Seven Myths on Crowding and Peripheral Vision

Abstract

Crowding has become a hot topic in vision research, and some fundamentals are now widely agreed upon. For the classical crowding task, one would likely agree with the following statements. (1) Bouma's law can be stated, succinctly and unequivocally, as saying that critical distance for crowding is about half the target's eccentricity. (2) Crowding is predominantly a peripheral phenomenon. (3) Peripheral vision extends to at most 90° eccentricity. (4) Resolution threshold (the minimal angle of resolution) increases strongly and linearly with eccentricity. Crowding increases at an even steeper rate. (5) Crowding is asymmetric as Bouma has shown. For that inner-outer asymmetry, the peripheral flanker has more effect. (6) Critical crowding distance corresponds to a constant cortical distance in primary visual areas like V1. (7) Except for Bouma's seminal article in 1970, crowding research mostly became prominent starting in the 2000s. I propose the answer is "not really" or "not quite" to these assertions. So should we care? I think we should, before we write the textbook chapters for the next generation.

Keywords: asymmetries; cortical map; crowding; fovea; perception; peripheral vision; psychophysics; reading; sensory systems; vision science; visual acuity; visual field.

Figure 1.

Simple Demonstration of Crowding. When fixating at the cross, the orientation for the duck on the left is seen but not that for the middle one on the right, even though the images are of the same size and at the same eccentricity. The phenomenon depends predominantly on eccentricity and pattern spacing and is mostly independent of target size. Duck painting by Ilse Maria Baumgart, Munich, 2019.

Figure 2.

Confusion of Acuity and Crowding in Goldstein’s 6th Edition (2002, p. 57) and 9th Edition (2013, p. 43), Chapter Neural Processing by Convergence, Subchapter The Cones Result in Better Detail Vision Than the Rods. The added arrow shows where to fixate.

Figure 3.

Example of a German Wimmelbild (Caro Wedekind, About the 31st Chaos Communication Congress (31C3) in Hamburg; Wedekind, 2014). Pictures like this show that visual search and crowding are connected subjects.

Figure 4.

Top: Bouma’s Crowding Stimulus Arrangement. On the left is a fixation point (+), to the right of which a target letter (“a”) appears that is surrounded by two equally spaced flankers (“x”). Target and flankers are in Times Roman font, with a variable number of fixed-width spaces in between. Bottom: Bouma’s law shown over the range that crowding has been studied so far, with Bouma’s empty-space definition of critical distance (left) and today’s centre-to-centre definition (right). The difference at that scale is too small to be visible but is seen when zooming in on the article (about 10-fold; inspect the origin; or see the next figure).

Figure 5.

(A) Comparison of Bouma’s law with critical distance defined as empty space (pink) versus centre-to-centre (blue). (B) A degenerated stimulus configuration with overlapping flankers that would result from an incorrect statement of Bouma’s law at small eccentricity.

Figure 6.

(A) Coates and Levi’s (2014) Figure 4, annotated, illustrating their “hockey stick model” that describes the dependence of centre-to-centre critical spacing on target size. The filled circles show Siderov et al.’s (2013) data for Sloan letters surrounded by bars. Note that the slope is ≈1.0, that is, an increase of letter size leads to an increase of centre-to-centre critical spacing by the same amount. The figure is annotated to emphasize that the abscissa is different from the previous figures and no eccentric data are shown. (B) A wide range of stimuli underlie the data shown in that figure, among them (top) the classical arrangement of Flom et al. (1963) or Toet and Levi's (1992) Ts (reproduced from Strasburger et al., 2011, Figure 19B, and A. Toet, personal communication, 19 Apr 2020, respectively) and also (bottom) various Gaussian and Gabor targets (Hariharan et al., 2005, from Figure 1 and Figure 2; blur intentional). (C) Possible shapes of Bouma’s law in the visual field’s very centre (with a slope of 0.5 = 22.5°) that would be compatible with the hockey stick model.

Figure 7.

(A) The visual field, as drawn by Traquair (1938, Figure 1) in his classical book, based on the data by Rönne (1915). The outermost contour was obtained with a somewhat larger stimulus of 160 mm diameter, presented at 1 m viewing distance, that is, of 9° size. (B) A recent visual field map obtained with reaction time-corrected, semiautomated kinetic perimetry (Vonthein et al., 2007, Figure 3A).

Figure 8.

(A) Ray-trace model of how light enters the eye at the maximum angle for a 5-mm pupil (Holladay & Simpson, 2017, Figure 3A). (B) Pupil as seen from an angle of 80° on the temporal side (Mathur et al., 2013, Figure 5). (C) Aspect ratio of the pupil’s shape as seen by an observer under different horizontal angles, with data from eight different studies in the literature (coloured symbols; Mathur et al., 2013, Figure 1). VFA = visual field angle; RFA = retinal field angle.

Figure 9.

Figures 2, 3, and 4 in Anstis (1974), Illustrating Cortical Magnification. (A) Letter sizes are according to an estimate of the cortical-magnification factor (left). (B) Letters are shown at a 10-fold increased size (middle). (C) Letter sizes are the same, but more letters are added, to increase crowding (right).

Figure 10.

Bouma’s Law (Continuous Line, as in Figure 4A), Compared With the Increase of the MAR With Eccentricity (Dashed Line; Data From Anstis, 1974, Figure 1). Critical distance and MAR are measured in the same units (visual angle) so that these can be directly compared. The graph is shown at two scales (Part A vs. B, as in Figure 4 vs. 5 above), to illustrate that, at a large scale, the slope difference matters most, whereas at a small scale, the intercept difference is more important. Part B of the figure has an additional line starting at 1° (dark green) that shows a hypothetical M-scaling function scaled the same as the acuity function in the graph (see the following text). MAR = minimal angle of resolution.

Figure 11.

Examples of Psychometric Functions Versus Flanker Distance. (A) For letter-T recognition (the red line; disregard the blue line; eccentricity 9°; flanker distance in multiples of 0.9°). Modified from Yeshurun and Rashal (2010, Figure 5). (B) Example from Rosen et al. (2014, Figure 9A) with novel patterns that allow widening the flankers; the inset shows the stimulus and the legend; eccentricity 12°. (C) Another recent example used for quantifying spatial attention (Albonico et al., 2018, Figure 4). The four conditions refer to the kinds of attentional cue used in the study; only “none,” that is, the no-cue condition, is relevant here. Foveal view.

Figure 12.

Schematic Depiction of Crowding as Defined Standardly, That Is, as the Impairment of Recognition Performance by the Presence of Flankers. (A) Psychometric function for proportion-correct performance in a crowding task, as in Figure 11. The effect of crowding, at some flanker distance d, is seen as the downward arrow on the right, starting from best performance (1–λ). (B) Crowding as in Part A, but now as a function of eccentricity. Part B results from Part A by mirroring the psychometric-function graph both horizontally and vertically and rescaling the y axis appropriately. The blue arrow serves as a graphical aid.

Figure 13.

Crowding Asymmetries. (A) Radially elongated interaction fields for two subjects from Toet and Levi (1992, Figure 6), showing the well-known radial-tangential anisotropy where flankers on a radius from the visual field centre exert more influence than those arranged tangentially. (B) The inner-outer asymmetry, first studied by Mackworth (1965), refers to a different critical distance of the more peripheral versus the more central flanker. It will lead to asymmetrically elongated interaction fields.

Figure 14.

Quotes on the Central-Peripheral (Inward-Outward, “In-Out”) Asymmetry of Crowding, by Mackworth (1965) and Bouma (1970). Emphasis added.

Figure 15.

The End-of-the-Word Effect to Which Mackworth (1965) Refers (Haslerud & Clark, 1957, Figure 1). Letter recognition in 7.6°-wide nine-letter words. Open symbols: women; filled: men. a: fragmentary responses; b: incorrect; and c: correct. Note that both the last and the first letter are outside in the visual field.

Figure16.

(A) Reverse Asymmetry in a Crowding Task Reported in Strasburger and Malania (2013, Figure 8A; modified). Confusions with the more central, but not the more peripheral, flanker depend on eccentricity. (B) Cartoon, as a memory aid for the mechanisms: (top) a peripheral letter part moving inward; (bottom) the more central flanker moving outward. Note that the cartoon does not quite capture the effect of features because these are a much more general concept than pattern parts.

Figure 17.

(A) Bouma’s law in the visual field and (B) its cortical equivalent, that is, how it translates to the cortical map in a primary visual area (Strasburger, 2019, Figure 8; see there for the specific parameters chosen for the estimation and note that kappa depends upon these).

Figure 18.

Essential Crowding Literature From 1923 to 2004. Abscissa: year of publication; ordinate: eccentricity in the visual field up to which crowding was studied in the article. (References given in Figure 19 up to 2004.)

Figure 19.

Crowding Literature From 1923 to 2004 Shown in Figure 18. Bold blue print: particularly important articles (in my subjective assessment). The column Limit ° shows (as before) the eccentricity of the target in the visual field up to which crowding was studied. The last column shows the number of citations from a Google Scholar search (November 2019).

Figure 20.

(A) Portrait of Ibn al-Haytham (c. 965 to c. 1040), with his perimeter superimposed (from Strasburger & Wade, 2015b). (B) Portrait of James Jurin (1684–1750) with a clock face superimposed, as the one described in his text and common at the time. Note that the number Four is not in correct roman notation, so crowding will have been more prominent (from Strasburger & Wade, 2015a; both artworks by Nicholas Wade, 2015).