Abstract

It has been noted that many of the perceptually salient image properties identified by the Gestalt psychologists, such as collinearity, parallelism, and good continuation, are invariant to changes in viewpoint. However, I show that viewpoint invariance is not sufficient to distinguish these Gestalt properties; one can define an infinite number of viewpoint-invariant properties that are not perceptually salient. I then show that generally, the perceptually salient viewpoint-invariant properties are minimal, in the sense that they can be derived by using less image information than for nonsalient properties. This finding provides support for the hypothesis that the biological relevance of an image property is determined both by the extent to which it provides information about the world and by the ease with which this property can be computed. [An abbreviated version of this work, including technical details that are avoided in this paper, is contained in K. Boyer and S. Sarker, eds., Perceptual Organization for Artificial Vision Systems (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 121–138.]

© 2003 Optical Society of America

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2003 (1)

G. Kayeart, I. Biederman, R. Vogels, “Shape tuning in macaque inferior temporal cortex,” J. Neurosci. 23, 3016–3027 (2003).

2001 (1)

R. Vogels, I. Biederman, M. Bar, A. Lorincz, “Inferior temporal neurons show greater sensitivity to nonaccidental than metric differences,” J. Cogn Neurosci. 13, 444–453 (2001).
[CrossRef] [PubMed]

1999 (4)

R. Basri, Y. Moses, “When is it possible to identify 3D objects from single images using class constraints?” Int. J. Comput. Vision 33, 1–22 (1999).

I. Biederman, M. Bar, “One-shot viewpoint invariance in matching novel objects,” Vision Res. 39, 2885–2899 (1999).
[CrossRef] [PubMed]

S. Zhu, “Embedding Gestalt laws in the Markov random fields,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1170–1187 (1999).
[CrossRef]

J. Wagemans, “Toward a better approach to goodness: comment on Van der Helm and Leeuwenberg 1996,” Psychol. Rev. 106, 610–621 (1999).
[CrossRef]

1997 (5)

L. Williams, D. Jacobs, “Local parallel computation of stochastic completion fields,” Neural Comput. 9, 859–881 (1997).
[CrossRef]

W. Hayward, M. Tarr, “Testing conditions for viewpoint invariance in object recognition,” J. Exp. Psychol. Hum. Percept. Perform. 23, 1511–1521 (1997).
[CrossRef] [PubMed]

D. Jacobs, “Matching 3-D models to 2-D images,” Int. J. Comput. Vis. 21(1/2), 123–153 (1997).
[CrossRef]

J. Feldman, “Curvilinearity, covariance, and regularity in perceptual groups,” Vision Res. 37, 2835–2848 (1997).
[CrossRef]

L. Williams, D. Jacobs, “Stochastic completion fields: a neural model of illusory contour shape and salience,” Neural Comput. 9, 837–858 (1997).
[CrossRef] [PubMed]

1996 (6)

N. Chater, “Reconciling simplicity and likelihood principles in perceptual organization,” Psychol. Rev. 103, 566–581 (1996).
[CrossRef] [PubMed]

M. Zerroug, R. Nevatia, “Three-dimensional descriptions based on the analysis of the invariant and quasi-invariant properties of some curved-axis generalized cylinders,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 237–966 (1996).
[CrossRef]

D. Jacobs, “The space requirements of indexing under perspective projection,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 330–333 (1996b).
[CrossRef]

P. Van der Helm, E. Leeuwenberg, “Goodness of visual regularities: a non-transformational approach,” Psychol. Rev. 103, 429–456 (1996).
[CrossRef] [PubMed]

G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local instrinsic dimensionality,” IEEE Trans. Image Process. 5, 1026–1042 (1996).
[CrossRef]

G. Guy, G. Medioni, “Inferring global perceptual contours from local features,” Int. J. Comput. Vision 20(1/2), 113–133 (1996).
[CrossRef]

1995 (2)

M. Tarr, H. Bülthoff, “Is human object recognition better described by geonstructural-descriptions or by multiple-views? Comment on Biederman and Gerhardstein 1993,” J. Exp. Psychol. Hum. Percept. Perform. 21, 1494–1505 (1995).
[CrossRef] [PubMed]

I. Biederman, P. Gerhardstein, “Viewpoint-dependent mechanisms in visual object recognition: reply to Tarr and Bülthoff,” J. Exp. Psychol. Hum. Percept. Perform. 21, 1506–1514 (1995).
[CrossRef]

1994 (3)

M. Kurbat, “Structural description theories: Is RBC/JIM a general-purpose theory of human entry-level object recognition?” Perception 23, 1339–1368 (1994).
[CrossRef] [PubMed]

L. Van Gool, T. Moons, E. Pauwels, J. Wagemans, “Invariance from the Euclidean geometer’s persepective,” Perception 23, 547–561 (1994).
[CrossRef]

J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
[CrossRef] [PubMed]

1993 (5)

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).

I. Biederman, P. Gerhardstein, “Recognizing depth-rotated objects: evidence and conditions for three-dimensional viewpoint invariance,” J. Exp. Psychol. Hum. Percept. Perform. 19, 1162–1182 (1993).
[CrossRef] [PubMed]

D. Field, A. Hayes, R. Hess, “Contour integration by the human visual system: evidence for a local ‘association field’,” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

J. Wagemans, L. Van Gool, V. Swinnen, J. Van Horebeek, “Higher-order structure in regularity detection,” Vision Res. 33, 1067–1088 (1993).
[CrossRef] [PubMed]

I. Weiss, “Geometric invariants and object recognition,” Int. J. Comput. Vision 10, 207–231 (1993).
[CrossRef]

1992 (3)

J. Hummel, I. Biederman, “Dynamic binding in a neural network for shape recognition,” Psychol. Rev. 99, 480–517 (1992).
[CrossRef] [PubMed]

D. Williams, B. Julesz, “Peceptual asymmetry in texture detection,” Proc. Natl. Acad. Sci. USA 89, 6531–6534 (1992).
[CrossRef]

J. Wagemans, L. Van Gool, G. d’Ydewalle, “Orientational effects and component processes in symmetry detection,” Q. J. Exp. Psychol. A 44, 475–508 (1992).
[CrossRef]

1991 (2)

D. Clemens, D. Jacobs, “Space and time bounds on model indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1007–1018 (1991).
[CrossRef]

J. Wagemans, L. Van Gool, G. d’Ydewalle, “Detection of symmetry in tachistoscopically presented dot patterns: effects of multiple axes and skewing.” Percept. Psychophys. 50, 413–427 (1991).
[CrossRef] [PubMed]

1990 (1)

T. Poggio, S. Edelman, “A network that learns to recognize 3D objects,” Nature 343, 263–266 (1990).
[CrossRef] [PubMed]

1989 (3)

S. Ullman, “Aligning pictorial descriptions: an approach to object recognition,” Cognition 32, 193–254 (1989).
[CrossRef] [PubMed]

J. Ponce, D. Chelberg, W. Mann, “Invariant properties of straight homogeneous generalized cylinders and their contours,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 951–966 (1989).
[CrossRef]

P. Parent, S. Zucker, “Trace inference, curvature consistency and curve detection,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 823–839 (1989).
[CrossRef]

1988 (1)

M. Corballis, “Recognition of disoriented shapes,” Psychol. Rev. 95, 115–123 (1988).
[CrossRef] [PubMed]

1987 (2)

I. Biederman, “Recognition-by-components: a theory of human image understanding,” Psychol. Rev. 94, 115–147 (1987).
[CrossRef] [PubMed]

I. Rock, J. DiVita, “A case of viewer-centered object perception,” Cogn. Psychol. 19, 280–293 (1987).
[CrossRef] [PubMed]

1986 (1)

M. Leyton, “A theory of information structure II. A theory of perceptual organization,” J. Math. Psychol. 30, 257–305 (1986).
[CrossRef]

1985 (1)

S. Grossberg, E. Mingolla, “Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading,” Psychol. Rev. 92, 173–211 (1985).
[CrossRef] [PubMed]

1984 (2)

J. Koenderink, “What does the occluding contour tell us about solid shape?” Perception 13, 321–330 (1984).
[CrossRef] [PubMed]

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984).
[CrossRef] [PubMed]

1983 (2)

J. Cutting, “Observations: four assumptions about invariance in perception,” J. Exp. Psychol. Hum. Percept. Perform. 9, 310–317 (1983).
[CrossRef] [PubMed]

P. Jolicoeur, S. Kosslyn, “Coordinate systems in the long-term memory representation of three-dimensional shapes,” Cogn. Psychol. 15, 301–345 (1983).
[CrossRef] [PubMed]

1982 (1)

J. Koenderink, A. van Doorn, “The shape of smooth objects and the way contours end,” Perception 11, 129–137 (1982).
[CrossRef] [PubMed]

1981 (2)

T. Binford, “Inferring surfaces from images,” Artif. Intell. 17, 205–244 (1981).
[CrossRef]

T. Kanade, “Recovery of the three-dimensional shape of an object from a single view,” Artif. Intell. 17, 409–460 (1981).
[CrossRef]

1977 (1)

E. Abravanel, “The figural simplicity of parallel lines,” Child Dev. 48, 708–710 (1977).
[CrossRef]

1971 (1)

E. Leeuwenberg, “A perceptual coding language for visual and auditory patterns,” Am. J. Psychol. 84, 307–349 (1971).
[CrossRef] [PubMed]

1954 (1)

F. Attneave, “Some informational aspects of visual perception,” Psychol. Rev. 68, 183–193 (1954).
[CrossRef]

Abravanel, E.

E. Abravanel, “The figural simplicity of parallel lines,” Child Dev. 48, 708–710 (1977).
[CrossRef]

Attneave, F.

F. Attneave, “Some informational aspects of visual perception,” Psychol. Rev. 68, 183–193 (1954).
[CrossRef]

Bar, M.

R. Vogels, I. Biederman, M. Bar, A. Lorincz, “Inferior temporal neurons show greater sensitivity to nonaccidental than metric differences,” J. Cogn Neurosci. 13, 444–453 (2001).
[CrossRef] [PubMed]

I. Biederman, M. Bar, “One-shot viewpoint invariance in matching novel objects,” Vision Res. 39, 2885–2899 (1999).
[CrossRef] [PubMed]

Basri, R.

R. Basri, Y. Moses, “When is it possible to identify 3D objects from single images using class constraints?” Int. J. Comput. Vision 33, 1–22 (1999).

D. Jacobs, P. Belhumeur, R. Basri, “Comparing images under variable illumination,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 610–617.

Belhumeur, P.

D. Jacobs, P. Belhumeur, R. Basri, “Comparing images under variable illumination,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 610–617.

D. Jacobs, P. Belhumeur, I. Jermyn, “Judging whether multiple silhouettes can come from the same object,” in Proceedings of the International Workshop on Visual Form (Springer-Verlag, Heidelberg, Germany, 2001), pp. 532–541.

Biederman, I.

G. Kayeart, I. Biederman, R. Vogels, “Shape tuning in macaque inferior temporal cortex,” J. Neurosci. 23, 3016–3027 (2003).

R. Vogels, I. Biederman, M. Bar, A. Lorincz, “Inferior temporal neurons show greater sensitivity to nonaccidental than metric differences,” J. Cogn Neurosci. 13, 444–453 (2001).
[CrossRef] [PubMed]

I. Biederman, M. Bar, “One-shot viewpoint invariance in matching novel objects,” Vision Res. 39, 2885–2899 (1999).
[CrossRef] [PubMed]

I. Biederman, P. Gerhardstein, “Viewpoint-dependent mechanisms in visual object recognition: reply to Tarr and Bülthoff,” J. Exp. Psychol. Hum. Percept. Perform. 21, 1506–1514 (1995).
[CrossRef]

I. Biederman, P. Gerhardstein, “Recognizing depth-rotated objects: evidence and conditions for three-dimensional viewpoint invariance,” J. Exp. Psychol. Hum. Percept. Perform. 19, 1162–1182 (1993).
[CrossRef] [PubMed]

J. Hummel, I. Biederman, “Dynamic binding in a neural network for shape recognition,” Psychol. Rev. 99, 480–517 (1992).
[CrossRef] [PubMed]

I. Biederman, “Recognition-by-components: a theory of human image understanding,” Psychol. Rev. 94, 115–147 (1987).
[CrossRef] [PubMed]

Binford, T.

T. Binford, “Inferring surfaces from images,” Artif. Intell. 17, 205–244 (1981).
[CrossRef]

T. Binford, T. Levitt, “Quasi-invariants: theory and exploitation,” in Proceedings of the DARPA Image Understanding Workshop (Defense Advanced Research Projects Agency, Arlington, Va., 1993), pp. 819–829.

Bülthoff, H.

M. Tarr, H. Bülthoff, “Is human object recognition better described by geonstructural-descriptions or by multiple-views? Comment on Biederman and Gerhardstein 1993,” J. Exp. Psychol. Hum. Percept. Perform. 21, 1494–1505 (1995).
[CrossRef] [PubMed]

Burns, J.

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Figures (7)

Fig. 1
Fig. 1

Polyhedron. The two lines connecting points four and seven and connecting points five and six are not parallel in three dimensions. However, there will be a circle of possible viewing directions from which these lines will appear parallel. Two such views are shown in the top of the figure. The lines will not appear parallel except from viewing directions lying on this circle.

Fig. 2
Fig. 2

p1, p2, p3 form an affine basis. p4 has coordinates (α4, β4) with respect to this coordinate system. The points form a parallelogram, for example, when (α4, β4)=(1, 1).

Fig. 3
Fig. 3

We define the scene plane as the plane formed by p1, p2, p3. For any affine coordinates, (α4, β4), some point in this plane, s4, has these coordinates. The fourth scene point, p4, projects to the same image point as s4 from one viewing direction, as shown; so from this direction, p4 appears in the image with affine coordinates (α4, β4).

Fig. 4
Fig. 4

p1, p2, p3 form an affine basis. At the top, the dashed line is described by β4=1. At the bottom, the dashed line is described by α4+2β4=2. If p4 falls on the line at the top, the four points form the corners of a trapezoid. At the bottom, a point on the dashed line has an equally viewpoint-invariant property that is not, however, perceptually salient.

Fig. 5
Fig. 5

Three points can be convex when one side of the curve joining them is distinguished as figure and the other is background.

Fig. 6
Fig. 6

We consider two fundamentally different types of edges. The position of surface discontinuities, such as discontinuities in orientation or reflectance, are not viewpoint dependent. Discontinuities between objects produce the silhouettes of smooth objects. The position on the object that produces these edges is entirely viewpoint dependent.

Fig. 7
Fig. 7

Convex objects, such as the box in the upper left, will produce a convex silhouette when viewed from any direction. Some other objects, like the starfish on the bottom, may produce concavities in their silhouettes when viewed from any angle (the legs of the starfish curve downward a bit, so even when viewed end on, as on the right, they will be somewhat visible). Other objects, such as the apple in the upper right, may have convex silhouettes when viewed from some directions and produce silhouettes with concavities from other directions.

Tables (1)

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Table 1 Minimality of Perceptually Salient Features a

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

p4=p1+α4(p2-p1)+β4(p3-p1).
p4=(0, 0)+x(1, 0)+y(0, 1).
q4=q1+α4(q2-q1)+β4(q3-q1).

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