Mechanism of Symmetry Detection

Symmetry is a higher-order image feature. A visual stimulus is symmetric if some part of this stimulus is a reflection of another part about an axis, called symmetry axis. To determine whether an image is symmetric, the observer has to compare whether two points of the image are identical, and, if yes, whether the middle points of these matches forms an axis. Such operation requires a higher-order visual mechanism to take the information from early stage into computation.

Currently, in the literature, two types of theories have been proposed to explain how the visual system achieves this task. The first, the relational structure theory, suggests that the visual system may simply analyze the spatial relationship among individual image elements and determine an image to be symmetric if the relative position of a sufficient proportion of image elements supports it. That is, symmetry detection would be based solely on the signal-to-noise ratio or “weight of evidence”

in the image (Csathó, van der Vloed, & van der Helm, 2004; van der Helm &

Leeuwenberg, 1996, 1999). The second, the spatial filtering theory, assumes that a band of linear filters, whose sensitivity profiles contain multiple excitatory and inhibitory regions, extract symmetry information from an image. (Dakin & Hess, 1997; Dakin & Watt, 1994; Gurnsey, Herbert, & Kenemy, 1998; Osorio, 1996;

Rainville & Kingdom, 1999, 2000, 2002; Scognamillo, Rhodes, Morrone, & Burr, 2003; Tjan & Liu, 2005). These filters may be oriented (Dakin & Watt, 1994;

Rainville & Kingdom, 2000) or have different phase sensitivity (Rainville &

Kingdom, 1999, 2000, 2002; Scognamillo et al., 2003). These filters operate on the input images. If an input image is symmetric, the filtered image would contain features at or across the symmetry axis that can be picked up by a second-order filter that has an orientation similar to that of the symmetry axis (Gurnsey et al., 1998;

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Scognamillo et al., 2003) or by a simple mathematical operator operating orthogonal to the symmetry axis (Dakin & Hess, 1997; Dakin & Watt, 1994; Rainville &

Kingdom, 1999, 2000, 2002).

Both theories propose a two-stage processing for symmetrical perception. For the relational structure theory, the symmetry detection mechanism has to decide which image elements have the spatial properties that are consistent with a symmetric pair (signal) and which are not (noise). Then a higher-order mechanism collects these local pairs to compute the overall signal-to-noise ratio. The spatial filtering theory also needs a higher-order filter to monitor the output of lower order linear filters, which extracts symmetry information from an image. For these two theories to work, however, one has to make an assumption about the location and orientation of the symmetry axis, on which all the operations on the image depend. However, mirror symmetry can occur at any orientation in a nature scene. While these two theories perform well to explain the data from experiments with a known symmetry axis orientation, their generalization is limited as they do not address the situation where the symmetry axis orientation is unknown to the observers. To solve this problem, Chen and Tyler (2010) manipulated the cueing of the axis orientation and the axis salience and measured the target detection threshold at various noise density levels under these conditions. Their results showed facilitation effect of both cueing of axis orientation and high axis salience. However, the amount of cueing effect and the nonlinear axis salience effect cannot be explained by the above two theories. Hence, they incorporated the property of two-stage encoding process, adding a nonlinear process that was neither addressed by the relational structure nor by the filter approach, to explain the effect of uncertainty about axis orientation in the framework of the Signal Detection Theory (Green & Swets, 1966).

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Their model contains two stages: a perception stage and a decision stage (Figure 1.1). In the perception stage, there are a band of orientation-selective symmetry encoders that are sensitive to symmetry in an image. Each encoder is sensitive to the mirror symmetry about one axis. The contribution of each encoder is limited by both the internal noise inherited in the system (Na in Figure 1.1) and the external noise provided by the noise patterns (Ne in Figure 1.1). The nonlinear response of the perception stage is sent to the decision stage. The detection performance relies on the maximum response of all monitored channels. The observers detect symmetry when the difference of responses between two intervals reaches unity. If the observers have prior knowledge of the axis orientation, the decision stage only needs to monitor a relevant channel, whose symmetry selectivity matches that of the symmetric image.

However, if there is uncertainty of the axis orientation, the decision stage needs to monitor more channels than the relevant one. This uncertainty impairs the performance of symmetry detection when there is no prior knowledge of the axis orientation.

Figure 1.1. Diagram of the model. See text for details.

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This model has an extra nonlinear process than the spatial filtering theory and relational structure theory as these two theories are incapable of explaining Chen and Tyler (2010) data. This model is therefore more powerful than other two approaches.

This model provides us a good theoretical basis for exploring the possible mechanisms underlying color processing in symmetry perception. In this thesis, we extend Chen-Tyler model (2010), taking the chromatic information into consideration, to investigate the mechanism of chromatic symmetry detection.