Motion-corrected eye tracking improves gaze accuracy during visual fMRI experiments

Domain: neuroscience
Published: 2025-12-18
Editorial outcome: minor_revision

Abstract
Human eye movements are essential for understanding cognition, yet achieving high-precision eye tracking in functional Magnetic Resonance Imaging (fMRI) remains challenging. Even slight head shifts from the initial calibration position can introduce drift in eye tracking data, leading to substantial gaze inaccuracies. To address this, we present Motion-Corrected Eye Tracking (MoCET), which corrects drift using head motion parameters derived from fMRI preprocessing. MoCET requires no additional hardware and can be applied retrospectively to existing datasets. We show that it outperforms conventional detrending methods with respect to accuracy of gaze estimation and offers higher spatial and temporal precision compared to magnetic resonance-based eye tracking approaches. By overcoming a key limitation in integrating eye tracking with fMRI, MoCET enables precise investigations of naturalistic vision and cognition in fMRI research.

Introduction
Human eye movements are closely linked to cognitive processes such as perception, attention, and memory1–3. Acquiring eye tracking data during functional magnetic resonance imaging (fMRI) experiments offers the possibility of better understanding these processes at both neural and behavioral levels. By combining eye tracking with fMRI data, we can link explicit behavioral signatures of mental states to underlying neural activity, thereby providing insights into how the brain responds to the visual world4–8. This integration becomes increasingly crucial as naturalistic free-viewing paradigms gain prominence in cognitive neuroscience: in naturalistic environments, precise eye tracking is necessary to understand the brain’s dynamic processing of visual information9–12.

Recent advances in eye tracking methods within fMRI research typically involve camera-based systems using endoscopic optic fiber13,14. These systems usually monitor one eye with a single camera, using computer vision techniques to detect pupil position. While this approach enables precise eye tracking data, it faces major technical challenges, such as hardware setup constraints in the MRI environment and limitations in calibration data quality.

Camera-based eye tracking accuracy relies critically on calibration that maps pupil positions to gaze positions. The MRI scanner’s limited visual field makes precise calibration difficult, as participants fixate closely-spaced calibration points. More importantly, even slight head movements from the calibration position compromise accuracy. Unlike behavioral experiments that can use chin rests or bite bars, such head restraints are not feasible in MRI. Consequently, head shifts significantly reduce gaze accuracy, as the calibrated model is misaligned with eye tracking data collected during the experiment15–17.

Behavioral experiments have recently introduced several methods for addressing head shifts, such as recording head movements through supplementary cameras, motion sensors, or a wide-field camera that captures both the participant’s eye and head, allowing for separate tracking of eye and head movements18–20. However, these solutions are challenging to implement in fMRI experiments. Installing additional cameras or motion sensors in the head coil is not feasible in most cases, and the narrow field of view (FOV) of the camera, focused on a single eye, limits the ability to capture head movements. This challenge emphasizes the need for new solutions that maintain accuracy despite the inevitable head movements that occur in fMRI experiments.

In this study, we investigate the impact of head motion on gaze accuracy during fMRI scans. We first develop computational simulations that confirm head movements significantly affect gaze estimation accuracy. Based on this finding, we then propose an eye tracking with head motion correction approach, which addresses head movement challenges without requiring additional hardware and can be retrospectively applied to existing data. Our approach, termed Motion-Corrected Eye tracking (MoCET), leverages head motion parameters derived from the preprocessing of fMRI data to correct errors in eye tracking data.

Using high-quality eye tracking data collected during free-viewing tasks, we demonstrate that MoCET consistently outperforms both uncorrected data and conventional detrending methods across independent datasets involving different tasks and MRI scanners. We further validate MoCET by showing that its corrected gaze accuracy closely matches that of behavioral eye tracking data collected under standard laboratory conditions. To enhance flexibility, we introduce an across-run variant of MoCET that enables calibration transfer across runs within the same session, allowing robust correction even when within-run calibration is limited or unavailable. Finally, we compare MoCET with magnetic resonance-based eye tracking21, which estimates gaze position directly from eyeball region signals in fMRI data. We find that while MR-based methods successfully capture general gaze direction, they lack spatial precision. In contrast, we show that MoCET provides precise gaze locations, making it more suitable for detailed behavioral and neuroimaging analyzes.

To facilitate the application of MoCET across diverse fMRI experiments, we provide a user-friendly Python package (https://github.com/jwparks/mocet). Additionally, we release the high-quality free-viewing eye tracking dataset used in this paper. This dataset, containing multiple calibration periods, enables both calibration and validation of eye tracking models, and may serve as a useful benchmark for advancing eye tracking methods, including MR-based eye tracking21–24.

Results
Impact of head motion on gaze tracking accuracy
We simultaneously collected fMRI and eye tracking data while participants engaged in interactive Minecraft25-based video game tasks (Fig. 1a). These tasks allowed free gaze movement (instead of central fixation) and were designed to provide a diverse range of visual stimuli and cognitive demands, enabling assessment of gaze tracking accuracy under different conditions. To assist in eye tracking, two eye tracking calibration stages were included during the actual data collection. For each stage, participants fixated on sequentially appearing green dots. The first calibration stage involved 24 dots (two repetitions of a 12-dot sequence), while the second validation stage occurring at the end of the experiment required fixation on 12 dots. The data collected from the initial calibration stage were used to fit our eye tracking model (Fig. 1b).

We hypothesized that small head movements during fMRI sessions prevent the calibration model from accurately tracking pupil positions. Specifically, in-plane head movements (those occurring in the px-py plane perpendicular to the eye tracking camera) shift the recorded pupil coordinates, creating discrepancies between the calibration and validation stages. These shifts lead to inaccuracies in mapping pupil positions to their corresponding screen locations. Importantly, we found that even minor head shifts typical in fMRI experiments can cause substantial inaccuracies in eye tracking results (Fig. 1f, r = 0.969, p < 0.001).

Head motion is a recognized challenge in gaze tracking15–17, often addressed by measuring head motion independently from eye movement, using motion sensors or video processing of visual features. However, implementing additional head motion sensors within an MRI scanner is technically challenging. Moreover, the limited FOV of endoscopic eye tracking cameras prevents capturing stable feature points, such as the nose, needed for head position estimation. Features visible within the camera’s FOV, like the lacrimal caruncle or eyelid, are highly sensitive to blinks and eye movements, rendering them unreliable for head motion estimation. These limitations highlight a critical need for an effective method to capture and compensate for head motion, ensuring accurate gaze tracking throughout fMRI experiments.

To rigorously demonstrate that participant head motion is the primary source of eye tracking errors rather than errors in instrumental setup or suboptimal fixations during calibration, we developed a computational simulation using a 3D geometry-based eyeball model. This approach offers a controlled framework to isolate and quantify the impact of head motion on gaze accuracy. The model included head and eyeball components that could each move independently. The head-ball component allowed six degrees of freedom (DoF): translational along x, y, and z axes, and rotation including roll, pitch, and yaw. The eyeball was physically connected to and moved with the head but was able to rotate independently to simulate gaze direction. Our simulation recorded pupil position on the eyeball using a virtual eye tracker and applied the same analysis procedures used for human participants (e.g., extract the pupil position, fit the eye tracking calibration model).

To simulate the impact of human head motion on gaze accuracy, we applied 6-DoF head motion parameters sampled from actual fMRI data to our model. The model performed an initial calibration task (same as human subjects) and then performed a central fixation task for about 13 minutes. During this central fixation task, changes in pupil coordinates directly reflected the applied head motion effects. Next, the model performed a validation task, which was used to evaluate gaze accuracy (Fig. 2a). The model parameters (head/eyeball radius, eye location) matched average Asian head proportions26–28, while the FOV of the camera, screen size, and eye-to-screen distance closely replicated our human fMRI experiment setup (See Supplementary Fig. 1 and Methods).

Our eyeball simulation provides two key insights: First, comparing simulated and human gaze trajectories reveals the amount of variance in human eye tracking data that is attributable to head motion. Similar trajectories between the simulated model and human participants indicate that the observed drift in pupil coordinates is driven by head motion rather than actual eye movements. Second, although head motion affects pupil coordinates in a complex, non-linear manner, the simulation allows us to assess whether these effects can be effectively corrected using linear techniques. If effects are approximately linear, this would justify the use of fMRI-derived head motion parameters in a linear regression procedure to correct for head motion effects.

Our model simulation demonstrated that both horizontal (px, average model similarity: r = 0.478) and vertical (py, average model similarity: r = 0.793) eye movements can be replicated using motion parameters derived from participants’ actual head motion, with vertical shifts (py) particularly well-aligned with model simulation due to characteristic pitching movements (Fig. 2b). To assess statistical significance, we generated randomized head motion parameters by randomly shuffling the phase spectra, and simulated eye movements based on these randomized parameters, creating a null distribution of similarity values (n = 100 per simulation). Comparing actual simulation similarity to this distribution, with results aggregated across datasets using Fisher’s method29, we find statistical significance for both horizontal and vertical pupil coordinates (p < 0.001), indicating that head motion drives global error in human eye movements.

We found that the model simulation accurately replicated both the magnitude of head shift from initial calibration to final validation and the resulting gaze inaccuracies caused by head motion in individual human eye tracking data. Head shifts in the simulation showed a strong linear relationship with estimated human head shifts (r = 0.917, p < 0.001). Similarly, the simulation reliably reproduced individual gaze inaccuracies, showing a strong positive correlation between simulated and actual gaze errors (r = 0.958, p < 0.001). While human gaze errors were slightly larger than simulation gaze errors (tpaired(132) = 12.75, p < 0.001) this likely reflects the fact that human fixations have limited accuracy.

These findings highlight the effectiveness of the geometry-based model in isolating head motion effects on eye tracking data. By factoring out task-related variability in eye position and human-specific idiosyncrasies, the simulation confirms that even minor head movements can introduce substantial inaccuracies in eye tracking data.

Compensating for head movement with motion-corrected eye tracking
Our model simulation demonstrated that head motion alone can cause global drift in eye tracking data, even in the absence of actual eye movement. While many MR-compatible eye trackers offer drift correction, these methods assume that participants fixate on known locations during the experiment. This assumption fails in free-viewing experiments such as movie-viewing or playing video games, since the participant’s gaze is not restricted to predefined targets. Without fixed fixation points, conventional drift correction cannot determine the actual offset between recorded and actual gaze positions.

Based on our computational simulation, which showed that head motion introduces systematic, approximately linear error in pupil coordinates, we developed a correction approach. Our method, MoCET, uses head motion parameters as nuisance regressors to account for motion-induced drift, thereby helping to isolate actual eye movements (Fig. 3a).

MoCET uses 6-DoF head motion parameters from fMRI data and polynomial regressors (up to the cubic order) to remove error in eye tracking data. The polynomial regressors address very low-frequency drift not fully captured by head motion parameters, such as instrumental shifts and vibrations in the MRI environment affecting the stability of the eye tracking camera. These drifts, unrelated to head motion, cannot be corrected by head motion parameters alone. By using both motion parameters and polynomial regressors, MoCET provides comprehensive correction. Head motion parameters effectively handle dynamic changes associated with head movements (high-frequency), while polynomial regressors address low-frequency drift from other sources unrelated to direct head motion, ensuring both dynamic and gradual error are corrected.

To assess the validity of using linear regression to remove head motion-related error, we compared the regression weights of six head motion parameters between human data and simulation containing only motion-related error. In both human and simulated data, horizontal head motions, such as translational movement along the x-axis (left-to-right) and rotational movement around the z-axis (rolling), primarily affected global drift in the x-axis of pupil coordinates, while vertical head motions, including translational movement along the y-axis (up-and-down) and rotational movement around the x-axis (pitching), affected vertical drift in the y-axis (Fig. 3b). These results indicate that the overall trends in regression weights across the six head motion parameters were consistent between human and simulation data. However, y-axis rotation (yawing) showed stronger effects in x-direction drift in human eye movement than in simulation, likely because the human brain sits above the eyes, unlike our model, where the yawing center of the head was close to the eye position, allowing yawing motion to have a greater influence on horizontal eye position.

To further test the linear assumption, we evaluated the non-linearity in the relationship between head motion and pupil coordinates across different types of head motion. We found that the linear and nonlinear variants of MoCET performed comparably across motion categories. Additional simulations with artificially amplified motion indicated that the linear MoCET model remained effective at motion levels typical of fMRI studies, while nonlinear models offered only limited additional benefit under extreme motion (for details, see Supplementary Fig. 3 and Methods). Overall, the regression-based approach used in MoCET successfully removed effects of physical head motion in both human and simulated eye tracking data.

MoCET enables high-precision eye tracking during free-viewing experiments
Global drift in eye tracking data during fMRI experiments is a well-known issue and is commonly addressed using heuristic detrending methods such as linear30,31 or quadratic polynomial detrending21. These methods assume that the average gaze position remains centered on the screen and drift occurs gradually rather than abruptly. A limitation of these methods is that they cannot correct transient effects such as those driven by abrupt head movements. Such head movements are especially pronounced in naturalistic tasks (e.g., free-viewing and video-game playing).

We compared the effectiveness of MoCET to conventional linear and polynomial detrending methods, as well as uncorrected data. Polynomial detrending up to the cubic order served as a baseline for comparison, while MoCET included additional 6-DoF head motion parameters. To evaluate drift correction performance, we employed three distinct metrics. First, we measured gaze accuracy during the validation stage, which evaluates eye tracking data by requiring participants to fixate on specific points across the screen (Fig. 4a). However, this metric cannot fully assess the quality of eye movements during the actual experiment and requires an additional validation stage. Thus, we introduced two additional performance metrics that do not require a validation stage and are also suitable for free-viewing experiments: the accuracy of eye tracking data in predicting participant behavior during the task (Fig. 4b) and the accuracy of mapping visual stimuli to retinotopic representations in the visual cortex (Fig. 4c, d). The latter constitutes a stringent test of eye tracking accuracy, since retinotopic representations are expressed relative to the exact gaze location.

For both model simulation and human eye movement data, MoCET outperformed other methods in reducing gaze inaccuracy during the validation stage (Fig. 4a, all ps < 0.001). To ensure the observed improvements were not simply due to MoCET’s use of a total of nine regressors compared to polynomial detrending’s three, we included additional polynomial detrending regressors up to the 12th order. Results showed that, for both model simulation and human eye tracking data, the performance of polynomial detrending saturated after the 5th order. MoCET demonstrated superior effectiveness in drift correction, even when using fewer regressors compared to 12th-order polynomial detrending (Supplementary Fig. 2, Model simulation: all ps < 0.01, Human eye movement, all ps < 0.001). Notably, gaze accuracy achieved by MoCET was not statistically different from that observed in behavioral eye tracking experiments conducted outside the scanner, indicating that MoCET recovers high-quality gaze signals even under the constraints of fMRI environments (t(20) = 1.34, p = 0.195).

To evaluate drift correction performance throughout the entire fMRI experiment, we assessed the ability of gaze data to predict participant behavior during the task. In the Minecraft-based video game task, participants were required to build or remove fence blocks inside a square arena. Previous research has shown that humans tend to fixate on the next target location before performing an action toward it1,32–35. Therefore, we hypothesized that motion-corrected gaze data should be able to predict participants’ next building action or target-removal action before the action occurs. We calculated the average hit rate over the 10-s period leading up to each action. A “hit” was defined as the participant’s gaze falling within 2 degrees of visual angle from the next target location. While both linearly detrended and uncorrected gaze data performed at near chance levels, MoCET demonstrated significantly better prediction performance compared to all other detrending methods (Fig. 2b; all ps < 0.001). We also demonstrated that the hit rate from MoCET was comparable to that observed in behavioral eye tracking, indicating reliable recovery of task-relevant gaze patterns during fMRI experiments (t(20) = 1.40, p = 0.175). These results suggest that the error correction achieved by MoCET effectively removes non-gaze-related artifacts, such as head motion or instrumental instability, while preserving actual eye movements throughout the task.

As an additional performance metric, we evaluated the ability of gaze data to enable the derivation of retinotopy during free-viewing conditions. Retinotopic mapping in the visual cortex refers to the spatial organization of neural representations of the visual field. Each region of the visual field is systematically represented in early visual areas, such as V1, V2, and V3, with maps that are defined relative to the gaze location36,37. This retinotopic organization provides a critical link between eye movements and neural activity, and deriving retinotopic organization during free-viewing requires high-accuracy gaze data. To transform free-viewing stimuli into gaze-centered stimuli, we corrected eye tracking data using various drift correction methods (MoCET, polynomial, linear detrending, and uncorrected data), and then calculated the spatiotemporal local contrast of the stimulus within small patches defined relative to gaze location38,39. Using this gaze-centered stimulus preparation, we fit a population receptive field (pRF) model40,41 to recover spatial tuning (i.e., polar angle and eccentricity) in the early visual cortex (for details, see Supplementary Fig. 5 and Methods). Results from free-viewing stimuli were compared to spatial tuning obtained from conventional pRF experiments using structured visual stimuli (wedges, rings, and bars) presented during central fixation.

While pRF experiments with structured stimuli provided the clearest polar angle maps, MoCET demonstrated the ability to accurately map free-viewing stimuli to brain activity and outperformed other detrending methods in recovering polar angles (all ps < 0.05). Although the video game stimuli showed limitations in mapping foveal representations, they more effectively mapped peripheral visual areas compared to the structured pRF experiment, even along the vertical meridian, where stimulus coverage was comparable to pRF stimuli. This advantage stems from free-viewing experiments naturally engaging the peripheral visual field, whereas structured pRF experiments conducted under central fixation are typically limited in their stimulation extent. Detailed retinotopic representations, including eccentricity maps, are presented in Supplementary Fig. 6.

In summary, our results demonstrate that MoCET significantly improves eye tracking accuracy during free-viewing experiments compared to conventional detrending methods. By combining head motion parameters and polynomial regressors, MoCET not only reduces drift-related errors but also enhances the predictive power of gaze data for behavior and neural response characterization. MoCET consistently outperformed other methods in gaze accuracy during validation stages, behavioral prediction during dynamic tasks, and retinotopic mapping of free-viewing visual stimuli, particularly in peripheral visual areas. These findings establish MoCET as a robust and versatile method for correcting eye tracking data, enabling more precise studies of behavioral and neural processes in naturalistic contexts.

MoCET generalizes across runs without repeated calibration
Thus far, our results demonstrated that MoCET substantially improves eye tracking accuracy within individual runs by correcting for intra-run head motion. However, head motion can also occur during inter-run intervals, such as brief resting periods or participant repositioning between scanning blocks. If eye tracking calibration is performed only once at the beginning of the experimental session, any shift in head position across runs may result in systematic errors that persist throughout subsequent runs (Fig. 5a). Conventional detrending methods or single-point re-centering strategies may not sufficiently address these across-run misalignments, particularly when rotation or non-translational motion is involved.

To evaluate whether MoCET can also correct across-run motion drift, we trained a motion-to-gaze regression model on a single calibration run (the run with the highest-quality calibration among the six) and applied it to all other runs using head motion parameters realigned to the first volume of the calibration run (Fig. 5b). As comparison baselines, we tested two alternatives: (1) a re-centering approach that re-aligns the calibration origin to the pupil center at the start of each new run, mimicking the manual drift correction used in eye tracking software; and (2) Re-centering and polynomial detrending of the raw gaze time series.

Our results show that across-run MoCET slightly underperforms within-run MoCET in overall accuracy, yet significantly outperforms both detrending and re-centering methods (Fig. 5c, all ps < 0.001). While re-centering can partially address translational drift, it fails to account for within-run motion and rotational shifts, limiting its effectiveness. Notably, across-run MoCET achieved robust performance even when runs were categorized as unusable, suggesting that effective across-run correction is possible despite suboptimal or missing within-run eye tracking calibration (Fig. 5c). These findings highlight MoCET’s potential to reduce experimental burden by requiring only a single calibration run per session, while preserving reliable gaze estimation across multiple runs.

Comparison of camera-based and MR-based eye tracking
Magnetic resonance (MR)-based eye tracking has been explored for decades as an alternative to traditional camera-based systems17,22–24. This approach eliminates the need for additional eye tracking hardware, as it relies solely on the fMRI data to infer gaze. Recent advancements, such as DeepMReye21, have advanced MR-based eye tracking by leveraging deep neural networks to decode gaze coordinates directly from MR signals with promising levels of accuracy. MR-based eye tracking not only simplifies experimental setups but also enables retrospective analysis of preexisting datasets, broadening its application across studies21,31. However, because MR-based methods are constrained by the spatial and temporal resolution of fMRI, it remains unclear whether they can substitute camera-based systems in applications requiring precise, moment-to-moment gaze tracking.

We compared the performance of camera-based and MR-based eye tracking methods. For the MR-based approach, we examined three DeepMReye models using (1) the original pretrained model weights (Pretrained), (2) pretrained weights finetuned with our dataset (Finetuned), and (3) weights trained from scratch exclusively on our dataset (Scratch). Both the Finetuned and Scratch models were trained on 24 calibration points during the calibration stage (Fig. 6a). While the Scratch and Finetuned models demonstrated low training losses and effectively captured gaze coordinates during calibration, the Pretrained model struggled to fit the training data, showing near-zero responses (Fig. 6b, Euclidean error: Scratch: 0.518 deg; Finetuned: 0.886 deg; Pretrained: 6.193 deg).

Although the re-trained MR-based models performed well on the calibration data, they exhibited limitations when applied to the rest of the experiments. Specifically, while the DeepMReye models successfully recovered general gaze directions (e.g., looking up, down, left, or right), demonstrating their ability to capture trends in gaze movement derived from fMRI data (Fig. 6c, d; Pearson’s correlation of horizontal direction: Scratch: r = 0.574, Finetuned: r = 0.562, Pretrained: r = 0.443; vertical direction: Scratch: r = 0.623, Finetuned: r = 0.421, Pretrained: r = -0.003), they showed reduced precision in mapping gaze locations, often predicting positions that deviated significantly from the ground truth (Fig. 6c, e; Euclidean error: Scratch: 5.521 deg, Finetuned: 5.525 deg, Pretrained: 6.184 deg).

In contrast, the camera-based eye tracking method, enhanced with MoCET, consistently outperformed MR-based methods, maintaining both precise gaze direction and spatial accuracy of gaze coordinates across the entire experiment (ps < 0.001 for all comparisons). We observed that MR-based models tended to predict gaze positions near the screen’s center, suggesting limited performance when generalizing to novel data. This pattern indicates that the deep neural network models had difficulty accurately mapping gaze locations beyond the distribution of their training data, leading to small-magnitude or near-zero responses when encountering unfamiliar fMRI data. The combination of high gaze direction accuracy but low spatial precision observed in our study is consistent with findings from previous studies utilizing MR-based eye tracking models21,31. These results suggest that while MR-based models hold promise for investigating gaze patterns related to cognitive processes in fMRI studies, they are currently less suitable for applications requiring eye tracking with high spatial and temporal precision.

Methods
Participants
Nineteen participants (8 females, mean age 24.02 ± 2.54 years) were recruited for the study. All participants provided written informed consent, with the study protocol approved by the Institutional Review Board of Sungkyunkwan University (2020-09-010-001) and received monetary compensation. Participants completed 12 runs of the Minecraft task across two or three fMRI sessions, depending on individual availability. Eye tracking data were evaluated based on specific validation criteria (see Methods—Eye tracking accuracy). One participant was excluded from the analysis as none of their runs met these criteria. As a result, data from 18 participants (average number of verifiable runs: 7.39 ± 3.03, see Fig. 1c) were included in the final analysis. All 18 participants also completed an additional fMRI session involving pRF experiments, which served as a reference for validating the retinotopic mapping results.

To further evaluate MoCET’s generalizability and accuracy, we analyzed three independent datasets: two movie-watching fMRI datasets collected at 3T and 7T scanners from separate groups of 12 participants each, and a behavioral eye tracking dataset from four participants who completed three runs of the Minecraft task outside the MRI scanner. The behavioral dataset enabled a direct comparison between standard laboratory eye tracking and MRI-compatible eye tracking corrected using MoCET.

Camera-based eye tracking system
Eye tracking during fMRI was conducted using an Avotec MRI-compatible endoscopic camera and illuminator, installed in front of the participant’s right eye inside both the 7T and 3T scanners, capturing eye image frames at 60 Hz. For behavioral experiments outside the scanner, pupil position was recorded at 1000 Hz using the EyeLink 1000 Plus (SR Research) and subsequently downsampled to 100 Hz for analysis. Post hoc image processing was applied to reduce high-frequency spatial noise in the eye video and to binarize the image for improved pupil detection. For accurate pupil detection and tracking, we implemented the Pupil Reconstructor with Subsequent Tracking (PuReST) algorithm47. The resulting pupil coordinates were then preprocessed to exclude low-confidence data caused by blinks, defined as frames with a pupil confidence score below 0.75. Additionally, we removed abnormal spikes in the pupil coordinates that exceeded three standard deviations from the local mean, which typically occurred when the algorithm mistakenly detected non-pupil dark, roundish areas during eye closure. The identical pupil detection and tracking procedure was applied to simulated eye tracking data. Note that no online or offline drift correction was applied to behavioral eye tracking data used for comparison.

Experimental procedure
For the main analysis, we used eye tracking data collected while participants performed a 13-min 3D Minecraft25-based video game task in a 7T MRI scanner. The stimulus was presented on a screen subtending 20.5° × 12.8°. Each participant completed two or three sessions, depending on individual availability, to complete twelve runs in which they played the video game on different maps. At the beginning and end of each run, participants underwent eye tracking calibration, in which they fixated on green dots sequentially displayed on the screen. The initial calibration involved two repetitions of a 12-dot sequence, resulting in participants fixating on a total of 24 dots. At the end of the video game, a validation stage required participants to fixate again on the same 12 dots. During the game, participant gaze was unrestricted, allowing for natural, free-viewing behavior. The video game task included a 3-min period during which participants built new blocks and removed existing blocks in a 3D environment. Eye tracking data from this period was used to predict subsequent building or breaking actions (See Methods—Predicting behaviors from gaze patterns for more details). For comparison, a behavioral version of the Minecraft task was conducted outside the scanner, with the display size matched to the MRI setup in visual angle. This study is neither approved nor endorsed by Mojang or Microsoft.

For the retinotopic mapping analysis, participants completed an additional fMRI session of pRF experiments. During the experiment, participants maintained fixation on a central dot and pressed a button whenever they detected a change in the dot’s color. The visual stimuli consisted of colorful cartoon images (toonotopy) that were viewed through moving wedge, ring, and bar apertures, designed to stimulate localized regions of the visual field48,49. The wedge runs used rotating wedges (counterclockwise or clockwise) to stimulate specific angular regions of the visual field, while the ring runs involved expanding or contracting concentric rings to map eccentricity. During the bar runs, bars with varying orientations (e.g., horizontal, vertical, or oblique) swept across the visual field in multiple directions. The pRF session comprised six runs, with a total duration of ~38 min.

To assess generalizability across tasks and MRI scanners, we analyzed two additional movie-watching fMRI datasets acquired from separate groups of 12 participants each, on 3T and 7T scanners. Each dataset included standard eye tracking calibration (24-point calibration at the beginning and 12-point validation at the end of each run). In the 3T dataset, participants viewed ~12 min of first person-view movie clips on a screen subtending 27.0° × 15.2°. In the 7T dataset, participants watched two 10-min runs of naturalistic movies on a screen subtending 20.5° × 12.8°.

fMRI data acquisition and preprocessing
Functional neuroimaging data were collected using a 7T Siemens MAGNETOM Terra MRI scanner equipped with a 32-channel Nova head coil, located at Sungkyunkwan University and the Institute for Basic Science, Center for Neuroscience Imaging Research. Blood oxygenation level-dependent (BOLD) contrast was measured using T2*-weighted functional images obtained with a dual-polarity GRAPPA (DPG) sequence (voxel size: 1.5 mm isotropic; TR: 1600 ms; TE: 21 ms; FOV: 210 × 210 mm; 96 slices covering the whole brain; flip angle: 50°). High-resolution anatomical images were acquired using an MP2RAGE sequence (voxel size: 0.7 mm isotropic; TR: 5888 ms; TE: 2.44 ms; FOV: 224 × 224 mm; 320 slices; flip angle 1: 4°; flip angle 2: 5°). The same protocol was also used for the 7T movie-watching dataset, while the 3T dataset was acquired using BOLD fMRI protocol described in our previous study50.

Preprocessing of both functional and anatomical data was conducted using fMRIprep51. Since the default skull-stripping for MP2RAGE data in fMRIprep was suboptimal, the skull was manually removed prior to preprocessing. Anatomical data were then processed for intensity non-uniformity correction, brain segmentation, and surface reconstruction. Functional data underwent motion correction and were aligned to the MNI152 standard space for analysis with DeepMReye. For voxel-wise pRF modeling, functional data were maintained in their native space to preserve precise spatial resolution. No additional preprocessing steps were applied.

Eye tracking analysis
Eye tracking model calibration. During the calibration period, we collected pupil coordinates at 24 points (4×3 grid, repeating each point twice) presented on the screen. Each calibration point appeared for 1.6 s as a green square with a central red dot. The square expanded to its largest size at 0.8 s and then began to shrink, creating a clear visual anchor for participants. To consider the saccadic delay and maximize calibration precision, we focused on a 0.5-s period during the middle of each presentation (when the square was largest) and averaged the x and y coordinates of the pupil within this time window. This resulted in a set of 24 averaged pupil coordinates paired with known screen coordinates for training the eye tracking model.

To predict gaze location from pupil coordinates, we employed a radial basis function (RBF) interpolation method52–54, which is widely used for mapping spatial coordinates. RBF interpolation is particularly effective for non-linear mappings when the relationship between input and output coordinates may not follow a simple linear path, such as mapping recorded pupil coordinates from an oblique field-of-view eye tracking camera to flattened screen coordinates. RBF interpolation calculates interpolated values as a weighted average of distances between known calibration points and input pupil coordinate, providing a smooth and continuous mapping from pupil coordinates to gaze location on the screen. The calibrated RBF model was applied to the entire set of pupil coordinates collected during the experiment, converting each pupil position to a predicted gaze location on the screen.

Eye tracking accuracy. To assess the accuracy of the eye tracking data, we calculated the Euclidean distance between the predicted gaze location (averaged within each 0.5-s window) and the ground truth, defined as the actual location of each calibration point on the screen. Since gaze location was averaged after applying the interpolation model, calibration error could exceed zero due to the inherent variability in gaze position within each 0.5-s calibration window.

We implemented a two-step quality control procedure to distinguish different sources of eye tracking inaccuracy, such as instrumental error, fixation instability during calibration, and head motion-induced error. Specifically, we evaluated gaze accuracy within both the calibration and validation periods using separate models trained and tested on data from the same period. Runs with gaze error below 1.0° in both periods were labeled as verifiable and included in subsequent analyzes related to eye tracking accuracy (e.g., Fig. 4a). If only the calibration phase met this threshold, the run was labeled as usable and retained for analyzes that relied only on calibration (e.g., behavioral prediction and visual field mapping; Fig. 4b, c). Runs that did not meet the threshold in either phase were labeled unusable but still contributed to across-run generalization analyzes (e.g., Fig. 5c), where no within-run calibration was required. The proportions of verifiable, usable, and unusable runs are shown in Fig. 1c. No data were excluded on the basis of fMRI data quality.

To examine the relationship between head motion and eye tracking error, we estimated head shift indirectly, as between-participant variation in camera-to-eye distance prevented direct measurement of actual distances from the camera. To approximate head shift in physical units, we conducted post-hoc measurements of each participant’s vertical palpebral fissure height (PFH). Thirteen of the original 18 participants were recontacted to obtain PFH in millimeters, and the corresponding PFH in pixels was extracted from their eye tracking videos to compute participant-specific pixel-to-millimeter scale factors. For the remaining five participants, we used the group-mean PFH (mean = 10.73 mm, s.d. = 1.31 mm) to estimate the scale. The estimated head shift (in mm) during the experiment was computed by multiplying this scaling factor by the mean change in pupil coordinates (in pixels) from initial calibration to the validation stage. This procedure provided a relative measure of head shift, which was then used to analyze its relationship with eye tracking error.

Motion-corrected eye tracking (MoCET)
To compensate for head motion effects in eye tracking data, we used participants’ head motion parameters obtained from fMRI preprocessing. These parameters consist of six degrees of freedom (6 DoF) motions, capturing translations along the x, y, and z axes as well as rotations around these axes. These parameters, used during the motion correction step, reflect the relative displacement of the head from a reference template image. To ensure that the head motion parameters calculated from the BOLD reference image estimated during fMRIprep preprocessing, aligned with the initial eye tracking calibration at the beginning of the experiment, we re-centered them by subtracting the head motion values of the first volume from all subsequent volumes. This adjustment yielded head motion displacements relative to the initial calibration position, which were then used to correct for head motion-induced error in the eye tracking data and to generate simulated eye movement under head motion in our computational model simulation.

To mitigate head motion-related error in the eye tracking data, we applied a signal denoising method based on linear regression. For the main analysis, our regressors included the six head motion parameters as well as polynomial terms up to the third degree (cubic). The head motion parameters were upsampled using linear interpolation to match the temporal resolution of the eye tracking data at 60 Hz. Using these combined regressors, we constructed a linear regression model to predict the x and y pupil coordinates. The model predictions were then subtracted from the original pupil coordinates, resulting in motion-corrected pupil coordinates. We applied polynomial detrending using a similar approach to compare eye tracking accuracy across different detrending methods.

Across run generalization. To test whether MoCET can correct inter-run eye tracking drift without repeated calibrations, we implemented an across-run correction protocol. For each participant, a single calibration run was selected (the run with the lowest validation error), and a linear regression model was trained to map 6-DoF head motion parameters to pupil displacement. To extend this model across runs, head motion parameters in the other runs were realigned to the same reference volume (i.e., the first volume of the calibration run), enabling prediction of motion-induced drift across separate scan runs. The learned model weights from the calibration run were then directly applied to all other runs without re-fitting.

In our full model, MoCET combines head motion regressors with low-order polynomial terms to capture both motion-induced and non-motion-related error. Since polynomial terms are time-dependent and cannot be reused across runs, we applied across-run MoCET in three steps: (1) apply motion correction using trained weights from the calibration run, and (2) fit new polynomial detrending per run to remove residual drift. We compared across-run MoCET to two baselines: (1) re-centering the gaze origin at the start of each run, mimicking manual drift correction, and (2) re-centering followed by polynomial detrending to reduce slow drift. Performance was assessed using validation error across non-calibration runs. We also evaluated performance separately for verifiable and unusable runs (based on calibration quality) to assess robustness of MoCET to poor or missing calibration data.

Nonlinear motion-correction. While MoCET assumes a linear relationship between head motion and drift in eye tracking data, this assumption may not hold under all circumstances. In particular, when head motion is large or abrupt, a simple linear regression model may be insufficient. To evaluate when the linearity assumption in MoCET remains valid and whether more complex, nonlinear models provide added value, we categorized eye tracking runs based on their head motion profiles and compared multiple versions of MoCET under these conditions. ‘Large motion’ runs were defined as those with a maximum in-plane displacement exceeding a +1 z-score threshold. To identify drift-like motion, we computed autocorrelations of each of the six head motion parameters over lags of one to five TRs, then averaged across lags and parameters. Runs with a z-scored mean autocorrelation above +1 were classified as drift. In contrast, spike-like motion was characterized by abrupt, transient movements, defined as runs with a z-scored mean autocorrelation below –1.

To test whether nonlinear modeling improves performance under different head motion types, we introduced two extended models. MoCET-Large incorporates squared terms and temporal derivatives of the head motion parameters to capture larger or more dynamic shifts. MoCET-Interaction includes pairwise interaction terms between head motion axes to account for cross-dimensional effects. These models were evaluated alongside the original linear approach to assess the benefit of increased model complexity.

To examine the validity of the linear assumption under more extreme conditions, we performed a simulation-based analysis. Because large head movements are difficult to elicit reliably during empirical fMRI sessions, we artificially amplified head motion by scaling the original motion parameters by 20% to 360%. This approach allowed us to systematically test MoCET and its nonlinear variants under a wide range of motion intensities, including cases beyond typical experimental variability.

Computational simulation of eye movement
Anthropometric parameters of model simulation. Anthropometric measurements of adult human heads adopted from previous studies26–28 were slightly adjusted to create an anisotropic, spherical head model for our simulation. For example, three head dimensions—head breadth (ear-to-ear distance), horizontal depth (back of head to nose), and vertical length (chin to top of head)—were averaged to define a single parameter representing the diameter of the model’s head sphere. The model’s eyeballs are physically attached to this head sphere, such that head movement affects the 3D geometric position of the eyeballs, while each eyeball can rotate independently to simulate gaze toward target locations. As the pupil is attached to the eyeball, its 3D coordinates change in accordance with the eyeball’s rotation, maintaining alignment along the direct line from the eyeball center to the target gaze location. Supplementary Fig. 1 provides detailed anthropometric parameters of the head and eyeball used in the computational model.

Optimization of eye tracking camera parameters. A virtual eye tracking camera was positioned in front of the model’s left eye to capture simulated eye movements. Due to variations in participant head size, eye position, and setup alignment, the direction of the actual camera installed within an MRI scanner may not be completely perpendicular to the eyeball, often resulting in slight tilts. To replicate realistic eye tracking as closely as possible, we customized the virtual camera’s direction, roll angle, and distance from the model’s eyeball, calibrating these parameters to match participant-specific eye tracking data. This was achieved by simulating a range of configurations for four camera parameters. For the camera’s orientation, the baseline direction was set to face the model’s eyeball directly; yaw and pitch angles were then varied by up to ±5 degrees along both horizontal and vertical axes. The camera’s roll angle was parameterized within a range of −90 to +90 degrees. Finally, the camera-to-eyeball distance was adjusted from 4.5 to 15 cm to account for natural variations in participant head and eye positioning relative to the fixed camera position in the head coil. This setup created ~36,000 unique combinations of four camera parameters (yaw, pitch, roll, and distance).

To determine the optimal camera parameters for each participant, we simulated the model’s gaze directed toward 12 calibration points on a screen, producing twelve 2D pupil locations as captured by the virtual eye tracking camera. These simulated pupil locations were then compared to the participant’s actual pupil coordinates recorded for the same 12 calibration points. For each of the 36,000 parameter combinations, we calculated the discrepancy between the model’s and participant’s pupil locations, and selected the optimal parameters for each participant through a grid search that minimized this difference. The optimized camera parameters averaged across participants and examples of parameters for individual participants are shown in Supplementary Fig. 1.

Incorporating head motion parameters. At each step of the simulation, we constructed a 3D rotational transformation matrix and a 3D translational transformation matrix from head motion parameters. These matrices were then applied to the coordinates of the model’s head and attached eyeball, enabling our simulation to precisely reproduce participants’ head motions in the simulation environment.

Analysis of simulated gaze. The model’s eye movement was recorded as a sequence of images using a virtual eye tracking camera. Ray casting was employed to generate 2D projections of 3D objects (head, eyeball, and pupil) by tracing rays from the virtual camera until they intersected with object surfaces, determining their visible positions55. For visualization (e.g., Fig. 2 and Supplementary Fig. 1), a light source and the Blinn-Phong reflection model56,57 were used to render realistic colors and shadows. However, for efficient simulation and accurate pupil tracking, rendering was simplified by assigning fixed colors to objects without light reflection, ensuring only the closest intersecting object was represented. This optimized both simulation speed and accuracy while preserving essential pupil location details.

Simulated eye tracking data were preprocessed and analyzed using the same procedure as the human eye tracking data. To examine the relationship between the magnitude of head motion and eye tracking error, we calculated the extent of head shift occurring within the px-py plane, from initial calibration to final validation. While the magnitude of head shift in human eye tracking data was estimated relative to the assumed pupil size, the model simulation allowed for the precise measurement of the actual physical distance of head shift in 3D space.

Permuted random head motion simulation. To assess the statistical significance of the relationship between head motion and pupil coordinates, we generated permuted random head motion parameters. The randomization was performed using a phase-shuffling approach, which preserves the power spectrum and temporal autocorrelation of the original head motion time series. Specifically, the Fourier transform of each head motion parameter was computed, and the phase components were randomly shuffled while keeping the amplitude spectrum intact. The inverse Fourier transform was then applied to reconstruct the randomized head motion time series.

This procedure ensures that the randomized head motion retains the same temporal structure as the original data but removes any relationships with the actual experimental conditions. We applied this method independently to each of the six head motion parameters. These randomized head motion parameters were then used to simulate pupil movements in the geometry-based eyeball model, producing a null distribution of gaze similarity metrics. Statistical significance was determined by comparing the actual simulation results with the null distribution obtained from 100 permutations for each dataset. To evaluate overall significance across the dataset, we aggregated individual p-values using Fisher’s method29, providing a robust summary statistic for group-level analyzes.

Predicting behaviors from gaze patterns
To evaluate the predictive power of drift-corrected gaze data for participant behavior, we analyzed data from the Minecraft-based video game task. In this task, participants sequentially built new fences or removed existing fences within a square arena to create a shortcut from their starting locations to a designated destination. Each participant’s decisions and actions were logged in-game, allowing us to identify their next target block (fence) based on their strategy. We used this behavioral dataset to compare the predictive performance of eye tracking data corrected using MoCET, linear detrending, polynomial detrending, and uncorrected data.

The in-game log file, recorded at 20 frames per second, included the 3D physical coordinates of each target block in the Minecraft world. To determine the target’s corresponding location on the screen, we used the participant’s in-game camera position, including their locations, yaw (horizontal rotation), and pitch (vertical rotation). These parameters were used to project the 3D world coordinates of the next target block onto 2D screen coordinates relative to the participant’s FOV. This process was repeated for each frame to account for participant movement or camera adjustments during the task.

For each moment, the next target block was identified based on the in-game log, and the distance between the participant’s gaze and the 2D screen coordinates of the target was calculated for a 10-s period preceding the action (building or removing a block). A “hit” was defined as a gaze position falling within a 2-degree visual angle from the target’s location on the screen. The hit rate of each action was then calculated as the percentage of frames within the 10-s window (i.e., 200 frames) in which a hit occurred. Chance-level performance was estimated based on the probability of a random gaze location falling within a 2-degree visual angle around the target. Specifically, the circular area corresponding to a 2-degree visual angle (πr2) was divided by the total screen area, assuming a uniform distribution of gaze locations across the screen. This provided a baseline probability of a random gaze intersecting the target. The overall hit rate for each participant was averaged across all actions. Statistical comparisons of hit rates between the different eye tracking data correction methods were performed using paired t-tests.

Visual field mapping from free-viewing visual stimuli
To evaluate the accuracy of retinotopic mapping using free-viewing visual stimuli, we used drift-corrected gaze data for pRF modeling40,41. The free-viewing stimuli consisted of the Minecraft video game display as participants played the task. Gaze data corrected using MoCET, polynomial detrending, linear detrending, and uncorrected data were used to generate gaze-centered stimulus representations and assess their impact on retinotopic mapping in the visual cortex.

Stimulus representation and spatiotemporal local contrast. For each frame of the video game display (original resolution: 1600 × 1000 pixels), we generated gaze-centered spatiotemporal local contrast by extracting stimulus patches relative to the participant’s gaze. To account for potential gaze coordinates outside the visible screen, the original frame was padded with gray borders, creating an expanded frame of 4800 × 4800 pixels. Using the gaze coordinates, a 3200 × 3200 pixels patch was cropped from the padded image, ensuring the gaze remained at the center of the extracted stimulus. The cropped patch was then resized to a resolution of 320 × 320 pixels. To compute spatiotemporal local contrast, each upsampled frame was divided into small 3D patches of 5 × 5 pixels spatially and 1.6 s temporally (48 frames). Standard deviation values were calculated within each 3D patch, resulting in a spatiotemporal local contrast representation with a resolution of 64 × 64 × 510. This stimulus energy signal served as the input to the pRF model39.

pRF model fitting and analysis. The pRF model estimated polar angle representations in the visual cortex by fitting a Gaussian receptive field centered on the predicted gaze location to voxelwise BOLD responses. The visual cortex mask was extracted from a resting-state functional atlas58. Model fitting utilized the spatiotemporal local contrast signal derived from gaze-corrected free-viewing stimuli as the input and voxelwise time-series data as the output. The Gaussian receptive field model predicted neural responses to the spatial location of stimuli, enabling the reconstruction of polar angle maps. Model performance was quantified by calculating angular errors between the estimated polar angles and canonical polar angles for ten cortical landmarks, including the calcarine sulcus and V1-V2 and V2-V3 boundaries (dorsal and ventral) in both hemispheres. Cortical landmarks were identified using retinotopic ROIs from the HCP dataset49, where key reference vertices (5–10 per landmark) were manually selected along the cortical boundaries. A geodesic pathfinding algorithm was then used to interpolate and connect these reference vertices, forming a continuous representation of each landmark. The extracted geodesic lines were used to derive ground-truth polar angles for evaluating model accuracy.

Training and validation of MR-based eye tracking models
To train and evaluate the MR-based DeepMReye models21, we first extracted eyeball voxel masks from the fMRI data. The masks were generated using the protocol described in the original DeepMReye reference, and their quality was manually inspected by researchers to ensure proper delineation of the eyeball regions. Three MR-based eye tracking models were compared: the Pretrained model, which utilized the original pre-trained DeepMReye weights without modification; the Finetuned model, where the pre-trained weights were further trained using our dataset to adapt to the current experimental settings; and the Scratch model, which was trained from scratch using only the calibration data from this study.

For the initial calibration stage, 24 volumes corresponding to the presentation of sequential calibration points were used to train the Finetuned and Scratch models. The calibration points appeared one per volume, providing labeled data for training. Most of the model training parameters, including the neural network architecture, loss function weights, batch size, and augmentation settings, were retained from the original configuration. However, specific adjustments were made to the number of training epochs and the learning rate decay schedule to ensure optimal model performance on the calibration data. These adjustments allowed the model to achieve sufficient convergence as assessed by the loss history during training.

After training, the models were applied to predict gaze coordinates across the entire fMRI experiment. The MR-based models produced one predicted gaze coordinate per fMRI volume. Performance validation was conducted for both the calibration and validation stages. During the validation stage, 12 gaze coordinates were predicted for the 12 validation points presented sequentially. Performance metrics, including gaze inaccuracy (Euclidean error) and directional accuracy (correlation with the ground truth), were calculated in the same manner as for camera-based eye tracking.

Statistics and reproducibility
All statistical analyzes followed the procedures described in the Methods. The relationship between head motion and pupil coordinates was assessed using simulation-based permutation testing, in which phase-shuffled head-motion parameters generated null distributions for evaluating significance. Eye tracking accuracy, behavioral prediction accuracy, and retinotopic mapping accuracy were compared across methods using paired t-tests. Sample sizes were based on prior naturalistic fMRI studies and matched common practice; no statistical method was used to predetermine sample size. Runs were categorized as verifiable, usable, or unusable based on pre-defined eye tracking accuracy thresholds and only runs with unusable calibration were excluded from analyzes that required accurate within-run calibration. The experiments were not randomized, and investigators were not blinded to allocation during data collection or analysis.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary\nMoCET is a retrospective motion correction framework for camera based eye tracking in fMRI. It combines six degree of\nfreedom (6 DoF) head motion parameters with cubic polynomial regressors to compensate gaze drift. Across both simulated\nand empirical data, the method exceeds traditional detrending and an MR based decoder (DeepMReye) on gaze precision,\nbehavioural prediction, and retinotopic mapping.\nAfter a detailed evaluation, I find the study’s methodological rigor, open data sharing, and clear demonstration of MoCET’s\nadvantages highly commendable; with only relatively small additions—chiefly clarifying the linear-model limits, refining the\npupil-scaling assumption, and expanding the comparison to a non-linear baseline—I believe the paper can be strengthened,\nand therefore I recommend acceptance subject to minor revision.\n________________________________________\nMajor Comments\n1. Linearity assumption\nThe model presumes a linear mapping between 6 DoF head motion and image plane drift, yet non linear effects can arise\nduring large translations or oblique camera angles. Please implement at least one non linear alternative—such as a model\nwith second order interaction terms or a kernel based regression—and compare it with the linear model using information\ncriteria or cross validated error. In parallel, quantify the motion range (e.g., > 5 mm translation or > 5° rotation/tilt) at which the\nlinear fit becomes inadequate. This can be done by mining high motion volumes already present or by collecting a short\nauxiliary scan in which participants deliberately move more.\n2. Pupil scale factor\nThe manuscript assumes a uniform 5 mm pupil diameter when converting pixel displacement to millimetres; in practice,\ninter-individual variation can be ±1 mm or more, producing scaling errors of 20 % or greater. A straightforward remedy would\nbe to place a small fiducial of known size (e.g. a 3 mm circular “target” sticker) on each participant’s cheek pad or forehead\nwithin the camera’s field of view. Because the sticker’s pixel width is constant across frames, it provides an individualised\nmillimetre-per-pixel scale that (i) eliminates the need to guess pupil size, (ii) remains valid even if pupil diameter changes\nwith arousal, and (iii) would allow MoCET, in principle, to be extended to pupillometry analyses that require absolute size\naccuracy.\n3. Temporal resolution mismatch\nBecause fMRI motion parameters are sampled every TR (1.6 s) while eye tracking is acquired at 60 Hz, the two signals differ\nin temporal resolution. Beyond the simulations already provided, please demonstrate how down sampling (i.e., subsampling\nthe 60 Hz eye-tracking signal to the fMRI TR of 1.6 s) the eye tracking data to the fMRI rate influences correction fidelity. A\nbrief supplementary figure comparing full rate and down sampled corrections would clarify the practical impact of this\nmismatch.\n4. DeepMReye calibration duration\nDeepMReye’s weaker performance may stem from the shortened fixation duration (1 TR) used during calibration—\nsubstantially briefer than the 4 s dwell time in the original protocol. Stable fixation is critical for accurate training; this\nlimitation should be explicitly acknowledged. Please also state whether hyper-parameter tuning or additional fine tuning was\nattempted for these abbreviated fixations, and briefly justify the conceptual value of comparing a camera based correction\n(MoCET) with a voxel based decoder (DeepMReye).\n5. Sample size rationale and run variability\nThe manuscript outlines recruitment and exclusion criteria but does not explain how the final sample sizes (n = 20 main;\nn = 18 pRF) were determined. Indicate whether these numbers were based on power analysis or prior work. Because valid\nruns per participant varied widely, explain how this variability was accommodated (e.g., weighting, run thresholds). Finally,\nclarify why 13 participants completed two sessions while eight completed one—was this a design decision, dropout, or\nexclusion? Note any fMRI specific exclusions (e.g., excessive motion) that shaped the final sample.\n6. To illustrate the generalisability of MoCET, I recommend two supplementary transfer-tests. First, assess \"cross-\nparticipant\" transferability by applying each participant’s regression coefficients to all other participants’ eye-tracking data,\nthen report the resulting gaze error relative to (i) participant-specific MoCET, (ii) polynomial detrending, and (iii) the\nuncorrected signal; this will quantify how strongly the model depends on individual camera-to-eye geometry. Second, evaluate \"within-participant\", across-session stability by re-using coefficients estimated in session 1 to correct session 2\n(acquired on a different day), and compare their performance with coefficients re-estimated from session 2’s own calibration;\nif cross-day error increases only marginally, it would highlight MoCET’s practical advantage of shortening or omitting\ncalibration in follow-up scans.\n________________________________________\nMinor Comment\nThe terms “drift,” “error,” and “noise” are used interchangeably throughout the manuscript. Please define them consistently at\nthe outset and use the preferred terms thereafter.\n(Remarks on code availability)\nGiven the limited review window, I did not have capacity to inspect the submitted code line-by-line; instead, I concentrated\non the conceptual soundness of the design, statistics, and interpretation. Because my comments request new analyses (e.g.,\na non-linear correction model and a sampling-rate sensitivity test), the code will necessarily change in the revision, at which\npoint a full code audit would be more appropriate.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "This work presents a method for motion correcting eye tracking data collected within an MRI scanner using MR-derived\nmotion parameters (MoCET). The authors document the challenges of in-scanner eye tracking by showing that eye tracking\nerror rates increase over the course of a single MRI run. They hypothesize that the errors are due to in-plane head\nmovement shifts and indeed find a high correlation between the validation eye tracking error and the in-plane head\nmovement as measured with standard MRI head tracking techniques. They further establish the strong relationship between\nin-plane head movement and eye tracking errors using a computational simulation of an eyeball being eye tracked, and\nagain find that eye tracker validation errors are a function of the in-plane head movement in their simulation. To correct for\nhead movement in the eye tracking data, the authors adapt standard fMRI motion-correction procedures for eye tracking by\nregressing out the 6DoF head position parameters from the eye tracking data, finding that this reduces the validation error\ndown to acceptable levels and outperforms other standard approaches for denoising eye tracking data. Next, they test\nMoCET in the context of two different tasks: predicting human behavior during an in-scanner freeviewing task and deriving\nretinotopic pRF maps, finding that MoCET-corrected data leads to the best performance on both tasks. Finally, they compare\ntheir method to DeepMReye, an MR-based method for decoding eye positions directly from the MRI data of the eye, and find\nthat MoCET outperforms DeepMReye.\nOverall, this is extremely high quality work both in execution and presentation. The methodological problem of collecting\nusable concurrent eye tracking data during MRI sessions is one that has been persistent throughout my own work and has\nstymied experiments over the years. I am very pleased to see an elegant approach that mostly solves the problem. The\nauthors thoroughly characterize the problem and the success of their correction procedure. The paper is clearly written. I\nhave one analysis request and several small comments.\nMain comment\n- I am curious how the drift in eye tracker error between calibration and validation, and the reduction in error from MoCET,\ncompare to standard within-run drift you see in standard eye tracking setups outside MRI scanners with head rests and/or\nbite bars.\nRelatedly, I’m curious for the behavioral prediction analysis what the prediction performance would be for standard eye\ntracking setups.\n- This could be addressed by repeating the in-scanner experiments on a standard eye tracking setup. I’m not familiar with the\nbrand of eye tracker used for the in-scanner experiments, but I don’t think the out-of-scanner tracker would necessarily need\nto exactly match the in-scanner tracker. Ideally it’s a setup with a chin rest for head stabilization, as this in my experience is\nthe most common setup for out-of-scanner head stabilization in eye tracking.\n- The benefits of this experiment are twofold.\n- First, it provides a reference frame for the in-scanner results. In the section “Impact of head motion on gaze tracking\naccuracy” and Figure 1, showing the calibration and validation error for an out-of-scanner eye tracker would provide a useful\nanchor for the scale of the problem for in-scanner eye tracking by showing the magnitude of the problem for in-scanner\nsetups vs out-of-scanner setups. In the section “Compensating for head movement with Motion-Corrected Eye Tracking” and\nFigure 4a, the validation error for a standard out-of-scanner eye tracker would provide a floor for the error that indicates the\ndegree of success. If MoCET reduces the validation error such that it is statistically the same as the validation error for an\nout-of-scanner eye tracking setup, that provides strong evidence that MoCET has functionally solved the targeted problem.\n- Second, it provides a reference frame for the behavioral prediction performance in the section “MoCET enables high-\nprecision eye tracking during free-viewing experiments” and Figure 4B. As currently presented, it’s clear that MoCET allows\nsome prediction performance improvements over standard in-scanner eye tracking correction approaches, but I’m not sure\nwhether the 15% hit rate is in line with what should be expected from standard head stabilized eye tracking.\nMinor comments\n- Page 23, “Eye tracking accuracy”, Paragraph 2 says that all data w/ calibration/validation errors of >1degree were excluded\nfrom subsequent analysis “to exclude errors stemming from fixation instability or individual gaze variability, thereby ensuring\nthat any remaining inaccuracies were not simply due to inconsistent eye movements.” I’m not sure how this could be the\ncase, given that much larger validation errors are reported in the paper. In the first Results section and Figure 1, the reported\nvalidation error is 7.093 degrees and in Figure 4 the uncorrected validation errors are in the range of 4-7 degrees. Please\nclarify if I misunderstood and adjust the text so the exclusion criteria are clear and consistent with the main text.\n- How big are the stimuli in the fMRI experiments in degrees of visual angle? I couldn’t find this anywhere in the main text or\nthe methods, and this is helpful for determining the size of the eye tracker errors (which are already reported in degrees)\nrelative to the stimuli.\n- DeepMReye comparison. Does the fMRI data need to be normalized to MNI space for the DeepMReye model to run?\nSince the analyses are within-participant, normalizing to MNI is not essential for group-level comparison, and DeepMReye\nmay show better performance in each participants native space.", "reviewer_4": "This paper by Park et al. presents a methodologically strong solution to correcting eye-movement measurement drift with\nhead-motion data in fMRI. The proposed method, Motion-Corrected Eye Tracking (MoCET), that retrospectively corrects for\nmotion-induced drift by leveraging the 6-degree-of-freedom head motion parameters that are a standard output of fMRI\npreprocessing. This approach makes a significant and accessible contribution to the field.\nStrengths\nBy capitalizing on data already generated in every standard fMRI pipeline, the method eliminates the need for additional\nhardware or complex setups. This lowers the barrier to high-quality eye-tracking research, making it accessible to a much\nbroader community of scientists. The ability to apply it retrospectively is a major advantage, potentially salvaging vast\namounts of existing data.\nThe authors employ an elegant dual-validation strategy that uses computational simulations effectively isolate the causal\neffects of head motion, confirming it as the primary source of drift. This is powerfully complemented by empirical data from\nhuman participants, where MoCET's performance is demonstrated across multiple, functionally relevant metrics. Further\nremarks below.\n1. Although the method is itself general and practical, the acquisition protocol perhaps less so. One would have liked to see\ngeneralization across more than one 7T dataset, one of which involved a fairly unusual task (Minecraft).\n2. Head motion can be quite variable across subjects. There may be a relationship between the characteristics of head-\nmotion across subject (more or less high-frequency events, variation is predominant motion type, etc.) that could affect the\neffectiveness of MOCET. If head-motion is more \"drift-like\" its will be more similar to the polynomial regressor approach. But\nif motion is more spiky, then these methods will diverge, an nonlinearities may be more important (or that robust regression\nmight yield better results). In general more discussion of individual variability in head-motion would be desirable; especially in\nlight of point 1 (generalization); for example, where different patient populations or age-groups might have different\ncharacteristic head-motion profiles.\n3. Related to above: there is an inherent discrepancy between the high sampling rate of eye-tracking (e.g., 60 Hz) and the\nlow sampling rate of fMRI-derived motion estimates (~0.5-1 Hz). Although the authors argue convincingly that head motion is\ndominated by low-frequency components, fast, transient movements (e.g., respiration-related) may not be perfectly corrected\nand could partially alias into the residual noise.\nOverall, MoCET is a well-motivated and rigorously evaluated solution that advances the fidelity of eye tracking in the\nchallenging MRI environment. The paper is technically sound, the validation is strong, and the open-source implementation\nsignificantly enhances its potential impact."}, "author_response": "Center for Neuroscience Imaging Research (CNIR),\nInstitute for Basic Science (IBS),\nSungkyunkwan University (SKKU),\nSuwon 16419, Republic of Korea\nTel: +82-31-299-4363 Fax: +82-31-299-4506\nResponse to Nature Communications Reviewers\nMotion-corrected eye tracking improves gaze accuracy during visual fMRI\nexperiments\nJiwoong Park, Jae Young Jeon, Royoung Kim, Kendrick N. Kay, Won Mok Shim\nWe sincerely thank the reviewers for their thoughtful and constructive feedback, which has\nsubstantially improved the clarity, rigor, and scope of our manuscript. In response, we have made\nsubstantial revisions to both the main text and supplementary materials, addressing each of the\nreviewers’ comments in detail.\nA key improvement in this revision is the expanded validation of MoCET’s performance and\napplicability. Specifically:\n● We implemented two nonlinear variants of MoCET to evaluate whether the linear model\nsufficiently captures the mapping between head motion and eye tracking drift. These\nvariants were compared using both simulations and human data. Results showed no significant\nadvantage of the nonlinear models, supporting the parsimonious linear assumption under\ntypical scanning conditions.\n● We conducted systematic simulations to evaluate the impact of large head motion,\nidentifying the range where linear assumptions may begin to degrade and where nonlinear\nmodels offer marginal gains.\n● We added an across-run variant of MoCET, which enables calibration transfer within\nthe same scan session. This method demonstrated high correction accuracy without requiring\nrepeated calibrations per run, offering a practical solution for in-scanner eye tracking\nexperiments.\n● To provide a baseline for comparison, we conducted behavioral eye tracking experiments\noutside the MRI scanner using a standard laboratory setup. These results show that in-scanner\neye tracking data, corrected by MoCET, were statistically comparable to out-of-scanner\nbehavioral eye tracking in both gaze accuracy and behavioral prediction performance,\nproviding a critical reference.\n● We added results from an independent replication dataset collected using a different free-\nviewing task and scanner, demonstrating that MoCET generalizes across tasks and imaging\nenvironments.\n● We addressed the temporal resolution mismatch between motion parameters and eye\ntracking signals by evaluating the impact of downsampling eye data to fMRI sampling rates.\nResults confirm MoCET’s robustness under realistic conditions.\n● We clarified the data inclusion criteria and the distribution of usable data across\nparticipants and runs, as requested, improving transparency about sample size and data quality\nthresholds.\n● The MoCET software package has been updated to support widely used eye tracking data\nformats (e.g., EDF files from EyeLink) and motion parameters from alternative preprocessing\ntools (e.g., FSL). All new features and analyses are reflected in the revised codebase.\n● For clarity, we have revised terminology throughout the manuscript.\nThese revisions address the reviewers’ concerns comprehensively and strengthen the contribution\nof MoCET as a robust, practical solution for in-scanner eye tracking during fMRI experiments.\nWe appreciate the reviewers’ insightful comments and hope that the revised manuscript meets the\njournal’s standards for publication.\nPlease see below for a point-by-point response to the reviewers’ comments. All revised text is\nmarked in red in the manuscript for ease of review.\nReviewer #1\n1. Linearity assumption: The model presumes a linear mapping between 6 DoF head motion\nand image plane drift, yet non linear effects can arise during large translations or oblique\ncamera angles. Please implement at least one non linear alternative—such as a model with\nsecond order interaction terms or a kernel based regression—and compare it with the\nlinear model using information criteria or cross validated error. In parallel, quantify the\nmotion range (e.g., > 5 mm translation or > 5° rotation/tilt) at which the linear fit becomes\ninadequate. This can be done by mining high motion volumes already present or by\ncollecting a short auxiliary scan in which participants deliberately move more.\nResponse: We thank the reviewer for highlighting this important issue regarding the linearity\nassumption in MoCET. While MoCET models a linear relationship between 6 DoF head motion\nparameters and pupil displacement on the image plane, we agree that nonlinear effects can\nemerge during large head translations or oblique camera angles due to the spherical geometry of\nthe head and optical distortions (Please see also Reviewer #4’s comment 2 for a similar concern).\nTo address this concern, we implemented and evaluated two nonlinear extensions of\nMoCET:\n● MoCET-Large, which includes 24 regressors, combining the original 6 DoF motion\nparameters with their temporal derivatives, squared terms, and squared derivatives, along\nwith polynomial terms up to cubic order.\n● MoCET-Interaction, which adds all pairwise second-order interaction terms among the 6\nmotion parameters, in addition to the original set and the same polynomial terms.\nWe classified empirical head motion into three types: large motion, spike-like motion, and drift-\nlike motion, based on in-plane displacement and autocorrelation measures (Supplementary Figs.\n3a and 3b). Using these categories, we compared correction accuracy between the linear model\nand the two nonlinear variants (Supplementary Fig. 3c). Across all conditions, we found no\nsignificant differences in correction accuracy between the linear and nonlinear models.\nTo further quantify the conditions under which the linear approximation might break down, we\nconducted a simulation in which head motion parameters were amplified by scaling their original\nvalues by 20% to 360% (Supplementary Fig. 3d). This allowed us to simulate scenarios with\nmoderate to extreme head motion. Results showed that the standard linear MoCET consistently\noutperformed the nonlinear models up to approximately 140% scaling. MoCET-Large began to\nshow advantages only when motion exceeded 200%, while MoCET-Interaction did not offer\nreliable improvements and was more susceptible to overfitting.\nThese results suggest that the linear assumption used in MoCET is well-suited for typical fMRI\nscanning conditions, where head motion is generally mild to moderate. While we agree that\ncollecting auxiliary scans with deliberate motion could offer additional insight, our simulations\napproximate a wide range of realistic motion levels observed in practice.\nFinally, to support broader use cases, we have included two nonlinear extensions of MoCET\nas optional modules in our open-source Python implementation, enabling users to apply\nthese models when higher-order motion effects are expected.\n“To further test the linear assumption, we evaluated the nonlinearity in the relationship between\nhead motion and pupil coordinates across different types of head motion. We found that the\nlinear and nonlinear variants of MoCET performed comparably across motion categories.\nAdditional simulations with artificially amplified motion indicated that the linear MoCET model\nremained effective at motion levels typical of fMRI studies, while nonlinear models offered only\nlimited additional benefit under extreme motion (for details, see Supplementary Fig. 3 and\nMethods)” —Results (page 11)\n“MoCET assumes a linear relationship between head motion and gaze error, which may become\ninadequate in cases of extreme head movement or when the eye tracking camera is installed at a\nsteep tilt relative to the gaze direction. In such conditions, nonlinear distortions in pupil\ncoordinates can introduce errors not fully accounted for by linear regression. However, our\nempirical evaluation across diverse head motion types, including large, spike-like, and drift-like\nmovements, showed that the linear MoCET model performed as well as more complex nonlinear\nvariants. Furthermore, simulations with systematically amplified motion confirmed that linear\nMoCET remains effective across a broad range of motion levels. Nonlinear extensions provided\nimprovements only under extreme head motion conditions, which are rarely encountered in\nempirical experiments (Supplementary Fig. 3). These findings support the validity of the linear\nassumption in typical fMRI settings, where head motion is often constrained by stabilization\ndevices such as foam padding, minimizing extreme deviations that could introduce nonlinear\ndistortions. To accommodate potential edge cases, we also provide these nonlinear MoCET\nvariants in our Python package, allowing users to apply more flexible correction models when\nneeded.” —Discussion (page 21)\n“While MoCET assumes a linear relationship between head motion and drift in eye tracking\ndata, this assumption may not hold under all circumstances. In particular, when head motion is\nlarge or abrupt, a simple linear regression model may be insufficient. To evaluate when the\nlinearity assumption in MoCET remains valid and whether more complex, nonlinear models\nprovide added value, we categorized eye tracking runs based on their head motion profiles and\ncompared multiple versions of MoCET under these conditions. ‘Large motion’ runs were defined\nas those with a maximum in-plane displacement exceeding a +1 z-score threshold. To identify\ndrift-like motion, we computed autocorrelations of each of the six head motion parameters over\nlags of one to five TRs, then averaged across lags and parameters. Runs with a z-scored mean\nautocorrelation above +1 were classified as drift. In contrast, spike-like motion was characterized\nby abrupt, transient movements, defined as runs with a z-scored mean autocorrelation below –1.\nTo test whether nonlinear modeling improves performance under different head motion types,\nwe introduced two extended models. MoCET-Large incorporates squared terms and temporal\nderivatives of the head motion parameters to capture larger or more dynamic shifts. MoCET-\nInteraction includes pairwise interaction terms between head motion axes to account for cross-\ndimensional effects. These models were evaluated alongside the original linear approach to\nassess the benefit of increased model complexity.\nTo examine the validity of the linear assumption under more extreme conditions, we performed\na simulation-based analysis. Because large head movements are difficult to elicit reliably during\nempirical fMRI sessions, we artificially amplified head motion by scaling the original motion\nparameters by 20% to 360%. This approach allowed us to systematically test MoCET and its\nnonlinear variants under a wide range of motion intensities, including cases beyond typical\nexperimental variability.” —Methods (page 29)\n—Supplementary Figure 3 (page 44)\n2. Pupil scale factor: The manuscript assumes a uniform 5 mm pupil diameter when\nconverting pixel displacement to millimetres; in practice, inter-individual variation can be\n±1 mm or more, producing scaling errors of 20 % or greater. A straightforward remedy\nwould be to place a small fiducial of known size (e.g. a 3 mm circular “target” sticker) on\neach participant’s cheek pad or forehead within the camera’s field of view. Because the\nsticker’s pixel width is constant across frames, it provides an individualised millimetre-\nper-pixel scale that (i) eliminates the need to guess pupil size, (ii) remains valid even if pupil\ndiameter changes with arousal, and (iii) would allow MoCET, in principle, to be extended\nto pupillometry analyses that require absolute size accuracy.\nResponse: We thank the reviewer for raising this important point regarding the assumptions\nunderlying our pupil size scaling. We clarify that MoCET’s primary contribution is to correct\npupil position, not pupil size. The assumed pupil diameter (5 mm) was used only to convert\ndisplacement values from pixels (px) to millimeters (mm) for figure visualization (e.g., Figs. 1d\nand 2c).\nHowever, we agree that a realistic, individualized millimeters-per-pixel scaling factor would\nimprove visualization accuracy and reliability and facilitate future pupillometry applications.\nBy contrast with behavioral eye tracking setups, the field of view (FOV) in MRI-compatible eye\ntracking systems is narrow and typically restricted to the immediate peri-ocular region (See Fig.\n1). This constraint makes it impractical to place a fiducial marker on the cheek or forehead\nwithout interfering with pupil detection.\nTo address this limitation, we conducted an additional post-hoc measurement study. We re-\ncontacted 13 out of the original 18 participants and measured vertical palpebral fissure\nheight (PFH). We then extracted the corresponding PFH in pixels from the eye-tracking videos\nto calculate participant-specific pixel-to-millimeter scale factors.\nWe used these participant-specific scale factors to revise figures reporting mm units. The updated\nplots show improved accuracy and robustness, supporting the reviewer’s suggestion to adopt\nmore realistic scaling.\nFor the remaining five participants who did not return for re-measurement, we used the group\nmean PFH from the 13 participants to estimate the scale. We thank the reviewer for raising this\npoint; it meaningfully improved the accuracy of our visualizations and enabled more precise\nsize-based analyses in future work.\n“To examine the relationship between head motion and eye tracking error, we estimated head\nshift indirectly, as between-participant variation in camera-to-eye distance prevented direct\nmeasurement of actual distances from the camera. To approximate head shift in physical units,\nwe conducted post-hoc measurements of each participant’s vertical palpebral fissure height\n(PFH). Thirteen of the original 18 participants were recontacted to obtain PFH in millimeters,\nand the corresponding PFH in pixels was extracted from their eye tracking videos to compute\nparticipant-specific pixel-to-millimeter scale factors. For the remaining five participants, we\nused the group-mean PFH (mean = 10.73 mm, s.d. = 1.31 mm) to estimate the scale. The\nestimated head shift (in mm) during the experiment was computed by multiplying this scaling\nfactor by the mean change in pupil coordinates (in pixels) from initial calibration to the validation\nstage. This procedure provided a relative measure of head shift, which was then used to analyze\nits relationship with eye tracking error.”—Methods (page 27)\n3. Temporal resolution mismatch: Because fMRI motion parameters are sampled every TR\n(1.6 s) while eye tracking is acquired at 60 Hz, the two signals differ in temporal resolution.\nBeyond the simulations already provided, please demonstrate how down sampling (i.e.,\nsubsampling the 60 Hz eye-tracking signal to the fMRI TR of 1.6 s) the eye tracking data\nto the fMRI rate influences correction fidelity. A brief supplementary figure comparing\nfull rate and down sampled corrections would clarify the practical impact of this mismatch.\nResponse: We thank the reviewer for raising this concern. While MoCET relies on motion\nestimates at a lower sampling rate, its core assumption is that head motion primarily contributes\nlow-frequency components to gaze drift, thus allowing low-frequency motion regressors to\ncapture and correct motion-related artifacts without attenuating rapid eye movements (see also\nReviewer #4’s comment 3).\nTo empirically test the impact of this time-resolution mismatch, we systematically\ndownsampled the original 60 Hz eye tracking data to lower sampling rates (down to 1Hz).\nFor each downsampled dataset, we applied MoCET as well as linear and polynomial detrending,\nand then evaluated eye tracking accuracy. As shown in Supplementary Fig. 7, MoCET\nmaintained robust correction performance down to 10 Hz, and outperformed standard\ndetrending methods even at extremely low sampling rates (e.g., 1 Hz). These results indicate\nthat MoCET is robust to temporal resolution mismatches and remains effective even when gaze\nsignals are corrected at the sampling rate of fMRI motion estimates.\n“To address this concern empirically, we systematically downsampled eye tracking data from\nMoCET’s accuracy remains stable down to 10 Hz, and even under extreme downsampling (to\n(page 21)\n—Supplementary Figure 7 (page 48)\n4. DeepMReye calibration duration: DeepMReye’s weaker performance may stem from the\nshortened fixation duration (1 TR) used during calibration—substantially briefer than the\n4 s dwell time in the original protocol. Stable fixation is critical for accurate training; this\nlimitation should be explicitly acknowledged. Please also state whether hyper-parameter\ntuning or additional fine tuning was attempted for these abbreviated fixations, and briefly\njustify the conceptual value of comparing a camera based correction (MoCET) with a voxel\nbased decoder (DeepMReye).\nResponse: First, we acknowledge that our calibration protocol used a shorter fixation duration\n(1 TR, 1.6 s) per target than the 4-second duration (5 TR) employed in the original DeepMReye\nprotocol. This shorter duration may increase variability in training samples due to unstable\nfixations. However, both the fine-tuned and scratch DeepMReye models showed strong\nperformance during training, indicating that the reduced fixation time did not substantially\nimpair model fitting. As shown in Fig. 6b, these models accurately captured the calibration data,\nsuggesting that our hyperparameters and protocol were sufficient for effective learning under\npractical constraints.\nWe also believe it is important to note the experimental trade-offs. Implementing longer fixation\ndurations would significantly increase the calibration burden, especially with larger numbers of\ntargets. In our case, extending to 5 TRs (8 seconds) per target across 24 locations would require\nover 3 minutes solely for calibration, which is often impractical in many fMRI protocols. If MR-\nbased eye tracking requires this level of calibration time to achieve competitive\nperformance, that represents an important limitation of such methods.\nFinally, we agree that the conceptual motivation for this comparison merited further clarification.\nIn the revised manuscript, we have expanded the rationale and emphasized the conceptual value\nof the comparison.\n“However, because MR-based methods are constrained by the spatial and temporal resolution of\nfMRI, it remains unclear whether they can substitute camera-based systems in applications\nrequiring precise, moment-to-moment gaze tracking.”—Results (page 16)\n5. Sample size rationale and run variability: The manuscript outlines recruitment and\nexclusion criteria but does not explain how the final sample sizes (n = 20 main;\nn = 18 pRF) were determined. Indicate whether these numbers were based on power analysis or prior\nwork. Because valid runs per participant varied widely, explain how this variability was\naccommodated (e.g., weighting, run thresholds). Finally, clarify why 13 participants\ncompleted two sessions while eight completed one—was this a design decision, dropout, or\nexclusion? Note any fMRI specific exclusions (e.g., excessive motion) that shaped the final sample.\nResponse: We appreciate the reviewer’s thoughtful observation regarding participant\nrecruitment and session variability. The present study was conducted as part of a large-scale\nneuroimaging data collection project that involved concurrent acquisition of fMRI and camera-\nbased eye tracking data. During the course of this project, we observed consistent inaccuracies\nin the eye tracking data, which led us to develop MoCET.\nThe participant sample reported in the original manuscript reflects the subset of participants\navailable at the time of the initial submission (𝑁 = 21). One participant was excluded based on\neye tracking quality criteria.\nThe original data collection project was structured to include both regular and extra sessions.\nParticipants were given the option to participate in the extra session after completing the\nregular session. As a result, at the time of the original submission, 13 participants had completed\nboth sessions (12 runs in total), while the remaining eight completed only the regular session (6\nruns), either because they chose not to continue or because the extra session had not yet\ncommenced.\nTo ensure consistency and robustness, we restricted analyses to participants who completed\nall 12 runs. Additionally, since the original submission, five participants who had previously\ncompleted only the regular session also completed the extra session as part of our ongoing\ndataset collection project. As a result, the updated dataset now includes 19 participants in total.\nAfter applying the same quality control criteria, 18 participants remained and were included in\nall analyses reported in the revised manuscript. All 18 participants also completed the pRF\nexperiment session. As a result of this update, approximately 33% more data now meet this\ncriterion compared to the previous manuscript. We also note that data exclusions were not\nmade on the basis of fMRI data quality (see also Reviewer #3’s comment 2).\nWe also conducted a power analysis based on the effect size observed in the original manuscript\ncomparing MoCET and polynomial detrending methods. This analysis indicated that a sample\nsize of at least 9 participants would be sufficient to achieve 80% power with Cohen's d of 1.14\nat significance level of 0.05. Therefore, our revised sample size exceeds this requirement and\nensures adequate statistical sensitivity.\n“Nineteen participants (8 females, mean age 24.02 ± 2.54 years) were recruited for the study.\nAll participants provided written informed consent, with the study protocol approved by the\nInstitutional Review Board of Sungkyunkwan University, and received monetary compensation.\nParticipants completed 12 runs of the Minecraft task across two or three fMRI sessions,\ndepending on individual availability. Eye tracking data were evaluated based on specific\nvalidation criteria (see Methods—Eye tracking accuracy). One participant was excluded from\nthe analysis as none of their runs met these criteria. As a result, data from 18 participants (average\nnumber of verifiable runs: 7.39 ± 3.03, see Fig. 1c) were included in the final analysis. All 18\nparticipants also completed an additional fMRI session involving pRF experiments, which\nserved as a reference for validating the retinotopic mapping results.” —Methods (page 22)\n“We implemented a two-step quality control procedure to distinguish different sources of eye\ntracking inaccuracy, such as instrumental error, fixation instability during calibration, and head\nmotion-induced error. Specifically, we evaluated gaze accuracy within both the calibration and\nvalidation periods using separate models trained and tested on data from the same period. Runs\nwith gaze error below 1.0° in both periods were labeled as verifiable and included in subsequent\nanalyses related to eye tracking accuracy (e.g., Fig. 4a). If only the calibration phase met this\nthreshold, the run was labeled as usable and retained for analyses that relied only on calibration\n(e.g., behavioral prediction and visual field mapping; Figs. 4b and 4c). Runs that did not meet\nthe threshold in either phase were labeled unusable but still contributed to across-run\ngeneralization analyses (e.g., Fig. 5c), where no within-run calibration was required. The\nproportions of verifiable, usable, and unusable runs are shown in Fig. 1c. No data were excluded\non the basis of fMRI data quality.” —Methods (page 26)\n6. To illustrate the generalisability of MoCET, I recommend two supplementary transfer-\ntests. First, assess \"cross-participant\" transferability by applying each participant’s\nregression coefficients to all other participants’ eye-tracking data, then report the resulting\ngaze error relative to (i) participant-specific MoCET, (ii) polynomial detrending, and (iii)\nthe uncorrected signal; this will quantify how strongly the model depends on individual\ncamera-to-eye geometry. Second, evaluate \"within-participant\", across-session stability by\nre-using coefficients estimated in session 1 to correct session 2 (acquired on a different day),\nand compare their performance with coefficients re-estimated from session 2’s own\ncalibration; if cross-day error increases only marginally, it would highlight MoCET’s\npractical advantage of shortening or omitting calibration in follow-up scans.\nResponse: Regarding cross-session generalizability, we agree that a generalizable correction\nmethod should ideally support calibration transfer across sessions. However, in our current\ndataset, across-session correction is limited by practical constraints. Specifically, we did not\nenforce a strictly identical camera setup or imaging volume alignment across sessions.\nConsequently, head motion parameters may not reflect a consistent displacement of the eye\nrelative to the camera, undermining correction accuracy. We now explicitly acknowledge this\nlimitation in the Discussion section of the revised manuscript.\nInstead, we implemented and evaluated an across-run version of MoCET, which performs\ncalibration transfer across multiple runs within the same session. Since camera placement\nand the imaging field-of-view are stable within a session, this setup allows for accurate motion-\nbased correction using a shared reference volume. Our results demonstrate that across-run\nMoCET maintains robust correction accuracy without requiring run-specific calibration, offering\na practical advantage for fMRI studies where within-run calibration is unavailable or unreliable.\nMoreover, this approach substantially reduces calibration demands for follow-up runs,\neffectively shortening experimental duration without sacrificing data quality. This\nfunctionality has now been added to the MoCET package, and its performance is presented in\nthe revised manuscript and Figure 5.\nWe also note that the reviewer’s comment was instrumental in motivating the development of\nthe across-run MoCET extension.\nRegarding cross-participant transferability, we agree this is a valuable direction for future work.\nHowever, MoCET’s core assumption relies on participant-specific camera-to-eye-to-head\ngeometry, which varies across individuals. Applying one participant’s regression model to\nanother would likely introduce substantial error due to differing eye positions, facial anatomy,\nand camera angles. For this reason, we did not include cross-subject transfer in the current\nevaluation but will consider it in future studies where these variables are better controlled or\nexplicitly modeled.\n“To enhance flexibility, we introduce an across-run variant of MoCET that enables calibration\ntransfer across runs within the same session, allowing robust correction even when within-run\ncalibration is limited or unavailable.” —Introduction (page 4)\n“To evaluate whether MoCET can also correct across-run motion drift, we trained a motion-to-\ngaze regression model on a single calibration run (the run with the highest-quality calibration\namong the six) and applied it to all other runs using head motion parameters realigned to the first\nvolume of the calibration run (Fig. 5b). As comparison baselines, we tested two alternatives: (1)\na re-centering approach that re-aligns the calibration origin to the pupil center at the start of each\nnew run, mimicking the manual drift correction used in eye tracking software; and (2) Re-\ncentering and polynomial detrending of the raw gaze time series.\nOur results show that across-run MoCET slightly underperforms within-run MoCET in overall\naccuracy, yet significantly outperforms both detrending and re-centering methods (Fig. 5c, all\nps<0.001). While re-centering can partially address translational drift, it fails to account for\nwithin-run motion and rotational shifts, limiting its effectiveness. Notably, across-run MoCET\nachieved robust performance even when runs were categorized as “unusable,” suggesting that\neffective across-run correction is possible despite suboptimal or missing within-run eye tracking\ncalibration (Fig. 5c). These findings highlight MoCET’s potential to reduce experimental burden\nby requiring only a single calibration run per session, while preserving reliable gaze estimation\nacross multiple runs.” —Results (page 16)\n“Beyond improving within-run eye tracking accuracy, MoCET also generalizes effectively\nacross multiple fMRI runs using a single calibration. By leveraging head motion parameters\naligned to a shared reference volume, MoCET enables accurate correction of inter-run drift\nwithout the need for recalibration, reducing experimental burden and facilitating application to\ndatasets with limited or inconsistent calibration. Nevertheless, while MoCET mitigates the need\nfor frequent recalibrations, we caution against relying solely on a single calibration per session.\nIf the only calibration run fails due to participant movement or tracking instability, recovery may\nbe difficult. Thus, collecting multiple calibration runs throughout the session remains a\nrecommended best practice to safeguard data quality and ensure fallback options when needed.\nMoreover, MoCET can be extended to enable drift correction across sessions, offering the\npotential for longitudinal eye tracking alignment without session-specific calibration. However,\nthis application requires strict control of experimental conditions, including consistent scanner\nsetup, identical camera configuration, and alignment of imaging coverage and reference volumes\nacross sessions. Without such consistency, head motion parameters may not accurately reflect\nthe relative displacement between the eye and camera, undermining correction accuracy.” —\nDiscussion (page 19)\n“To test whether MoCET can correct inter-run eye tracking drift without repeated calibrations,\nwe implemented an across-run correction protocol. For each participant, a single calibration run\nwas selected (the run with the lowest validation error), and a linear regression model was trained\nto map 6-DoF head motion parameters to pupil displacement. To extend this model across runs,\nhead motion parameters in the other runs were realigned to the same reference volume (i.e., the\nfirst volume of the calibration run), enabling prediction of motion-induced drift across separate\nscan runs. The learned model weights from the calibration run were then directly applied to all\nother runs without re-fitting.\nIn our full model, MoCET combines head motion regressors with low-order polynomial terms\nto capture both motion-induced and non-motion-related error. Since polynomial terms are time-\ndependent and cannot be reused across runs, we applied across-run MoCET in three steps: (1)\napply motion correction using trained weights from the calibration run, and (2) fit new\npolynomial detrending per run to remove residual drift. We compared across-run MoCET to two\nbaselines: (1) re-centering the gaze origin at the start of each run, mimicking manual drift\ncorrection, and (2) re-centering followed by polynomial detrending to reduce slow drift.\nPerformance was assessed using validation error across non-calibration runs. We also evaluated\nperformance separately for verifiable and unusable runs (based on calibration quality) to assess\nrobustness of MoCET to poor or missing calibration data.” —Methods (page 28)\n—Figure 5 (page 15)\n7. The terms “drift,” “error,” and “noise” are used interchangeably throughout the\nmanuscript. Please define them consistently at the outset and use the preferred terms\nthereafter.\nResponse: We thank the reviewer for pointing out this issue. In the revised manuscript, we have\nstandardized our terminology for clarity and consistency. Specifically, we now use “drift”\nexclusively to describe systematic changes in head position over time that contribute to camera-\neye misalignment during fMRI experiments. We use “error” to refer to gaze inaccuracies. We\nhave removed the term “noise” to avoid ambiguity. These definitions have been clarified early\nin the Methods section, and the revised terminology is now used consistently throughout.\n8. Given the limited review window, I did not have capacity to inspect the submitted code\nline-by-line; instead, I concentrated on the conceptual soundness of the design, statistics,\nand interpretation. Because my comments request new analyses (e.g., a non-linear\ncorrection model and a sampling-rate sensitivity test), the code will necessarily change in\nthe revision, at which point a full code audit would be more appropriate.\nResponse: We appreciate the reviewer’s thoughtful evaluation. In response to the reviewer’s\ncomments and suggestions, we have substantially updated the MoCET Python package to\ninclude:\n1. Nonlinear correction models, including variants with squared terms, temporal derivatives,\nand pairwise interaction terms.\n2. Across-run MoCET, which supports calibration transfer across multiple fMRI runs within\nthe same session.\n3. Expanded data compatibility, including support for EDF files from the EyeLink system and\nmotion parameters derived from FSL-based preprocessing pipelines.\nAll updated code and documentation are available in the latest version of the repository. We\nthank the reviewer for encouraging these improvements, which we believe substantially enhance\nMoCET’s robustness and flexibility.\nReviewer #2\n1. I co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nResponse: We thank constructive feedback provided, which has significantly helped us improve\nthe clarity, rigor, and impact of our manuscript.\nReviewer #3\n1. I am curious how the drift in eye tracker error between calibration and validation, and the\nreduction in error from MoCET, compare to standard within-run drift you see in standard\neye tracking setups outside MRI scanners with head rests and/or bite bars. Relatedly, I’m\ncurious for the behavioral prediction analysis what the prediction performance would be\nfor standard eye tracking setups. This could be addressed by repeating the in-scanner\nexperiments on a standard eye tracking setup. I’m not familiar with the brand of eye\ntracker used for the in-scanner experiments, but I don’t think the out-of-scanner tracker\nwould necessarily need to exactly match the in-scanner tracker. Ideally it’s a setup with a\nchin rest for head stabilization, as this in my experience is the most common setup for out-\nof-scanner head stabilization in eye tracking. The benefits of this experiment are twofold.\na. First, it provides a reference frame for the in-scanner results. In the section “Impact of\nhead motion on gaze tracking accuracy” and Figure 1, showing the calibration and\nvalidation error for an out-of-scanner eye tracker would provide a useful anchor for\nthe scale of the problem for in-scanner eye tracking by showing the magnitude of the\nproblem for in-scanner setups vs out-of-scanner setups. In the section “Compensating\nfor head movement with Motion-Corrected Eye Tracking” and Figure 4a, the\nvalidation error for a standard out-of-scanner eye tracker would provide a floor for the\nerror that indicates the degree of success. If MoCET reduces the validation error such\nthat it is statistically the same as the validation error for an out-of-scanner eye tracking\nsetup, that provides strong evidence that MoCET has functionally solved the targeted\nproblem.\nb. Second, it provides a reference frame for the behavioral prediction performance in the\nsection “MoCET enables high-precision eye tracking during free-viewing experiments”\nand Figure 4B. As currently presented, it’s clear that MoCET allows some prediction\nperformance improvements over standard in-scanner eye tracking correction\napproaches, but I’m not sure whether the 15% hit rate is in line with what should be\nexpected from standard head stabilized eye tracking.\nResponse: We thank the reviewer for this suggestion. In response, we conducted an additional\nbehavioral eye tracking experiment outside the scanner using a stabilized laboratory setup\n(EyeLink 1000 Plus at 1000 Hz with a chin rest and head post) to benchmark MoCET’s\nperformance against standard out-of-scanner conditions.\nTo establish a reference frame, we compared calibration and validation errors between in-\nscanner eye tracking data from fMRI experiments and behavioral eye tracking data collected\noutside the scanner. The results showed that validation error from motion-corrected, in-scanner\neye tracking data was statistically comparable to that for out-of-scanner behavioral eye tracking,\nindicating that MoCET reduces drift to levels comparable to high-quality out-of-scanner setups.\nThese results are reported in the revised manuscript (Fig. 4a).\nWe also evaluated behavioral prediction performance (hit rate) under the same task using the\nbehavioral eye tracking data. The hit rate obtained from the behavioral eye tracking data was\nstatistically comparable to that from in-scanner eye tracking data corrected by MoCET,\nsupporting the conclusion that MoCET enables behavioral inference accuracy comparable to\nstandard setups. This comparison is included in the revised manuscript (Fig. 4b).\nWe thank the reviewer again for this valuable suggestion, which has led to a substantial\nenhancement to the manuscript.\n“We further validate MoCET by showing that its corrected gaze accuracy closely matches that\nof behavioral eye tracking data collected under standard laboratory conditions.” —Introduction\n(page 4)\n“Notably, gaze accuracy achieved by MoCET was not statistically different from that observed\nin behavioral eye tracking experiments conducted outside the scanner, indicating that MoCET\nrecovers high-quality gaze signals even under the constraints of fMRI environments (𝑡(20) =\n1.34,𝑝 = 0.195)” —Results (page 13)\n“We also demonstrated that the hit rate from motion-corrected eye tracking was comparable to\nthat observed in behavioral eye tracking, indicating reliable recovery of task-relevant gaze\npatterns during fMRI experiments (𝑡(20) = 1.40,𝑝 = 0.175).” —Results (page 13)\n“To further evaluate MoCET’s generalizability and accuracy, we analyzed three independent\ndatasets: two movie-watching fMRI datasets collected at 3T and 7T scanners from separate\ngroups of 12 participants each, and a behavioral eye tracking dataset from four participants who\ncompleted three runs of the Minecraft task outside the MRI scanner. The behavioral dataset\nenabled a direct comparison between standard laboratory eye tracking and MRI-compatible eye\ntracking corrected using MoCET.” —Methods (page 23)\n“For behavioral experiments outside the scanner, pupil position was recorded at 1000 Hz using\nthe EyeLink 1000 Plus (SR Research) and subsequently downsampled to 100 Hz for analysis”\n—Methods (page 23)\n—Figure 4 (page 12)\n2. Page 23, “Eye tracking accuracy”, Paragraph 2 says that all data w/ calibration/validation\nerrors of >1degree were excluded from subsequent analysis “to exclude errors stemming\nfrom fixation instability or individual gaze variability, thereby ensuring that any\nremaining inaccuracies were not simply due to inconsistent eye movements.” I’m not sure\nhow this could be the case, given that much larger validation errors are reported in the\npaper. In the first Results section and Figure 1, the reported validation error is 7.093\ndegrees and in Figure 4 the uncorrected validation errors are in the range of 4-7 degrees.\nPlease clarify if I misunderstood and adjust the text so the exclusion criteria are clear and\nconsistent with the main text.\nResponse: We thank the reviewer for this observation. Eye tracking inaccuracies can arise from\nseveral distinct sources, including instrumental error, fixation instability during calibration, and\nmotion-induced drift. To accurately evaluate MoCET’s performance and distinguish these\nsources, we implemented a two-step quality control procedure.\nSpecifically, we applied the calibration procedure separately to the calibration and\nvalidation periods, and computed within-period gaze error using the same data segment\nused for model training. If both within-period errors were sufficiently low (i.e., below 1.0°),\nthe data were deemed verifiable and used to compute the cross-period validation error, as this\nindicated stable participant fixation and the absence of substantial instrumental error.\nTherefore, the large validation errors reported in Figure 1 are not in conflict with our exclusion\ncriterion. These values reflect the cross-period validation error (i.e., after training the model\non the calibration period and testing on the validation period). The exclusion criterion based on\nwithin-period accuracy ensures that such large validation errors are not simply attributable to\ninconsistent eye movements.\nTo further clarify this point, we have revised the manuscript to explicitly distinguish between\nwithin-period accuracy (used for classification and exclusion) and cross-period validation error\n(used for analysis). We have also updated Figure 1c to visualize this classification.\n“We implemented a two-step quality control procedure to distinguish different sources of eye\ntracking inaccuracy, such as instrumental error, fixation instability during calibration, and head\nmotion-induced error. Specifically, we evaluated gaze accuracy within both the calibration and\nvalidation periods using separate models trained and tested on data from the same period. Runs\nwith gaze error below 1.0° in both periods were labeled as verifiable and included in subsequent\nanalyses related to eye tracking accuracy (e.g., Fig. 4a). If only the calibration phase met this\nthreshold, the run was labeled as usable and retained for analyses that relied only on calibration\n(e.g., behavioral prediction and visual field mapping; Figs. 4b and 4c). Runs that did not meet\nthe threshold in either phase were labeled unusable but still contributed to across-run\ngeneralization analyses (e.g., Fig. 5c), where no within-run calibration was required. The\nproportions of verifiable, usable, and unusable runs are shown in Fig. 1c. No data were excluded\non the basis of fMRI data quality.” —Methods (page 26)\n—Figure 1 (page 5)\n3. How big are the stimuli in the fMRI experiments in degrees of visual angle? I couldn’t find\nthis anywhere in the main text or the methods, and this is helpful for determining the size\nof the eye tracker errors (which are already reported in degrees) relative to the stimuli.\nResponse: We thank the reviewer for pointing this out and apologize for the oversight. While\nthe visual angle of the stimuli used in the fMRI experiments was illustrated in Figure 2A, we\nagree that it should also be stated in the Methods. To address this, we have revised the Methods\nto explicitly report stimulus size in degrees of visual angle. Additionally, we have included\nvisual angle information for the video-watching dataset acquired on the 3T MRI scanner (as\nsuggested by Reviewer #4), as well as for the behavioral eye tracking dataset. We believe these\nadditions provide clearer context for interpreting the magnitude of eye tracking errors relative to\nstimulus dimensions.\n“For the main analysis, we used eye tracking data collected while participants performed a 13-\nmin 3D Minecraft-based video game task in a 7T MRI scanner. The stimulus was presented on\na screen subtending 20.5° × 12.8°.” —Methods (page 23)\n“For comparison, a behavioral version of the Minecraft task was conducted outside the scanner,\nwith the display size matched to the MRI setup in visual angle.” —Methods (page 24)\n“To assess generalizability across tasks and MRI scanners, we analyzed two additional movie-\nwatching fMRI datasets acquired from separate groups of 12 participants each, on 3T and 7T\nscanners. Each dataset included standard eye tracking calibration (24-point calibration at the\nbeginning and 12-point validation at the end of each run). In the 3T dataset, participants viewed\napproximately 12 minutes of first-person-view movie clips on a screen subtending 27.0° × 15.2°.\nIn the 7T dataset, participants watched two 10-minute runs of naturalistic movies on a screen\nsubtending 20.5° × 12.8°.” —Methods (page 24)\n4. DeepMReye comparison. Does the fMRI data need to be normalized to MNI space for the\nDeepMReye model to run? Since the analyses are within-participant, normalizing to MNI\nis not essential for group-level comparison, and DeepMReye may show better performance\nin each participants native space.\nResponse: We confirmed that the original implementation of DeepMReye was performed\nin MNI space, as explicitly stated in their reporting summary. Additionally, the pre-trained\nmodels and tutorials from DeepMReye use eyeball masks defined in MNI space, which are\nrequired to extract voxel signals from the eyeball region. For this reason, we spatially normalized\nthe data to MNI space to ensure compatibility with their pipeline and to apply the published\nvoxel selection procedure as intended. While DeepMReye may benefit from native-space\ndecoding in future work, we followed the original implementation to enable a fair and\nreproducible comparison.\nReviewer 4\n1. Although the method is itself general and practical, the acquisition protocol perhaps less\nso. One would have liked to see generalization across more than one 7T dataset, one of\nwhich involved a fairly unusual task (Minecraft).\nResponse: We agree and have addressed this concern by replicating our findings in two\nadditional datasets: a 7T movie-watching dataset and a 3T video-watching dataset. These\ndatasets use different tasks and scanner settings compared to the original 7T Minecraft dataset.\nIn both datasets, MoCET consistently outperformed uncorrected data and conventional\ndetrending methods, supporting its generalizability across tasks and acquisition protocols. These\nresults are now described in the revised manuscript and shown in Supplementary Figure 4. We\nappreciate the reviewer for highlighting this point.\n“Using high-quality eye tracking data collected during free-viewing tasks, we demonstrate that\nMoCET consistently outperforms both uncorrected data and conventional detrending methods\nacross independent datasets involving different tasks and MRI scanners.” —Introduction (page\n4)\n“Consistent results were observed in two independent replication datasets (Supplementary Fig.\n4).” —Figure 4 caption (page 12)\n“To further evaluate MoCET’s generalizability and accuracy, we analyzed three independent\ndatasets: two movie-watching fMRI datasets collected at 3T and 7T scanners from separate\ngroups of 12 participants each, and a behavioral eye tracking dataset from four participants who\ncompleted three runs of the Minecraft task outside the MRI scanner. The behavioral dataset\nenabled a direct comparison between standard laboratory eye tracking and MRI-compatible eye\ntracking corrected using MoCET.” —Methods (page 23)\n“To assess generalizability across tasks and MRI scanners, we analyzed two additional movie-\nwatching fMRI datasets acquired from separate groups of 12 participants each, on 3T and 7T\nscanners. Each dataset included standard eye tracking calibration (24-point calibration at the\nbeginning and 12-point validation at the end of each run). In the 3T dataset, participants viewed\napproximately 12 minutes of first-person-view movie clips on a screen subtending 27.0° × 15.2°.\nIn the 7T dataset, participants watched two 10-minute runs of naturalistic movies on a screen\nsubtending 20.5° × 12.8°.” —Methods (page 24)\n—Supplementary Figure 4 (page 45)\n2. Head motion can be quite variable across subjects. There may be a relationship between\nthe characteristics of head-motion across subject (more or less high-frequency events,\nvariation is predominant motion type, etc.) that could affect the effectiveness of MOCET.\nIf head-motion is more \"drift-like\" its will be more similar to the polynomial regressor\napproach. But if motion is more spiky, then these methods will diverge, an nonlinearities\nmay be more important (or that robust regression might yield better results). In general\nmore discussion of individual variability in head-motion would be desirable; especially in\nlight of point 1 (generalization); for example, where different patient populations or age-\ngroups might have different characteristic head-motion profiles.\nResponse: We agree with the reviewer that variability in head motion characteristics could\ninfluence correction performance. As noted in our response to Reviewer #1’s Comment 1, we\nexamined the performance of both linear and nonlinear variants of MoCET across\ndifferent motion profiles, including drift-like and spike-like motion. We found no significant\nadvantage of nonlinear models across head motion types. As the reviewer suggested, polynomial\nregressors performed better specifically under drift-like motion, highlighting that motion\ncharacteristics can influence correction performance. We acknowledge the importance of\nindividual variability and have expanded discussion to address this point in the revised\nmanuscript.\n“To further test the linear assumption, we evaluated the nonlinearity in the relationship between\nhead motion and pupil coordinates across different types of head motion. We found that the\nlinear and nonlinear variants of MoCET performed comparably across motion categories.\nAdditional simulations with artificially amplified motion indicated that the linear MoCET model\nremained effective at motion levels typical of fMRI studies, while nonlinear models offered only\nlimited additional benefit under extreme motion (for details, see Supplementary Fig. 3 and\nMethods)” —Results (page 11)\n“MoCET assumes a linear relationship between head motion and gaze error, which may become\ninadequate in cases of extreme head movement or when the eye tracking camera is installed at a\nsteep tilt relative to the gaze direction. In such conditions, nonlinear distortions in pupil\ncoordinates can introduce errors not fully accounted for by linear regression. However, our\nempirical evaluation across diverse head motion types, including large, spike-like, and drift-like\nmovements, showed that the linear MoCET model performed as well as more complex nonlinear\nvariants. Furthermore, simulations with systematically amplified motion confirmed that linear\nMoCET remains effective across a broad range of motion levels. Nonlinear extensions provided\nimprovements only under extreme head motion conditions, which are rarely encountered in\nempirical experiments (Supplementary Fig. 3). These findings support the validity of the linear\nassumption in typical fMRI settings, where head motion is often constrained by stabilization\ndevices such as foam padding, minimizing extreme deviations that could introduce nonlinear\ndistortions. To accommodate potential edge cases, we also provide these nonlinear MoCET\nvariants in our Python package, allowing users to apply more flexible correction models when\nneeded.” —Discussion (page 21)\n“While MoCET assumes a linear relationship between head motion and drift in eye tracking\ndata, this assumption may not hold under all circumstances. In particular, when head motion is\nlarge or abrupt, a simple linear regression model may be insufficient. To evaluate when the\nlinearity assumption in MoCET remains valid and whether more complex, nonlinear models\nprovide added value, we categorized eye tracking runs based on their head motion profiles and\ncompared multiple versions of MoCET under these conditions. ‘Large motion’ runs were defined\nas those with a maximum in-plane displacement exceeding a +1 z-score threshold. To identify\ndrift-like motion, we computed autocorrelations of each of the six head motion parameters over\nlags of one to five TRs, then averaged across lags and parameters. Runs with a z-scored mean\nautocorrelation above +1 were classified as drift. In contrast, spike-like motion was characterized\nby abrupt, transient movements, defined as runs with a z-scored mean autocorrelation below –1.\nTo test whether nonlinear modeling improves performance under different head motion types,\nwe introduced two extended models. MoCET-Large incorporates squared terms and temporal\nderivatives of the head motion parameters to capture larger or more dynamic shifts. MoCET-\nInteraction includes pairwise interaction terms between head motion axes to account for cross-\ndimensional effects. These models were evaluated alongside the original linear approach to\nassess the benefit of increased model complexity.\nTo examine the validity of the linear assumption under more extreme conditions, we performed\na simulation-based analysis. Because large head movements are difficult to elicit reliably during\nempirical fMRI sessions, we artificially amplified head motion by scaling the original motion\nparameters by 20% to 360%. This approach allowed us to systematically test MoCET and its\nnonlinear variants under a wide range of motion intensities, including cases beyond typical\nexperimental variability.” —Methods (page 29)\n3. Related to above: there is an inherent discrepancy between the high sampling rate of eye-\ntracking (e.g., 60 Hz) and the low sampling rate of fMRI-derived motion estimates (~0.5-1\nHz). Although the authors argue convincingly that head motion is dominated by low-\nfrequency components, fast, transient movements (e.g., respiration-related) may not be\nperfectly corrected and could partially alias into the residual noise.\nResponse: We appreciate the reviewer’s comment. As noted in our response to Reviewer #1’s\nComment 3, we conducted additional analyses to assess the impact of temporal resolution\nmismatch between motion parameters and eye tracking. Our results demonstrate that\nMoCET maintains robust correction accuracy even when applied to data downsampled to 1Hz,\nsuggesting that MoCET is robust to temporal resolution mismatches and remains effective even\nwhen gaze signals are corrected at the sampling rate of fMRI motion estimates.\nEven fast, transient head movements can be captured in fMRI if they cause net displacement\nbetween consecutive volumes. We agree, however, that rapid, oscillatory motion occurring\nentirely within a single TR (e.g., a brief move-and-return) may not result in a detectable\ndisplacement in the brain images. In such cases, motion parameters from fMRI may\nunderestimate the movement, reducing correction accuracy. We have explicitly acknowledged\nthis limitation in the revised manuscript.\n“However, rare, fast head movements within a single TR, such as a quick shift-and- return, may\nnot produce detectable displacement in the fMRI images. In such cases, fMRI-derived motion\nparameters may underestimate the movement, reducing correction accuracy.” —Discussion\n(page 21)\nSincerely,\nJiwoong Park (jiwoongpark@skku.edu)\nJae Young Jeon (bluejay94@skku.edu)\nRoyoung Kim (royoungkim@skku.edu)\nKendrick N. Kay (kay@umn.edu)\nWon Mok Shim (wonmokshim@skku.edu)"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have no further substantive requests. I accept the revisions and thank you again for your thorough work.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The updates and response address my critiques of the original manuscript, and I'm happy to recommend publication. Thank you to the authors for extremely thorough responses to the reviews and completing multiple new experiments for the updated version. This is excellent work overall, and I look forward to using MoCET in my own research."}, "author_response": ""}]

Decision letter