Quantifying Eye Stability During a Fixation Task: A Review of Definitions and Methods

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Several definitions, measurements, and implicit meanings of ‘fixation stability’ have been used in clinical vision research, leading to some confusion. One definition concerns eye movements observed within fixations (i.e., within periods separated by saccades) when observing a point target: drift, microsaccades and physiological tremor all lead to some degree of within-fixation instability. A second definition relates to eye position during multiple fixations (and saccades) when patients fixate a point target. Increased between-fixation variability, combined with within-fixation instability, is known to be associated with poorer visual function in people with retinal disease such as age-related macular degeneration. In this review article, methods of eye stability measurement and quantification are summarised. Two common measures are described in detail: the bivariate contour ellipse area (BCEA) and the within-isolines area. The first measure assumes normality of the underlying positions distribution whereas the second does not. Each of these measures can be applied to two fundamentally different kinds of eye position data collected during a period of target observation. In the first case, mean positions of eye fixations are used to obtain an estimate of between-fixation variability. In the second case, often used in clinical vision research, eye position samples recorded by the eyetracker are used to obtain an estimate that confounds within- and between-fixation variability.

We show that these two methods can produce significantly different values of eye stability, especially when reported as BCEA values. Statistical techniques for describing eye stability when the distribution of eye positions is multimodal and not normally distributed are also reviewed.

Quantifying Eye Stability During a Fixation Task: A Review of Definitions and Methods

in Seeing and Perceiving

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Figures

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    Scatterplot of 100 points drawn from a bivariate Gaussian random variable. 95 and 68% isolines are superimposed (solid lines). 68% BCEA is represented by a dashed line. Probability density is mapped to grey levels.

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    Scatterplots of 100 points drawn from a bivariate non-Gaussian random variable. Isolines obtained with 4 different window widths (sd of Gaussian kernel) are shown. (Top left) x width = 0.21, y width = 0.44. Peak density = 0.089. (Top right) x and y widths = 1. Peak density = 0.061. (Bottom left) x and y widths = 2. Peak density = 0.042. (Bottom right) x and y widths = 4. Peak density = 0.026. The 68% BCEA is represented by a dashed line.

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    Mixture of two bivariate Gaussian distributions. (a) 300 data points are displayed along with isolines (solid lines) and the two local BCEAs (dashed lines). The dashed-line ellipse encompassing both local modes is the BCEA that would be obtained if the standard global BCEA method was applied. (b) 3D representation of the probability density function.

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    Mixture of two bivariate non-Gaussian distributions. (a) 300 data points are displayed along with 68% isolines (solid lines). (b) 3D representation of the probability density function.

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    Same data as in Fig. 4 with two different smoothing parameters. (Left) window width = 1°. (Right) window width = 2°.

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    Scatterplot of eye data for trial 1. (a) Fixational eye stability plotted by sample (FSs). To help visualize the superimposition of data points (crosses), a slight random spatial jitter was added to each point and transparency was used. (b) Fixational eye stability plotted by fixation (FSf). Both plots are on the same axis scale. Black ellipses represent 68% BCEAs. White contours represent 68% isolines.

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    Scatterplots of ocular data for five trials (Subject 1). (a) Eye position samples (FSs). To help visualize the superimposition of data points, transparency was used: at least 100 data points at a given position are necessary to induce a solid contour; (b) eye fixations (FSf). 68% BCEAs and 68% isolines are represented by black and white contours respectively.

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    Sample eye position is plotted against time for the 5 trials.

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    Fixation duration is plotted against time for the 5 trials. Straight lines represent linear regressions performed for each of the 5 trials.

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    Scatterplot of eye data for trial 1 when removing the first 1.5 s (Patient 1). (a) Fixational eye stability plotted by sample. A slight spatial jitter was added to each point (cross) and transparency was used. (b) Fixational eye stability plotted by eye fixation. 68% BCEAs and 68% isolines are represented by solid black and white contours respectively. Dashed lines represent the contours calculated for the full data set (see Fig. 6 with different scale) to allow an easy comparison.

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    Scatterplots of ocular data for five trials (Subject 2). (a) Eye position samples (FSs). To help visualize the superimposition of data points, transparency was used: at least 100 data points at a given position are necessary to induce a solid contour. (b) Eye fixations (FSf). 68% BCEAs and 68% isolines are represented by black and white contours respectively.

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