Academic journal article Attention, Perception and Psychophysics

Weber-Fechner Behavior in Symmetry Perception?

Academic journal article Attention, Perception and Psychophysics

Weber-Fechner Behavior in Symmetry Perception?

Article excerpt

The literature contains several allusions to the idea that detection of (mirror) symmetry in the presence of noise follows the Weber-Fechner law. This law usually applies to first-order structures, such as length, weight, or pitch, and it holds that just-noticeable differences in a signal vary in proportion to the strength of the signal. Symmetry, however, is a higher order structure, and this theoretical note starts from the idea that, in noisy symmetry, the regularity-to-noise ratio defines the strength of the signal to be considered. We argue that the detectability of the symmetry follows a psychophysical law that also holds for Glass patterns. This law deviates from the Weber-Fechner law in that it implies that, in the middle range of noise proportions, the sensitivity to variations in the regularity-to-noise ratio is disproportionally higher than in both outer ranges.

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1. INTRODUCTION

Within the general field of visual symmetry research (for reviews, see Tyler, 1996; van der Helm & Leeuwenberg, 1996; Wagemans, 1997), this theoretical note investigates whether detection of (mirror) symmetry in the presence of noise follows the Weber-Fechner law (Fechner, 1860; Weber, 1834). This law holds that just-noticeable differences in a signal vary in proportion to the strength of the signal. Our claim (mine in collaboration with others in my lab) is that detection of noisy symmetry follows another psychophysical law that implies that, in the middle range of noise proportions, the sensitivity to variations in regularity-to-noise ratios is disproportionally higher than in both outer ranges. To avoid misunderstandings, keep in mind that the Weber-Fechner law is about change-tosignal ratios, not about regularity-to-noise ratios.

To elaborate our claim, we next introduce the topic of noisy-symmetry detection. Then, in Section 2, we discuss this psychophysical law and review the available empirical evidence on noisy-symmetry detection. Finally, in Section 3, by means of formal analyses, we compare this psychophysical law to the Weber-Fechner law.

1.1. Imperfect Symmetry

Symmetry is a visual regularity-that is, one of the regularities to which the visual systems of humans and many other species are sensitive (see, e.g., Barlow & Reeves, 1979; Giurfa, Eichmann, & Menzel, 1996; Horridge, 1996). Accordingly, symmetry detection is believed to be an integral part of the perceptual organization process that is applied to every incoming visual stimulus. In human perception research, for instance, symmetry has been shown to play a relevant role in issues such as object recognition (e.g., Pashler, 1990; Vetter & Poggio, 1994), figure-ground segregation (e.g., Driver, Baylis, & Rafal, 1992; Leeuwenberg & Buffart, 1984; Machilsen, Pauwels, & Wagemans, 2009), and amodal completion (e.g., Kanizsa, 1985; van Lier, van der Helm, & Leeuwenberg, 1995).

The relevant point here is that natural symmetries are nearly always imperfect. In biology, for instance, the amount of asymmetry in the basically symmetrical shape of flowers and potential mates is believed to be a marker of genetic quality, and it is believed to influence pollinating and mating behaviors (see, e.g., Grammer & Thornhill, 1994; Johnstone, 1994; Møller, 1992, 1995; Swaddle & Cuthill, 1994; Thornhill & Gangestad, 1994; Watson & Thornhill, 1994). This indicates that it is both ecologically and perceptually relevant to assess how or how well the visual system deals with imperfect symmetry.

Also, repetition (e.g., van der Helm & Treder, 2009) and Glass patterns (e.g., Dakin & Bex, 2001; Earle, 1985; Glass, 1969; Glass & Pérez, 1973; Glass & Switkes, 1976; Khuu & Hayes, 2005; Maloney, Mitchison, & Barlow, 1987; Prazdny, 1984) are considered to be visual regularities, but here, we focus on imperfect symmetry. Sidelong, we do consider imperfect Glass patterns, which, as we discuss, behave similarly, but we do not consider imperfect repetition, which behaves differently (e. …

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