Processing convexity and concavity along a 2-D contour: figure–ground, structural shape, and attention

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims—for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure–ground organization and in parsing, but other, more specific claims are not (yet) well supported.

[1]  Ernst Mach,et al.  The analysis of sensations and the relation of the physical to the psychical , 1914, The Mathematical Gazette.

[2]  K. Koffka.  Principles Of Gestalt Psychology , 1936 .

[3]  F. Attneave.  Some informational aspects of visual perception. , 1954, Psychological review.

[4]  R. Arnheim.  Art and visual perception: A psychology of the creative eye, New version , 1955 .

[5]  P Salapatek,et al.  Visual scanning of geometric figures by the human newborn. , 1968, Journal of comparative and physiological psychology.

[6]  Walter Gerbino,et al.  Convexity and Symmetry in Figure-Ground Organization , 1976 .

[7]  Mary Henle,et al.  Vision and artifact , 1977 .

[8]  D. Marr,et al.  Representation and recognition of the spatial organization of three-dimensional shapes , 1978, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[9]  J. Koenderink,et al.  The Shape of Smooth Objects and the Way Contours End , 1982, Perception.

[10]  Donald D. Hoffman,et al.  Parts of recognition , 1984, Cognition.

[11]  J J Koenderink,et al.  What Does the Occluding Contour Tell Us about Solid Shape? , 1984, Perception.

[12]  John M Kennedy,et al.  Shape and Contour: The Points of Maximum Change are Least Useful for Recognition , 1985, Perception.

[13]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[14]  Michael Brady,et al.  The Curvature Primal Sketch , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  I. Biederman.  Recognition-by-components: a theory of human image understanding. , 1987, Psychological review.

[16]  A Treisman,et al.  Feature analysis in early vision: evidence from search asymmetries. , 1988, Psychological review.

[17]  Donald D. Hoffman,et al.  Parts of Visual Objects: An Experimental Test of the Minima Rule , 1989, Perception.

[18]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[19]  Richard G. Kurial,et al.  Representation and recognition , 1990 .

[20]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[21]  G. Saliba,et al.  The Optics of Ibn Al-Haytham: Books I-III, on Direct Vision , 1992 .

[22]  B. Gibson,et al.  Shape Recognition Inputs To Figure-Ground Organization in Three-Dimensional Displays , 1993, Cognitive Psychology.

[23]  V Bruce,et al.  Independent Effects of Lighting, Orientation, and Stereopsis on the Hollow-Face Illusion , 1993, Perception.

[24]  G. Baylis,et al.  Visual attention and objects: evidence for hierarchical coding of location. , 1993, Journal of experimental psychology. Human perception and performance.

[25]  B. Gibson.  Visual attention and objects: one versus two or convex versus concave? , 1994, Journal of experimental psychology. Human perception and performance.

[26]  Jon Driver,et al.  Parallel computation of symmetry but not repetition within single visual shapes , 1994 .

[27]  Jon Driver,et al.  Obligatory edge-assignment in vision: The role of figure and part segmentation in symmetry detection. , 1995 .

[28]  I. Howard.  Alhazen's Neglected Discoveries of Visual Phenomena , 1996, Perception.

[29]  K Siddiqi,et al.  Parts of Visual Form: Psychophysical Aspects , 1996, Perception.

[30]  David W. Jacobs,et al.  Robust and Efficient Detection of Salient Convex Groups , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Donald D. Hoffman,et al.  Salience of visual parts , 1997, Cognition.

[32]  M Kubovy,et al.  Detection of symmetry and perceptual organization: the way a lock-and-key process works. , 1997, Acta psychologica.

[33]  J. Wolfe,et al.  Preattentive Object Files: Shapeless Bundles of Basic Features , 1997, Vision Research.

[34]  Donald D. Hoffman,et al.  Part Boundaries Alter the Perception of Transparency , 1998 .

[35]  C. A. Burbeck,et al.  Scaled medial axis representation: evidence from position discrimination task , 1998, Vision Research.

[36]  P. Cavanagh,et al.  A shape-contrast effect for briefly presented stimuli. , 1998, Journal of experimental psychology. Human perception and performance.

[37]  W. Hayward.  Effects of outline shape in object recognition , 1998 .

[38]  M J Tarr,et al.  Recognizing Silhouettes and Shaded Images across Depth Rotation , 1999, Perception.

[39]  R. Basri,et al.  The role of convexity in perceptual completion: beyond good continuation , 1999, Vision Research.

[40]  Johan Wagemans,et al.  Rapid Integration of Contour Fragments: From Simple Filling-in to Parts-based Shape Description , 1999 .

[41]  Donald D. Hoffman,et al.  Parsing silhouettes: The short-cut rule , 1999, Perception & psychophysics.

[42]  Paul L. Rosin.  Shape Partitioning by Convexity , 1999, BMVC.

[43]  Nava Rubin,et al.  Measuring convexity for figure/ground separation , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[44]  J. Friedenberg,et al.  Contour symmetry detection: the influence of axis orientation and number of objects. , 2000, Acta psychologica.

[45]  W. D. Craft,et al.  Foundations of spatial vision: from retinal images to perceived shapes. , 2000, Psychological review.

[46]  J. Hulleman,et al.  Concavities as basic features in visual search: Evidence from search asymmetries , 2000, Perception & psychophysics.

[47]  Glyn W. Humphreys,et al.  A Search Asymmetry Reversed by Figure-Ground Assignment , 2000, Psychological science.

[48]  H. Barlow.  Vision Science: Photons to Phenomenology by Stephen E. Palmer , 2000, Trends in Cognitive Sciences.

[49]  J T Todd,et al.  Ambiguity and the ‘Mental Eye’ in Pictorial Relief , 2001, Perception.

[50]  H H Bülthoff,et al.  A Prior for Global Convexity in Local Shape-from-Shading , 2001, Perception.

[51]  Hsing-Kuo Kenneth Pao,et al.  A Continuous Shape Descriptor by Orientation Diffusion , 2001, EMMCVPR.

[52]  R. Bhatt,et al.  Pictorial cues and three-dimensional information processing in early infancy. , 2001, Journal of experimental child psychology.

[53]  Jon Driver,et al.  Perception of symmetry and repetition within and across visual shapes: Part-descriptions and object-based attention , 2001 .

[54]  H. Ross,et al.  Information Concentration along the Boundary Contours of Naturally Shaped Solid Objects , 2001, Perception.

[55]  S. Suzuki,et al.  Attention-dependent brief adaptation to contour orientation: a high-level aftereffect for convexity? , 2001, Vision Research.

[56]  R. Rosenholtz.  Search asymmetries? What search asymmetries? , 2001, Perception & psychophysics.

[57]  M. Bertamini,et al.  The Importance of Being Convex: An Advantage for Convexity when Judging Position , 2001, Perception.

[58]  C. Connor,et al.  Population coding of shape in area V4 , 2002, Nature Neuroscience.

[59]  Paul L. Rosin,et al.  A Convexity Measurement for Polygons , 2002, BMVC.

[60]  Toshio Inui,et al.  A Feature-Segmentation Model of Short-Term Visual Memory , 1999, Perception.

[61]  Yaoda Xu,et al.  Early computation of part structure: Evidence from visual search , 2002, Perception & psychophysics.

[62]  M. Bertamini,et al.  No within-object advantage for detection of rotation. , 2002, Acta psychologica.

[63]  Toby J. Lloyd-Jones,et al.  Outline shape is a mediator of object recognition that is particularly important for living things , 2002, Memory & cognition.

[64]  T. Shipley,et al.  PART-BASED REPRESENTATIONS OF VISUAL SHAPE AND IMPLICATIONS FOR VISUAL COGNITION , 2002 .

[65]  R. Dhandapani,et al.  Role of scale in partitioning shape , 2002, Proceedings. International Conference on Image Processing.

[66]  A. W..  Inferring three-dimensional shapes from two-dimensional silhouettes , 2002 .

[67]  Jacob Feldman,et al.  Visual comparisons within and between object parts: evidence for a single-part superiority effect , 2003, Vision Research.

[68]  Marco Bertamini,et al.  The shape of holes , 2003, Cognition.

[69]  Satoru Suzuki,et al.  Attentional selection of overlapped shapes: a study using brief shape aftereffects , 2003, Vision Research.

[70]  Jacob Feldman,et al.  Detection of change in shape: an advantage for concavities , 2003, Cognition.

[71]  L. Vaina,et al.  The largest convex patches: A boundary-based method for obtaining object parts , 2004, Biological Cybernetics.

[72]  J. Wolfe,et al.  What attributes guide the deployment of visual attention and how do they do it? , 2004, Nature Reviews Neuroscience.

[73]  Anastasia V. Flevaris,et al.  Exogenous Spatial Attention Influences Figure-Ground Assignment , 2004 .

[74]  F. Ohl,et al.  Fallacies in behavioural interpretation of auditory cortex plasticity , 2004, Nature Reviews Neuroscience.

[75]  Marco Bertamini,et al.  Early Computation of Contour Curvature and Part Structure: Evidence from Holes , 2004, Perception.

[76]  Charles E Connor,et al.  Underlying principles of visual shape selectivity in posterior inferotemporal cortex , 2004, Nature Neuroscience.

[77]  J. Feldman,et al.  Information along contours and object boundaries. , 2005, Psychological review.

[78]  Manish Singh,et al.  What change detection tells us about the visual representation of shape. , 2005, Journal of vision.

[79]  Marco Bertamini,et al.  Detection of change in shape and its relation to part structure. , 2005, Acta psychologica.

[80]  Johannes Burge,et al.  Ordinal configural cues combine with metric disparity in depth perception. , 2005, Journal of vision.

[81]  W. Gerbino,et al.  Contour curvature polarity and surface interpolation , 2005, Vision Research.

[82]  J. Joseph,et al.  Infants' perception of information along object boundaries: concavities versus convexities. , 2006, Journal of experimental child psychology.

[83]  Marco Bertamini,et al.  The Perceived Structural Shape of Thin (wire-like) Objects is Different from That of Silhouettes , 2006, Perception.

[84]  Marco Bertamini,et al.  Errors in Judging Information about Reflections in Mirrors , 2006, Perception.

[85]  Marco Bertamini,et al.  Amodal completion and visual holes (static and moving). , 2006, Acta psychologica.

[86]  Marco Bertamini,et al.  Who Owns the Contour of a Visual Hole? , 2006, Perception.

[87]  Jacqueline M. Fulvio,et al.  Surface geometry influences the shape of illusory contours. , 2006, Acta psychologica.

[88]  J. Wagemans,et al.  Segmentation of object outlines into parts: A large-scale integrative study , 2006, Cognition.

[89]  Scott L. Brincat,et al.  Dynamic Shape Synthesis in Posterior Inferotemporal Cortex , 2006, Neuron.

[90]  Jacob Feldman,et al.  Determination of visual figure and ground in dynamically deforming shapes , 2006, Cognition.

[91]  Marco Bertamini,et al.  Visual search for a circular region perceived as a figure versus as a hole: Evidence of the importance of part structure , 2006, Perception & psychophysics.

[92]  Manish Singh,et al.  Geometric determinants of shape segmentation: Tests using segment identification , 2007, Vision Research.

[93]  Johan Wagemans,et al.  The concavity effect is a compound of local and global effects , 2007, Perception & psychophysics.

[94]  Jitendra Malik,et al.  Local figure-ground cues are valid for natural images. , 2007, Journal of vision.

[95]  M. Leyton,et al.  Shape as Memory , 2007 .

[96]  Johan Hulleman,et al.  Concavities count for less in symmetry perception , 2007, Psychonomic bulletin & review.

[97]  Matthias S. Treder,et al.  Symmetry versus repetition in cyclopean vision: A microgenetic analysis , 2007, Vision Research.

[98]  Marco Bertamini,et al.  Detection of convexity and concavity in context. , 2008, Journal of experimental psychology. Human perception and performance.

[99]  Aditya Murthy,et al.  Covert inhibition potentiates online control in a double-step task. , 2008, Journal of vision.

[100]  Nancy Kanwisher,et al.  Privileged coding of convex shapes in human object-selective cortex. , 2008, Journal of neurophysiology.

[101]  Rolf Nelson,et al.  Figure – Ground Effects on Shape Memory for Objects versus Holes , 2008, Perception.

[102]  Alice R. Albrecht,et al.  Attentional selection and the representation of holes and objects. , 2008, Journal of vision.

[103]  Johan Wagemans,et al.  Identification of Everyday Objects on the Basis of Fragmented Outline Versions , 2008, Perception.

[104]  Mary A Peterson,et al.  Inhibitory competition between shape properties in figure-ground perception. , 2008, Journal of experimental psychology. Human perception and performance.

[105]  Jasna Martinovic,et al.  Integration of ordinal and metric cues in depth processing. , 2008, Journal of vision.

[106]  Elan Barenholtz,et al.  Visual judgment of similarity across shape transformations: evidence for a compositional model of articulated objects. , 2008, Acta psychologica.

[107]  M. Peterson,et al.  Inhibitory competition in figure-ground perception: context and convexity. , 2008, Journal of vision.

[108]  Johan Wagemans,et al.  Identification of Everyday Objects on the Basis of Silhouette and Outline Versions , 2007, Perception.

[109]  J. Wagemans,et al.  Perceptual saliency of points along the contour of everyday objects: A large-scale study , 2008 .

[110]  Marco Bertamini,et al.  Rapid Figure – Ground Responses to Stereograms Reveal an Advantage for a Convex Foreground , 2008, Perception.

[111]  Jacob Feldman,et al.  Globally inconsistent figure/ground relations induced by a negative part. , 2009, Journal of vision.

[112]  Johan Wagemans,et al.  Detection of symmetry and repetition in one and two objects. Structures versus strategies. , 2009, Experimental psychology.

[113]  Johan Wagemans,et al.  Time-course contingencies in perceptual organization and identification of fragmented object outlines. , 2009, Journal of experimental psychology. Human perception and performance.

[114]  D. Leopold,et al.  Visual adaptation to convexity in macaque area V4 , 2009, Neuroscience.

[115]  Stephen E. Palmer,et al.  Shape memory for intrinsic versus accidental holes , 2009, Attention, perception & psychophysics.

[116]  Barton L Anderson,et al.  Failure of facial configural cues to alter metric stereoscopic depth. , 2009, Journal of vision.

[117]  Lin Chen,et al.  Topological change disturbs object continuity in attentive tracking , 2010, Proceedings of the National Academy of Sciences.

[118]  Johan Wagemans,et al.  Identification of everyday objects on the basis of Gaborized outline versions , 2010, i-Perception.

[119]  Charless C. Fowlkes,et al.  Natural-Scene Statistics Predict How the Figure–Ground Cue of Convexity Affects Human Depth Perception , 2010, The Journal of Neuroscience.

[120]  J. Koenderink,et al.  The shading cue in context , 2010, i-Perception.

[121]  Todd S. Horowitz,et al.  Can we track holes? , 2011, Vision Research.

[122]  Kechen Zhang,et al.  A Sparse Object Coding Scheme in Area V4 , 2011, Current Biology.

[123]  Sherryse L. Corrow,et al.  Six-Month-Old Infants Perceive the Hollow-Face Illusion , 2011, Perception.

[124]  J. Wagemans,et al.  Switching dynamics of border ownership: A stochastic model for bi-stable perception , 2011, Vision Research.

[125]  Flip Phillips,et al.  Fechner, information, and shape perception , 2011, Attention, perception & psychophysics.

[126]  Johan Wagemans,et al.  Light fields and shape from shading. , 2011, Journal of vision.

[127]  R. Bhatt,et al.  Parts, cavities, and object representation in infancy. , 2011, Journal of experimental psychology. Human perception and performance.

[128]  Anne Treisman,et al.  Feature Analysis in Early Vision , 2012 .

[129]  S. Palmer,et al.  A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure-ground organization. , 2012, Psychological bulletin.

[130]  Ik Soo Lim,et al.  Curvature and the visual perception of shape: theory on information along object boundaries and the minima rule revisited. , 2012, Psychological review.

[131]  Jacob Feldman,et al.  Principles of contour information: Reply to Lim and Leek (2012). , 2012, Psychological review.

[132]  A. Johnston,et al.  Recognising Faces: Effects of Lighting Direction, Inversion, and Brightness Reversal , 2013, Perception.

[133]  Naoki Kogo,et al.  The “side” matters: How configurality is reflected in completion , 2013, Cognitive neuroscience.

[134]  Marco Bertamini,et al.  The role of convexity in perception of symmetry and in visual short-term memory , 2013, Quarterly journal of experimental psychology.