Visual Representation of Contour and Shape

Abstract

Contours provide an essential source of information about shape and, along contours, points with the greatest magnitude of curvature tend to be most informative. This concentration of information is closely tied to internal generative models of contours employed by the visual system. In going from open to closed contours, the sign of curvature becomes perceptually significant, with negative-curvature (concave) sections of a contour being more informative, and playing an important role in part segmentation. The visual system represents complex shapes by segmenting them into simpler parts ("simpler" because they have less negative curvature). Points of negative minima of curvature provide an important cue for part segmentation; however being entirely local and contour-based features, they cannot fully predict part segmentation. The visual system employs not only a contour-based representation of shape, but also a region-based one, making explicit properties such as axis curvature, local width of the shape, and locally-parallel and locally-symmetric structure. A region-based representation of shape based on Bayesian estimation of the shape skeleton provides a successful account of part segmentation. Moreover, psychophysical results from a variety of domains provide evidence for the representation of region-based geometry by human vision, based on the shape skeleton. Even at the level of so-called "illusory contours," nonlocal region-based geometry exerts a strong influence. We conclude that, as far as the visual representation of shape is concerned, contour geometry cannot ultimately be studied in isolation, but must be considered conjointly with region-based geometry.

Mental structures

“…In other words, it segments contours and shapes into simpler ‘parts’ and organizes shape representations using these parts and their spatial relationships. Far from being arbitrary subsets, these perceptual parts are highly systematic, and segmented using predictable geometric ‘rules’ (Singh, 2015, p. 242‐3).…”

“…Masking or adapting to one curved segment of a contour does not entail masking of or adaptation to other segments of the same curvature at different positions on the contour (Habak et al., 2004; Gheorghiu & Kingdom, 2007). Barenholtz and Feldman (2003) argue for a related conclusion, that saliently distinct “parts” of objects, such as the lobes of the “peanut” patterns in Figure 5, receive distinct representations even when the parts have the same outline curvature (see also Green, 2017; Hoffman & Richards, 1984; Singh, 2015). Barenholtz and Feldman tasked subjects with determining whether two marks or probes on such a figure—small, textured line‐segments like those illustrated in Figure 5—were identical or not.…”

“…Still, many of the studies cited here demonstrate capacities for attributing the same shapes to contours despite differences in the registered retinal sizes, positions, local orientations, and luminance profiles that the contours project to the eye. Further, it is plausible that the perceptual states in question are the products of processes such as shape segmentation, contour integration, and completion (Hoffman & Richards, 1984; Kellman et al., 2013; Singh, 2015), which are known to be sensitive to the locations and orientations of contours in three‐dimensional space (Hess, Hayes, & Kingdom, 1997; Kellman, Garrigan, & Shipley, 2005) and to produce contour representations according to principles that reflect objective regularities in how contours are organized in the environment (Geisler, Perry, Super, & Gallogly, 2001; Hoffman & Richards, 1984). These characteristics suggest that the perceptual states in question function to represent the shapes of objective, distal contours rather than features of proximal stimuli.In any case, I allow that mere sensory states can also have a kind of constituent structure.…”

Automatic structuring of organic shapes from a single drawing

“…Given that a drawing is only composed of lines, several approaches have been proposed to identify which visual mechanisms are used to help interpret the drawn lines in terms of self-consistent shapes and contours [2]. Several methods address specific aspects of this complex process and techniques have been developed to evaluate them on well-defined data sets.…”

Investigating shape representation using sensitivity to part- and axis-based transformations

“…A skeleton or axis-based representation, by contrast, explicitly represents geometric properties of the enclosed region, such as the width of a part, whether or not two points are “locally symmetric” across an axial branch, etc. Informally, the former may be viewed as a rubber-band representation; the latter as a cardboard-cutout representation (Singh, in press). …”