Quantification of local symmetry: application to texture discrimination

Abstract

Symmetry is one of the most prominent cues in visual perception as well as in computer vision. We have recently presented a Generalized Symmetry Transform that receives as input an edge map, and outputs a symmetry map, where every point marks the intensity and orientation of the local generalized symmetry. In the context of computer vision, this map emphasizes points of high symmetry, which, in turn, are used to detect regions of interest for active vision systems. Many psychophysical experiments in texture discrimination use images that consist of various micro-patterns. Since the Generalized Symmetry Transform captures local spatial relations between image edges, it has been used here to predict human performance in discrimination tasks. Applying the transform to micro-patterns in some well-studied quantitative experiments of human texture discrimination, it is shown that symmetry, as characterized by the present computational scheme, can account for most of them.

A biologically plausible model of human shape symmetry perception

“…Many models of symmetry employ some variation where luminance or contrast properties of the image are compared pointwise on either side of a potential axis of symmetry. For texture symmetry, most models are variants of filter-rectify-filter approaches (Dakin & Hess, 1997;Dakin & Watt, 1994;Gurnsey, Herbert, & Kenemy, 1998;Rainville & Kingdom, 1999, but other image-filtering approaches have been proposed (e.g., Bonneh, Reisfeld, & Yeshurun, 2002;Palmer, 1983;Royer, 1981) as well as more quantitative approaches (Dry, 2008;van der Helm & Leeuwenberg, 1996, 2004. Image properties on either side of the potential axis of symmetry are compared using a correlation, a difference, or some related measure (e.g., Dakin & Watt, 1994;Dry, 2008;Gurnsey et al, 1998;Hong & Pavel, 2002;Latimer, Joung, & Stevens, 2002;Mancini et al, 2005;Rainville & Kingdom, 2000).…”

Difference magnitude is not measured by discrimination steps for order of point patterns

“…Journal of Vision, 16(9):2, 1-17, doi:10.1167/16.9.2. texture attribute, the degree of order is essential for texture discrimination and segmentation (Bonneh, Reisfeld, & Yeshurun, 1994;Ouhnana, Bell, Solomon, & Kingdom, 2013;Vancleef et al, 2013). Order also interacts with other perceptual dimensions, and its precise control in stimuli configurations is crucial for psychophysical experiments.…”

Symmetry Sensitivities of Derivative-of-Gaussian Filters

“…The detection and classification of image symmetry has been studied in the context of Computer [42], [43], [44], [45], [46], [47] and Biological Vision [48], [49], [50], [51], [52], [53], [54], [55]. As discussed in Section 3.2, there are many types of symmetries potentially relevant to image understanding, but often detection of the reflectional type only has been considered; less often considered are skew-reflectional (reflect and shear) [56], antireflectional [54], and periodictranslational [47], [51].…”

“…Researchers in Biological Vision generally focus on global symmetry, which, having an established definition, makes it suitable for stimulus characterization. Researchers in Computational Vision, recognizing that global symmetry is a rather rare circumstance in natural images, often focus on advancing definitions of local symmetry and algorithms for its detection [42], [43], [57], [58], [59], [60], [61]. For biologists and psychologists, the interest in symmetry arises mostly from informal observation of sensitivity, from the suggestion of it as a Gestalt grouping principle, from its potential for use in detecting biological structures such as faces and flowers [62], and for its role in mate selection [63].…”