@article{EngbertMergenthaler2005,
  author    = {Engbert, Ralf and Mergenthaler, Konstantin},
  title     = {Statistics of fixational eye movements and oculomotor control},
  issn      = {0301-0066},
  year      = {2005},
  language  = {en}
}
@phdthesis{Mergenthaler2009,
  author    = {Mergenthaler, Konstantin K.},
  title     = {The control of fixational eye movements},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29397},
  school      = {Universit{\"a}t Potsdam},
  year      = {2009},
  abstract  = {In normal everyday viewing, we perform large eye movements (saccades) and miniature or fixational eye movements. Most of our visual perception occurs while we are fixating. However, our eyes are perpetually in motion. Properties of these fixational eye movements, which are partly controlled by the brainstem, change depending on the task and the visual conditions. Currently, fixational eye movements are poorly understood because they serve the two contradictory functions of gaze stabilization and counteraction of retinal fatigue. In this dissertation, we investigate the spatial and temporal properties of time series of eye position acquired from participants staring at a tiny fixation dot or at a completely dark screen (with the instruction to fixate a remembered stimulus); these time series were acquired with high spatial and temporal resolution. First, we suggest an advanced algorithm to separate the slow phases (named drift) and fast phases (named microsaccades) of these movements, which are considered to play different roles in perception. On the basis of this identification, we investigate and compare the temporal scaling properties of the complete time series and those time series where the microsaccades are removed. For the time series obtained during fixations on a stimulus, we were able to show that they deviate from Brownian motion. On short time scales, eye movements are governed by persistent behavior and on a longer time scales, by anti-persistent behavior. The crossover point between these two regimes remains unchanged by the removal of microsaccades but is different in the horizontal and the vertical components of the eyes. Other analyses target the properties of the microsaccades, e.g., the rate and amplitude distributions, and we investigate, whether microsaccades are triggered dynamically, as a result of earlier events in the drift, or completely randomly. The results obtained from using a simple box-count measure contradict the hypothesis of a purely random generation of microsaccades (Poisson process). Second, we set up a model for the slow part of the fixational eye movements. The model is based on a delayed random walk approach within the velocity related equation, which allows us to use the data to determine control loop durations; these durations appear to be different for the vertical and horizontal components of the eye movements. The model is also motivated by the known physiological representation of saccade generation; the difference between horizontal and vertical components concurs with the spatially separated representation of saccade generating regions. Furthermore, the control loop durations in the model suggest an external feedback loop for the horizontal but not for the vertical component, which is consistent with the fact that an internal feedback loop in the neurophysiology has only been identified for the vertical component. Finally, we confirmed the scaling properties of the model by semi-analytical calculations. In conclusion, we were able to identify several properties of the different parts of fixational eye movements and propose a model approach that is in accordance with the described neurophysiology and described limitations of fixational eye movement control.},
  language  = {en}
}
@article{EngbertMergenthaler2006,
  author    = {Engbert, Ralf and Mergenthaler, Konstantin},
  title     = {Microsaccades are triggered by low retinal image slip},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.0509557103},
  year      = {2006},
  abstract  = {Even during visual fixation of a stationary target, our eyes perform rather erratic miniature movements, which represent a random walk. These "fixational" eye movements counteract perceptual fading, a consequence of fast adaptation of the retinal receptor systems to constant input. The most important contribution to fixational eye movements is produced by microsaccades; however, a specific function of microsaccades only recently has been found. Here we show that the occurrence of microsaccades is correlated with low retinal image slip approximate to 200 ms before microsaccade onset. This result suggests that microsaccades are triggered dynamically, in contrast to the current view that microsaccades are randomly distributed in time characterized by their rate-of-occurrence of 1 to 2 per second. As a result of the dynamic triggering mechanism, individual microsaccade rate can be predicted by the fractal dimension of trajectories. Finally, we propose a minimal computational model for the dynamic triggering of microsaccades},
  language  = {en}
}
@article{MergenthalerEngbert2010,
  author    = {Mergenthaler, Konstantin and Engbert, Ralf},
  title     = {Microsaccades are different from saccades in scene perception},
  year      = {2010},
  abstract  = {Eye-fixation durations are among the best and most widely used measures of ongoing cognition in visual tasks, e.g., reading, visual search or scene perception. However, fixations are characterized by ongoing motor activity (or fixational eye movements) with microsaccades as their most pronounced components. Recent work demonstrated the similarities of microsaccades and inspection saccades. Here, we show that distinct properties of microsaccades and inspection saccades can be found in a scene perception task, based on descriptive measures (e.g., a bimodal amplitude distribution) as well as functional characteristics (e.g., inter saccadic-event intervals and generating processes). Besides these specific differences, microsaccade rates produced by individual participants in a fixation paradigm are correlated with microsaccade rates extracted from fixations in scene perception, indicating a common neurophysiological basis. Finally, we observed that slow fixational eye movements, called drift, are significantly reduced during long fixations in scene viewing, which informs about the control of eye movements in scene viewing.},
  language  = {en}
}
@article{RomanoThielKurthsetal.2009,
  author    = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Mergenthaler, Konstantin and Engbert, Ralf},
  title     = {Hypothesis test for synchronization : twin surrogates revisited},
  issn      = {1054-1500},
  doi       = {10.1063/1.3072784},
  year      = {2009},
  abstract  = {The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes.},
  language  = {en}
}
@article{EngbertMergenthalerSinnetal.2011,
  author    = {Engbert, Ralf and Mergenthaler, Konstantin and Sinn, Petra and Pikovskij, Arkadij},
  title     = {An integrated model of fixational eye movements and microsaccades},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {108},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {39},
  publisher = {National Acad. of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1102730108},
  pages     = {E765 -- E770},
  year      = {2011},
  abstract  = {When we fixate a stationary target, our eyes generate miniature (or fixational) eye movements involuntarily. These fixational eye movements are classified as slow components (physiological drift, tremor) and microsaccades, which represent rapid, small-amplitude movements. Here we propose an integrated mathematical model for the generation of slow fixational eye movements and microsaccades. The model is based on the concept of self-avoiding random walks in a potential, a process driven by a self-generated activation field. The self-avoiding walk generates persistent movements on a short timescale, whereas, on a longer timescale, the potential produces antipersistent motions that keep the eye close to an intended fixation position. We introduce microsaccades as fast movements triggered by critical activation values. As a consequence, both slow movements and microsaccades follow the same law of motion; i.e., movements are driven by the self-generated activation field. Thus, the model contributes a unified explanation of why it has been a long-standing problem to separate slow movements and microsaccades with respect to their motion-generating principles. We conclude that the concept of a self-avoiding random walk captures fundamental properties of fixational eye movements and provides a coherent theoretical framework for two physiologically distinct movement types.},
  language  = {en}
}