution [25], the resulting photocurrent I_ph(t) exhibits fluctuations as seen in Fig. S1B, which are referred to as shot noise:

where {\overline{I}}_{\text{ph}} is the average photocurrent and i_shot(t) is the time varying current noise. The expression of the noise is given by [26]:

where q = 1.602176634 × 10⁻¹⁹ C is the electrical charge carried by a proton and Δf is the frequency range.

The shot noise of photocurrent, i_shot(t), can be quantified by calculating its noise power, which is expressed in terms of the current noise spectral density, S_i. The current noise spectral density due to shot noise is given by:

When a current signal passes through an impedance Z(f), the voltage signal generated by the current noise across the impedance is given by Ohm's law v_shot(f) = i_shot(f)Z(f). Thus, the PSD of the voltage noise S_v:

The pixel circuitry as represented in Fig. 1 is composed of 2 capacitors C₁ and C₂ in series. Thus, the impedance equation Z(f) is:

where C_total = 1/C₁ + 1/C₂ and f is the frequency.

From Eqs. 4 to 6, the PSD of the voltage temporal noise S_v, as a function of frequency f is:

In a circuit with 2 capacitors in series without any resistance, the thermal noise arises from the parasitic resistance within the capacitors themselves, referred to as the equivalent series resistance (ESR) [27]. Each capacitor (C₁ and C₂) has an associated ESR (R₁ and R₂), which can be modeled as a resistor in series with the capacitor as seen in Fig. S1A. The circuit can then be considered as 2 resistor–capacitor (RC) branches connected in series. The total ESR R_total = R₁ + R₂ is the sum of the individual ESRs.

The thermal noise voltage v_thermal in this context can be calculated using the Johnson–Nyquist noise formula [28]:

where k = 1.38 ∗ 10⁻²³ J/K is the Boltzmann constant, T is the temperature in kelvin, R_total is the total resistance in ohms, and Δf is the bandwidth.

The thermal noise current i_thermal(f) is calculated by dividing the noise voltage v_thermal(f) by the total impedance Z_total(f) of the equivalent circuit:

where Z_total = (−j/(2πfC₁)) + R₁ + (−j/(2πfC₂)) + R₂ is the equivalent impedance of the 2 capacitors and 2 resistors in series.

Since the capacitors are in series, the noise current will be the same for both capacitors. The noise voltage across each capacitor (v_nC1 and v_nC2 ) can be calculated using Ohm's law:

where Z_C1(f) =  − j/(2πfC₁) and Z_C2(f) =  − j/(2πfC₂) are the individual capacitor impedances. To find the total noise voltage power density, the power across each capacitor (S_vnC1 and S_vnC2) needs to be calculated:

Thus, to find the total thermal voltage noise power density S_vnTotal as function of f, the power of both capacitors is summed and divides it by Δf:

where α₁ = (1 + C₁/C₂)² and α₂ = (1 + C₂/C₁)².

Intrinsic noise in event cameras originates from internal hardware factors, with 2 notable sources being leak noise and hot-pixel noise. Leak noise stems from spontaneous ON events, while hot-pixel noise is a result of persistently overactive pixels within the sensor. In this context, DVS pixels can encounter spontaneous ON events, or leak events, exhibiting a polarity of +1. These events transpire at a rate of 0.1 Hz [10] and are predominantly induced by reverse diode leakage currents in reverse-biased p–n junctions between the deep n-well and source–drain node [19], in addition to parasitic photocurrents from the change detector reset switch. It is important to note that leak events do not display temporal or spatial correlation with genuine generated events, underscoring their unique nature and the necessity for meticulous examination in DVS system analysis and optimization.

In addition, DVS systems can present a small proportion of pixels (approximately 0.7% [19]) with irregular firing rates due to hardware interference, referred to as hot pixels, as depicted in Fig. S2A. Hot pixels can induce high-frequency burst events and elevated noise in the output of DVS systems. To minimize the incidence of false event detection and the associated high-frequency noise, researchers have recommended implementing a refractory period, during which a pixel remains inactive for a specified duration after its previous response, thereby reducing false event detection and the corresponding high-frequency noise [19].

The analysis of PSD plots, as seen in Fig. S2B, for dominant voltage noises provides a comprehensive understanding of noise behavior, which, in turn, enables the optimization of filter design to address noise within the appropriate frequency range. In the case of temporal noise, the voltage noise spectral density S_v(f) (Eq. 7) increases as the frequency decreases. This behavior is frequently observed in circuits containing capacitive elements, where low-frequency noise is often more pronounced because of the increased impedance of capacitors at lower frequencies. Regarding thermal noise, the frequency in the voltage noise spectral density S_vnTotal(f) is multiplied by the small R_total, rendering the denominator in Eq. 12 constant and equal to α_{1, 2}. As a result, for low frequencies, the power density of thermal noise remains constant and only begins to decrease beyond a certain threshold when the frequency surpasses the diminutive value of R_total. This observation emphasizes the importance of understanding the technical aspects of noise behavior to effectively design and optimize filters for noise attenuation within the appropriate frequency spectrum.

In neuromorphic cameras, the impact of certain noise types is also correlated with the extent of low-light conditions. Specifically, in dim light situations, the number of incident photons decreases compared to normal lighting conditions (less than 10⁻² photons·μ⁻²·s⁻¹ for starlight condition compare to greater than 10⁸ photons·μ⁻²·s⁻¹ for bright sunlight [29]). As a result, the photocurrent I_ph produced in the photodetector is reduced, regarding the lower quantity of incident photons. This decreasing in signal level renders the system more sensitive to fluctuations. Thus, under these low-light conditions, shot noise (temporal noise), arising from the random arrival of photons, gains prominence. In fact, with fewer photons present in dim light situations, the accurate detection of brightness changes becomes more challenging as the signal-to-noise ratio of the system decreases significantly. Contrary to temporal noise, intrinsic and thermal noise are not directly affected by the brightness of the light. Instead, their origins lie in the camera's internal electronic components and their physical properties. In addition, in bright light, I_ph generated in the photodetector is larger, resulting in a higher signal level. With an increased signal strength, the system can better tolerate the presence of all type of noise, leading to a higher signal-to-noise ratio.

Event cameras represent a profound departure from conventional imaging paradigms, emphasizing changes in the visual scene over static intensity values. These devices operate in a 3D space ℝ³ defined by spatial coordinates (x,  y) and temporal coordinate t, presenting unique challenges and opportunities. In this context, when one considers the idea of converting this event stream into time images, the endeavor to make the data compatible with traditional image processing algorithms might inadvertently compromise its temporal integrity. The richness and granularity that event-based data offers could be blurred, obscuring rapid shifts and subtleties in the visual field. Any event that unfolds between 2 slices might be averaged out, thereby potentially misrepresenting or even omitting swift luminance changes, diminishing the fidelity that the native stream would otherwise convey. Further exacerbating this issue, the noise-filtering process becomes particularly challenged. In the native stream, transient noise events are discernible because of their isolated temporal occurrence. However, in time images, these sporadic noise events might get integrated into the visual representation, possibly interpreted as genuine scene changes. Consequently, noise-filtering algorithms applied to these images may either fail to detect such artifacts or, in their attempts to rectify them, might unintentionally diminish genuine rapid scene transitions that manifest temporally rather than spatially. Such misrepresentations not only hamper the true depiction of a dynamic environment but can also lead to cascading inaccuracies in downstream processing tasks, undermining the inherent advantage of event-based vision systems.

In dissecting the challenges of event-based data processing, the compelling analogies offered by the retina's biological intricacies can be drawn. RGCs work with a discernment intricately rooted in their biophysical properties. Their response patterns are shaped by meticulously orchestrated ion channel dynamics, coupled with modulator inhibitory inputs from interneurons. These mechanisms establish precise firing thresholds, such that only stimuli with intensities within a certain period of time surpassing these thresholds elicit action potentials. This selective mechanism ensures that RGCs can underscore salient intensity changes in the visual scene while effectively sidelining inconsequential noise. Drawing a parallel to the computational realm, the 3D HDBSCAN algorithm's core tenets echo these selective principles of the retina. At the heart of 3D HDBSCAN is the core distance, a metric analogously setting a benchmark for cluster determination. Just as only potent stimuli lead to RGC responses, only data regions with densities along the time axis, surpassing this core distance are designated as bona fide clusters. Moreover, HDBSCAN's nimbleness, manifested in its ability to detect clusters of disparate densities in heterogeneous data, mirrors the adaptive thresholds seen in neural entities. In response to fluctuating input patterns, both neural circuits and 3D HDBSCAN can dynamically adapt to the situation. Indeed, neurons might modulate their sensitivity through processes like synaptic plasticity, while 3D HDBSCAN can adjust parameters in tandem with the prevalent event density in the data landscape by retrain to fit the new data.

Delving deeper into the retinal architecture unravels a sophisticated interplay of cellular components and processes. The retina does not merely operate through isolated neural entities but rather a meticulously coordinated cascade of signal processing from a population of neurons. Crucially, these neurons exhibit adaptive behavior in their responses. Their activity is not static but dynamically modulates based on local (neighbor–neuron interactions) and global (overall network dynamics) stimuli. For instance, under high-luminance conditions (high neuronal activity), mechanisms like synaptic depression and altered ion channel conductances kick in, modifying the neuron's sensitivity and responsiveness to prevent saturation. This ensures that the retina remains a reliable sensory organ across a vast range of environmental light conditions. Drawing parallels with this adaptive retinal machinery, our method's functionality is not rigid. It does not only cluster data points based on a fixed set of parameters but also evaluates data contextually. In scenarios where the overall event density of the data is high, 3D HDBSCAN can dynamically adjust its input parameters, particularly the core distance and minimum samples, regarding its PA. This adaptability ensures that the algorithm does not group too many events into an oversized cluster or fail to discern between proximate but distinct clusters. By aligning its clustering thresholds with the prevalent data density, much like how retinal neurons adapt their thresholds to ambient luminance, HDBSCAN showcases an inherent a context-awareness, ensuring optimal performance across a diverse array of data landscapes.

Finally, in the comprehensive findings elucidated in our results section, our approach showcases a notable proficiency in discerning and subsequently negating persistent low-frequency events, which predominantly correspond to the ambient, static background. This step is instrumental in our advanced data compression protocol. The underpinnings of this process are deeply rooted in the intricate neurophysiological processes of the retina. The mammalian retina uses a combination of temporal filtering and spatial antagonistic receptive fields. The horizontal cells, a different type of retinal interneuron, use a phenomenon known as lateral inhibition. By inhibiting adjacent photoreceptors in response to intense light stimulation, they fine-tune and enhance the contrast at visual edges, serving as a sort of spatial high-pass filter. This mechanism ensures that static, unchanging stimuli produce diminished responses over time, while transient or changing stimuli are accentuated. RGCs, which are the output neurons of the retina, further integrate these signals and relay them to the brain. Through a cascade of excitatory and inhibitory synaptic interactions, the retina effectively emphasizes rapid changes in luminance or contrast while suppressing consistent, unchanging inputs. Building on these insights, our computational method integrates temporal differentiation mechanisms, akin to the temporal filtering in retinal cells, to efficiently isolate events that represent dynamic changes in the visual scene. In other words, our approach effectively suppresses the low-frequency, static components of the data. This biologically inspired methodology ensures that while the consistent, redundant background is efficiently compressed, the salient and dynamic event details are retained with high fidelity. In essence, by integrating principles from retinal neuroscience, we have crafted a compression technique that emphasizes the dynamic and reduces the redundant, optimizing the representation for subsequent analytical tasks.

Our strategy borrows foundational principles from biological systems, specifically the human visual system as seen in the section above. Indeed, signal processing incorporates both spatial and temporal summation [30]. Spatial summation is a process wherein signals from multiple cells are synthesized into a singular output, while temporal summation refers to the integration of these signals over a defined temporal scale. These operations enhance photoreceptivity and amplify the signal-to-noise ratio. Considering the analogy between the function of pixels in event cameras and the role of RGCs, we model the event stream as a 3D discrete signal, with due emphasis on the temporal dimension. This model offers an avenue for the use of advanced signal processing techniques, thereby augmenting the efficacy of the denoising process.

Incorporating the 3D HDBSCAN [31], an unsupervised machine learning algorithm, offers a novel bioinspired approach for event data processing. This method interprets events as 3D noisy signals, allowing for effective clustering along the temporal axis. This technique leverages the high temporal resolution and dynamic nature of event streams, enabling efficient processing of larger event quantities within an extended time window. HDBSCAN operates with 2 primary parameters: MinPts, defining the minimum number of points required to form a dense region, and MinClusterSize, setting the smallest size grouping considered meaningful. Unlike DBSCAN [32], HDBSCAN constructs a hierarchy of clusters without a need for a global distance parameter (ϵ). It is used instead of DBSCAN particularly when datasets present significant density variations introduced by factors such as artificial lights. By adjusting these 2 parameters, the sensitivity of the clustering process can be finely tuned, enabling more effective identification of event clusters. Indeed, as seen in Algorithm 1, first, the events structure is transformed to “spikes” to calculate PA. The spike matrix is a representation of the event data transformed into a binary form known as spikes, effectively mapping the spatiotemporal event data onto a grid. The spike matrix will have dimensions of the total number of pixels (height by width) by number of time steps. The value at a specific position [i,  j] in the matrix indicates whether the pixel i has fired (has a spike) at the time step j. Although it is represented in a 2D matrix, the spike matrix is conceptually a 3D structure. The (x,  y) coordinates of each pixel are converted to a column index, and the time steps represent the temporal dimension. Thus, each entry in the spike matrix can be seen as the state (fired or not fired) of a pixel at a specific point in time. Upon computation of the “spikes”, the evaluation of PA can be performed. In the context of neuroscience, PA refers to the coordinated firing or activity patterns exhibited by a collective group of neurons within a specific region or network in the brain. Importantly, PA provides a significant understanding of the motion perceived by the retina. The collective neuronal firing patterns can encode information about the direction, speed, and complexity of moving objects within the visual field [33]. For example, a surge in PA might correspond to rapid movements in the environment, while a steady, low-level activity could be indicative of stationary or slow-moving objects. The precise patterning and timing of neuronal firing provide a dynamic and nuanced representation of the moving elements within the environment. This offers a deeper understanding of how motion is encoded and interpreted in the visual processing system. In this context, the calculation of PA, expressed in hertz, can be carried out as follows:

where t is the time stamp, n is the number of pixels firing at each time step Δt, and N is the total number of pixel.

Upon computing the PA, adjustments to the parameters MinPts and MinClusterSize are made to better align with the environmental dynamics captured by the event camera and the observed data sparsity. When PA values are low, it suggests a sparsity in the event data, commonly seen in environments with little to no motion. Conversely, as PA values rise, it indicates the event camera's operation in a lively, motion-intensive environment. In such contexts, the parameters MinPts and MinClusterSize are dictated by the function f(PA), described as f = λ ∗ PA. Here, λ serves as an adjustable constant, fine-tuning the denoising process. The function f(PA) is designed to scale the unsupervised machine learning algorithm parameters in relation to the PA. In dynamic settings filled with motion, event cameras relay denser data, logging events that are spatially and temporally proximate. Thus, elevating the values of these parameters in such scenarios ensures precise clustering, reducing the risk of unrelated events being mistakenly clustered due to data density. However, when the function f(PA) decreases, it signifies a need to accommodate for less dense data, requiring a reduction in the HDBSCAN's parameters to ensure that genuine clusters are not dismissed or overlooked.

This adaptability ingrained in the HDBSCAN algorithm allows it to respond aptly to changes in environmental dynamics and data sparsity, resulting in a context-sensitive and more accurate denoising process