A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation.

Kovács, Ilona; Julesz, Béla

doi:10.1073/pnas.90.16.7495

Cited by 455 publications

(322 citation statements)

References 9 publications

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“…And this claim has been corroborated in a number of experimental contexts (e.g., Elder & Zucker, 1993;Kovacs & Julesz, 1993;Garrigan, 2012). However, because closed contours automatically define an enclosed region, it is less clear whether this advantage of closure obtains at the level of contour geometry (see Tversky, Geisler & Perry, 2004), or at the level of region-based geometry, i.e., the geometry of the region enclosed by the contour.…”

Section: Interactions Between Contour and Region Geometrymentioning

confidence: 91%

Visual Representation of Contour and Shape

Singh

2014

Oxford Handbooks Online

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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.

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Section: Interactions Between Contour and Region Geometrymentioning

confidence: 91%

Visual Representation of Contour and Shape

Singh

2014

Oxford Handbooks Online

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“…An interesting stream of vision research started with the two papers [15,19]. Both experiments presented specially prepared images to human subjects who were asked to (quickly and reflexively) judge whether the images were 'purely random' or 'contained a curve buried in clutter'.…”

Section: Traveling Salesman Problemmentioning

confidence: 99%

“…As mentioned in the Introduction, this problem is motivated by perceptual psychophysics [15,19], where human subjects are shown pictures containing many randomly-oriented objects. It may or may not be the case in a given showing that a small fraction of objects lie distributed along a smooth curve, with each object oriented parallel to the curve.…”

Section: Extension: Connect-the-dartsmentioning

confidence: 99%

Connect the dots: how many random points can a regular curve pass through?

et al. 2005

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Suppose n points are scattered uniformly at random in the unit square [0, 1] 2 . Question: How many of these points can possibly lie on some curve of length λ? Answer, proved here:We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classes of interest include (in addition to the rectifiable curves mentioned above): Lipschitz graphs, monotone graphs, twice-differentiable curves, graphs of smooth functions with m-bounded derivatives. In each case we get order-of-magnitude estimates; for example, there are twice-differentiable curves containing as many as O P (n 1/3 ) uniform random points, but not essentially more than this.We also consider generalizations to higher dimensions and to hypersurfaces of various codimensions. Thus, twice-differentiable k-dimensional hypersurfaces in R d may contain as many as O P (n k/(2d−k) ) uniform random points. We also consider other notions of 'passing through' such as passing through given space/direction pairs. Thus, twice-differentiable curves in R 2 may pass through at most O P (n 1/4 ) uniform random location/direction pairs.We give both concrete approaches to our results, based on geometric multiscale analysis, and abstract approaches, based on ε-entropy.Stylized applications in image processing and perceptual psychophysics are described.

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“…It is likely that the integration of local features is driven by both bottom-up stimulus properties such as collinearity, proximity and connectedness (see e.g. Kofka 1935;Kovacs and Julesz 1993), as well as by top-down biases from stored object representations (Humphreys and Forde 2001).…”

Section: Introductionmentioning

confidence: 99%

“…These studies have used stimuli-Glass patterns, Gabor or simple line element displays-that generate the perception of a global form when their constituent elements (oriented dot pairs or Gabor/line elements) are organized as global conWgurations. Concentric and parallel global organization have some aspects in common-in that at certain scales concentric forms also have locally parallel texture-but concentric forms diVer in a number of important ways, e.g., in being made up of curved contours and closed contours (Kovacs and Julesz 1993) and in having a more compelling global circular shape and symmetry. Comparisons of responses to these forms should therefore provide insight into the critical factors contributing to the global representation of form.…”

Section: Introductionmentioning

confidence: 99%

Differential human brain activation by vertical and horizontal global visual textures

et al. 2010

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Mid-level visual processes which integrate local orientation information for the detection of global structure can be investigated using global form stimuli of varying complexity. Several lines of evidence suggest that the identiWcation of concentric and parallel organisations relies on diVerent underlying neural substrates. The current study measured brain activation by concentric, horizontal parallel, and vertical parallel arrays of short line segments, compared to arrays of randomly oriented segments. Six subjects were scanned in a blocked design functional magnetic resonance imaging experiment. We compared percentage BOLD signal change during the concentric, horizontal and vertical blocks within early retinotopic areas, the fusiform face area and the lateral occipital complex. Unexpectedly, we found that vertical and horizontal parallel forms diVerentially activated visual cortical areas beyond V1, but in general, activations to concentric and parallel forms did not diVer. Vertical patterns produced the highest percentage signal change overall and only area V3A showed a signiWcant diVerence between concentric and parallel (horizontal) stimuli, with the former better activating this area. These data suggest that the diVerence in brain activation to vertical and horizontal forms arises at intermediate or global levels of visual representation since the diVerential activity was found in mid-level retinotopic areas V2 and V3 but not in V1. This may explain why earlier studies-using methods that emphasised responses to local orientation-did not discover this vertical-horizontal anisotropy.

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A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation.

Cited by 455 publications

References 9 publications

Visual Representation of Contour and Shape

Visual Representation of Contour and Shape

Connect the dots: how many random points can a regular curve pass through?

Differential human brain activation by vertical and horizontal global visual textures

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