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

in Seeing and Perceiving
Restricted Access
Get Access to Full Text

Have an Access Token?

Enter your access token to activate and access content online.

Please login and go to your personal user account to enter your access token.


Have Institutional Access?

Access content through your institution. Any other coaching guidance?


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



AguilarC.CastetE. (2011). Gaze-contingent simulation of retinopathy: some potential pitfalls and remediesVision Research 519971012.

AmadorX. F.MalaspinaD.SackeimH. A.ColemanE. A.KaufmannC. A.HasanA.GormanJ. M. (1995). Visual fixation and smooth pursuit eye movement abnormalities in patients with schizophrenia and their relativesJ. Neuropsychiat. Clin. Neurosci. 7197206.

BedellH. E. (1980). A functional test of foveal fixation based upon differential cone directional sensitivityVision Research 20557560.

BellmannC.FeelyM.CrosslandM. D.KabanarouS. A.RubinG. S. (2004). Fixation stability using central and pericentral fixation targets in patients with age-related macular degenerationOphthalmology 11122652270.

BowmanA. W.AzzaliniA. (1997). Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations. Oxford Science PublicationsOxford, UK.

CaldaraR.MielletS. (2011). iMap: a novel method for statistical fixation mapping of eye movement dataBehav. Res. Methods 43864878.

CarpenterR. (1988). Movements of the Eyes. PionLondon, UK.

CollewijnH.KowlerE. (2008). The significance of microsaccades for vision and oculomotor controlJ. Vision 8121.

CrosslandM. D.RubinG. S. (2002). The use of an infrared eyetracker to measure fixation stabilityOptom. Vis. Sci. 79735739.

CrosslandM. D.CulhamL. E.KabanarouS. A.RubinG. S. (2002). The use of an infra-red eyetracker in the assessment of macular disease: a comparison with the scanning laser ophthalmoscope in: 7th Intl Conf. Low Vision Goteburg Sweden.

CrosslandM. D.CulhamL. E.RubinG. S. (2004a). Fixation stability and reading speed in patients with newly developed macular diseaseOphthalmol. Physiol. Optic. 24327333.

CrosslandM. D.KabanarouS. A.RubinG. S. (2004b). An unusual strategy for fixation in a patient with bilateral advanced age related macular diseaseBrit. J. Ophthalmol. 8814791480.

CrosslandM. D.CulhamL. E.KabanarouS. A.RubinG. S. (2005). Preferred retinal locus development in patients with macular diseaseOphthalmology 11215791585.

CrosslandM. D.DunbarH. M. P.RubinG. S. (2009). Fixation stability measurement using the Mp1 microperimeterRetina — J. Retinal Vitreous Diseases 29651656.

CrosslandM. D.LuongV. A.RubinG. S.FitzkeF. W. (2011). Retinal specific measurement of dark-adapted visual function: validation of a modified microperimeterBMC Ophthalmol. 115.

CulhamL. E.FitzkeF. W.TimberlakeG. T.MarshallJ. (1993). Assessment of fixation stability in normal subjects and patients using a scanning laser ophthalmoscopeClin. Vis. Sci. 8551561.

CulhamL. E.FitzkeF. W.MarshallJ. (1997). Training of patients with age-related macular disease (AMD) using a scanning laser ophthalmoscope (SLO)Ophthalmol. Physiol. Optic. 17542.

DeLucaM.Di PaceE.JudicaA.SpinellD.ZoccolottiP. (1999). Eye movement patterns in linguistic and non-linguistic tasks in developmental surface dyslexiaNeuropsychologia 3714071420.

DeruazA.MatterM.WhathamA. R.GoldschmidtM.DuretF.IssenhuthM.SafranA. B. (2004). Can fixation instability improve text perception during eccentric fixation in patients with central scotomas? Brit. J. Ophthalmol. 88461463.

Di RussoF.PitzalisS.SpinelliD. (2003). Fixation stability and saccadic latency in elite shootersVision Res. 4318371845.

DunbarH. M.CrosslandM. D.RubinG. S. (2010). Fixation stability: a comparison between the Nidek MP-1 and the Rodenstock scanning laser ophthalmoscope in persons with and without diabetic maculopathyInvestigat. Ophthalmol. Vis. Sci. 5143464350.

EdenG. F.SteinJ. F.WoodH. M.WoodF. B. (1994). Differences in eye movements and reading problems in dyslexic and normal childrenVision Res. 3413451358.

EngbertR. (2006). Microsaccades: a microcosm for research on oculomotor control, attention, and visual perceptionProg. Brain Res. 154177192.

EngbertR.KlieglR. (2004). Microsaccades keep the eyes’ balance during fixationPsychol. Sci. 15431436.

FalkenbergH.RubinG.BexP. (2007). Acuity, crowding, reading and fixation stabilityVision Res. 47126135.

FletcherD. C.SchuchardR. A. (1997). Preferred retinal loci relationship to macular scotomas in a low-vision populationOphthalmology 104632638.

FujiiG. Y.De JuanE.Jr.SunnessJ. S.HumayunM. S.PieramiciD. J.ChangT. S. (2002). Patient selection for macular translocation surgery using the scanning laser ophthalmoscopeOphthalmology 10917371744.

GoodingD. C.GrabowskiJ. A.HendershotC. S. (2000). Fixation stability in schizophrenia, bipolar, and control subjectsPsychiatry Res. 97119128.

HendersonJ. M. (2003). Human gaze control during real-world scene perceptionTrends Cognit. Sci. 7498504.

IhakaR.GentlemanR. (1996). R: A language for data analysis and graphicsJ. Computat. Graph. Stat. 5299314.

MacedoA. F.CrosslandM. D.RubinG. S. (2008). The effect of retinal image slip on peripheral visual acuityJ. Vision 8111.

Martinez-CondeS. (2006). Fixational eye movements in normal and pathological visionProg. Brain Res. 154151176.

Martinez-CondeS.MacKnikS. L.HubelD. H. (2004). The role of fixational eye movements in visual perceptionNat. Rev. Neurosci. 5229240.

Martinez-CondeS.MacKnikS. L.TroncosoX. G.DyarT. A. (2006). Microsaccades counteract visual fading during fixationNeuron 49297305.

MergenthalerK.EngbertR. (2010). Microsaccades are different from saccades in scene perceptionExper. Brain Res. (Experimentelle Hirnforschung. Experimentation Cerebrale) 203753757.

NilssonU. L.FrennessonC.NilssonS. R. G. (1998). Location and stability of a newly established eccentric retinal locus suitable for reading, achieved through training of patients with a dense central scotomaOptom. Vis. Sci. 75873878.

NystromM.HolmqvistK. (2010). An adaptive algorithm for fixation, saccade, and glissade detection in eyetracking dataBehav. Res. Methods 42188204.

Otero-MillanJ.TroncosoM. G.MacKnikS. L.Serrano-PedrazaI.Martinez-CondeS. (2008). Saccades and microsaccades during visual fixation, exploration, and search: foundations for a common saccadic generatorJ. Vision 8118.

OverE. A.HoogeI. T.ErkelensC. J. (2006). A quantitative measure for the uniformity of fixation density: the Voronoi methodBehav. Res. Methods 38251261.

PutnamN. M.HoferH. J.DobleN.ChenL.CarrollJ.WilliamsD. R. (2005). The locus of fixation and the foveal cone mosaicJ. Vision 5632639.

RaymondJ. E.OgdenN. A.FaganJ. E.KaplanB. J. (1988). Fixational instability and saccadic eye movements of dyslexic children with subtle cerebellar dysfunctionAmer. J. Optom. Physiol. Opt. 65174181.

RaynerK. (1998). Eye movements in reading and information processing: 20 years of researchPsychol. Bull. 124372422.

ReinhardJ.MessiasA.DietzK.MackebenM.LakmannR.SchollH. P.Apfelstedt-SyllaE.WeberB. H.SeeligerM. W.ZrennerE.Trauzettel-KlosinskiS. (2007). Quantifying fixation in patients with Stargardt diseaseVision Res. 4720762085.

RohrschneiderK.BeckerM.KruseF. E.FendrichT.VolckerH. E. (1995). Stability of fixation: results of fundus-controlled examination using the scanning laser ophthalmoscopeGer. J. Ophthalmol. 4197202.

RohrschneiderK.BeckerM.SchumacherN.FendrichT.VolckerH. E. (1998). Normal values for fundus perimetry with the scanning laser ophthalmoscopeAmer. J. Ophthalmol. 1265258.

RolfsM. (2009). Microsaccades: small steps on a long wayVision Res. 4924152441.

RosseR. B.MalhotraA. K.KimS. Y.DeutschS. I. (1992). Visual fixation deficits and evidence of cognitive impairment in schizophreniaBiol. Psychiatry 31412414.

RucciM.IovinR.PolettiM.SantiniF. (2007). Miniature eye movements enhance fine spatial detailNature 447851854.

SansburyR. V.SkavenskiA. A.HaddadG. M.SteinmanR. M. (1973). Normal fixation of eccentric targetsJ. Opt. Soc. Amer. 63612614.

SchuchardR. A.FletcherD. C. (1994). Preferred retinal locus: a review with applications in low vision rehabilitationOphthalmol. Clin. North Amer. 7243256.

SnodderlyD. M.KurtzD. (1985). Eye position during fixation tasks: comparison of macaque and humanVision Res. 258398.

SteinmanR. M. (1965). Effect of target size, luminance, and color on monocular fixationJ. Optic. Soc. Amer. 5511581165.

SteinmanR. M.CushmanW. B.MartinsA. J. (1982). The precision of gaze. A reviewHuman Neurobiol. 197109.

StelmackJ. A.MassofR. W.StelmackT. R. (2004). Is there a standard of care for eccentric viewing training? J. Rehabil. Res. Dev. 41729738.

Tarita-NistorL.GonzalezE. G.MarkowitzS. N.SteinbachM. J. (2008). Fixation characteristics of patients with macular degeneration recorded with the mp-1 microperimeterRetina 28125133.

Tarita-NistorL.GonzalezE. G.MarkowitzS. N.SteinbachM. J. (2009). Plasticity of fixation in patients with central vision lossVision Neurosci. 26487494.

The R Development Core Team (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.

TimberlakeG. T.MainsterM. A.PeliE.AugliereR. A.EssockE. A.ArendL. E. (1986). Reading with a macular scotoma. I. Retinal location of scotoma and fixation areaInvestigat. Ophthalmol. Vis. Sci. 2711371147.

TimberlakeG. T.SharmaM. K.GroseS. A.GobertD. V.GauchJ. M.MainoJ. H. (2005). Retinal location of the preferred retinal locus relative to the fovea in scanning laser ophthalmoscope imagesOptom. Vis. Sci. 82177185.

van der GeestJ. N.FrensM. A. (2002). Recording eye movements with video-oculography and scleral search coils: a direct comparison of two methodsJ. Neurosci. Methods 114185195.

VingoloE. M.SalvatoreS.CavarrettaS. (2009). Low-vision rehabilitation by means of MP-1 biofeedback examination in patients with different macular diseases: a pilot studyAppl. Psychophysiol. Biofeedback 34127133.

VogelC. R.ArathornD. W.RoordaA.ParkerA. (2006). Retinal motion estimation in adaptive optics scanning laser ophthalmoscopyOptic. Express 14487497.

WhiteJ. M.BedellH. E. (1990). The oculomotor reference in humans with bilateral macular diseaseInvestigat. Ophthalmol. Vis. Sci. 3111491161.

WhittakerS. G.BuddJ.CummingsR. W. (1988). Eccentric fixation with macular scotomaInvestigat. Ophthalmol. Vis. Sci. 29268278.

ZeffrenB. S.ApplegateR. A.BradleyA.van HeuvenW. A. (1990). Retinal fixation point location in the foveal avascular zoneInvestigat. Ophthalmol. Vis. Sci. 3120992105.


  • View in gallery

    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.

  • View in gallery

    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.

  • View in gallery

    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.

  • View in gallery

    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.

  • View in gallery

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

  • View in gallery

    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.

  • View in gallery

    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.

  • View in gallery

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

  • View in gallery

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

  • View in gallery

    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.

  • View in gallery

    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.

Index Card

Content Metrics

Content Metrics

All Time Past Year Past 30 Days
Abstract Views 31 31 17
Full Text Views 9 9 9
PDF Downloads 3 3 3
EPUB Downloads 0 0 0