The Bouma law of crowding, revised: Critical spacing is equal across parts, not objects

Abstract

Crowding is the inability to identify an object among flankers in the periphery. It is due to inappropriate incorporation of features from flanking objects in perception of the target. Crowding is characterized by measuring critical spacing, the minimum distance needed between a target and flankers to allow recognition. The existing Bouma law states that, at a given point and direction in the visual field, critical spacing, measured from the center of a target object to the center of a similar flanking object, is the same for all objects (Pelli & Tillman, 2008). Because flipping an object about its center preserves its center-to-center spacing to other objects, according to the Bouma law, crowding should be unaffected. However, because crowding is a result of feature combination, the location of features within an object might matter. In a series of experiments, we find that critical spacing is affected by the location of features within the flanker. For some flankers, a flip greatly reduces crowding even though it maintains target-flanker spacing and similarity. Our results suggest that the existing Bouma law applies to simple one-part objects, such as a single roman letter or a Gabor patch. Many objects consist of multiple parts; for example, a word is composed of multiple letters that crowd each other. To cope with such complex objects, we revise the Bouma law to say that critical spacing is equal across parts, rather than objects. This accounts for old and new findings.

Crowding in the S-cone pathway

“…The rule-of-thumb known as “Bouma’s law” refers to the linear change in critical spacing as a function of eccentricity (Bouma, 1970; Pelli et al, 2004, 2007; Rosen et al, 2014; Strasburger, 2005; Strasburger et al, 2011). The precise expression specifying critical spacing in terms of center-to-center target-flanker spacing is d=b×E+w , where b is the slope or “Bouma constant,” w is the y-intercept, and E is the target eccentricity in degrees.…”

“…Its spatial extent, called the critical spacing , has been extensively quantified (Bouma, 1970; Levi et al, 1985; Pelli et al, 2004; Strasburger et al, 1991; Toet and Levi, 1992), usually with a constant that determines the change in critical spacing as a function of eccentricity. Although this measure (the “Bouma constant”) can vary amongst individual subjects (Pelli et al, 2007) and the stimuli used (Rosen et al, 2014), its value, especially the linear relationship with eccentricity (Bouma, 1970; Jacobs, 1979; Pelli et al, 2004; Toet and Levi, 1992), can be used to evaluate within-subject differences resulting from changes in the stimulus. For example, reducing contrast (Coates et al, 2013a) or shortening the stimulus duration (Chung and Mansfield, 2009; Kooi et al, 1994; Tripathy and Cavanagh, 2002; Tripathy et al, 2014; Wallace et al, 2013) have both been found to cause an enlargement of the crowding zone, yielding possible clues in determining the neural basis of crowding.…”

The neural origins of visual crowding as revealed by event-related potentials and oscillatory dynamics

“…The idea is that crowding is strong when the flankers can be grouped with the target because they have equal length. Crowding is weaker, instead, when flankers are longer and the target can be segregated from them (Malania, Herzog, & M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 This approach, however, fails to address the effect of critical spacing, one of the fundamental variable when studying visual crowding (Bouma, 1970;Whitney & Levi, 2011;Rosen, Chakravarthi, & Pelli, 2014).…”

What crowding can tell us about object representations

“…Most models of crowding have three main characteristics in common. First, crowding occurs only in a restricted region according to Bouma's law, which states that only flanking elements within a window of about half the eccentricity of target presentation compromise target processing (Bouma, 1970;Pelli, 2008;Pelli, Palomares, & Majaj, 2004;Pelli & Tillman, 2008;Rosen, Chakravarthi, & Pelli, 2014). Second, flankers are treated as mere noise; therefore, increasing their number can only lead to increases in crowding strength (Parkes et al, 2001;Wilkinson et al, 1997).…”