## Perceptual Completion of Occluded Surfaces (1994)

Citations: | 31 - 5 self |

### BibTeX

@MISC{Williams94perceptualcompletion,

author = {Lance R. Williams},

title = {Perceptual Completion of Occluded Surfaces},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

Researchers in computer vision have primarily studied the problem of visual reconstruction of environmental structure that is plainly visible. In this thesis, the conventional goals of visual reconstruction are generalized to include both visible and occluded forward facing surfaces. This larger fraction of the environment is termed the anterior surfaces. Because multiple anterior surface neighborhoods project onto a single image neighborhood wherever surfaces overlap, surface neighborhoods and image neighborhoods are not guaranteed to be in one-to-one correspondence, as conventional "shape-from" methods assume. The result is that the topology of threedimensional scene structure can no longer be taken for granted, but must be inferred from evidence...

### Citations

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Pattern classification and scene analysis
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- 1973
(Show Context)
Citation Context ... special significance when straight-sided surfaces are allowed. For these reasons, 2 it proved useful to divide the set of completions into three categories and employ a multicategory Bayes classifier=-=[10]-=- to select among them (see Figure 4.5). The category minimizing squared Mahalanobis distance[10] (i.e. covari2 Together with the need to distinguish corners from other completions, as required by obje... |

1406 |
Robot vision
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(Show Context)
Citation Context ...(in the case of stereo), and the second term is a regularization term, which introduces a bias for smooth solutions. For example, one of the simplest functionals of this sort is for shape-from shading=-=[23]-=-: Z Z I [(E(x; y) \Gamma R(p; q)) 2 + (p 2 x + p 2 y + q 2 x + q 2 y )] dx dy (1:1) where E is the image brightness function, R is the reflectance map in gradient space and p x ; p y ; q x and q y are... |

1276 |
K.: Combinatorial Optimization: Algorithms and Complexity
- Papadimitriou, Steiglitz
- 1998
(Show Context)
Citation Context ...ted by writing a fixed set of integer linear inequalities, as described in the last chapter, for each of the vertices and edges of G planar . The ILP is solved by the method of branch and bound search=-=[40, 51]-=-. In branch and bound search, all integer points within the feasible region are enumerated (either explicitly or implicitly), and the optimal feasible solution is selected. This process is greatly fac... |

735 | Visual Reconstruction
- Blake, Zisserman
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(Show Context)
Citation Context ... surface orientation and depth. Marr[38] proposed that one-dimensional discontinuities in surface orientation and depth are explicitly represented in the 2 1 2 -D sketch. Recently, Blake and Zisserman=-=[5]-=- have developed a method by which these discontinuities can be identified during reconstruction, so that smoothness assumptions have appropriate scope. But this addition does not change the fundamenta... |

469 |
The interpretation of visual motion
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(Show Context)
Citation Context ...neously maximizes likelihood and minimizes surprise. Consequently, variable weights range from negative infinity to positive infinity. In comparison, the log-likelihood weighting function which Ullman=-=[58]-=- proposed for the correspondence problem in apparent motion uses exclusively negative weights (i.e. log-likelihoods). While maximizing a linear objective function with exclusively negative weights wou... |

447 |
Perceptual Organization and Visual Recognition
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(Show Context)
Citation Context ...n understood to mean correspondence between components of a stored geometric model and contours in an image, together with knowledge of the object's pose, or spatial orientation relative to the camera=-=[47, 37]-=-. Of course, the fundamental difficulty in establishing such a correspondence is the combinatorially prohibitive number of possible 19 A B C D E F G A(1) B(1) C(2) C(1) D(1) E(1) F(1) E(2) E(3) F(2) B... |

349 |
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(Show Context)
Citation Context ...nd curvature field consistent with local orientation and curvature measurements produced by operators analogous to simple cells in the visual cortex. Their network solves a relaxation labeling problem=-=[27, 50]-=-. A relaxation labeling problem requires that one element of a set of labels be assigned to each element of a set of objects. The probability that object i has labelsis denoted by p i (). The compatib... |

252 |
On the Foundations of Relaxation Labeling Processes
- Hummel, Zucker
- 1983
(Show Context)
Citation Context ...nd curvature field consistent with local orientation and curvature measurements produced by operators analogous to simple cells in the visual cortex. Their network solves a relaxation labeling problem=-=[27, 50]-=-. A relaxation labeling problem requires that one element of a set of labels be assigned to each element of a set of objects. The probability that object i has labelsis denoted by p i (). The compatib... |

220 |
The Logic of Perception
- Rock
- 1983
(Show Context)
Citation Context ...tail in the previous chapter, we consider the second source of constraints, which will be termed the stimulus conformity requirement. The importance of this requirement has been stressed by Irvin Rock=-=[48], who observed that -=-"the [perceptual] solution must not contradict the stimulus" and "must contain everything implied by the stimulus." Regarding illusory contour displays, Rock hypothesized that the ... |

178 | Inferring global perceptual contours from local features
- Guy, Medioni
- 1996
(Show Context)
Citation Context ... Hough transform[24], where the components of the percept vector represent individual straight lines parameterized by their orientation and distance from the origin. In a recent paper, Guy and Medioni=-=[16]-=- describe an abstract transform for computing a tangent field representing global image structure from local tangent measurements. Like the Hough transform, the key to their approach is the local summ... |

155 |
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- Huffman
- 1971
(Show Context)
Citation Context ...he representation computed by the figural completion process is more general than (and probably subsumes) the labeled knot-diagrams developed here. Towards this end, it is worth re-examining Huffman's=-=[26] influenti-=-al paper "Impossible Objects as Nonsense Sentences." While this paper is widely cited as one source of the Huffman-Clowes junction catalog for trihedral scenes, the last few pages are actual... |

149 |
Gestalt Psychology
- Köhler
- 1929
(Show Context)
Citation Context ... statement is actually somewhat of a misrepresentation. Gestalt philosophy, in small part, was an early 20th century attempt to describe a set of phenomena in human vision using metaphors from physics=-=[34, 35]. For exam-=-ple, the Gestalt "field" is the medium through which visual stimuli exhert influence on one another in the process of perceptual organization. This is analogous to the electromagnetic field,... |

83 |
Filling-in the gaps: the shape of subjective contours and a model for their generation
- Ullman
- 1976
(Show Context)
Citation Context ...ugh no comprehensive theory exists, computational models have been proposed for the shape of illusory contours joining boundary fragments with orientation difference significantly less than 2 . Ullman=-=[57]-=- originally hypothesized that the curve used by the human visual system to join two contour fragments is constructed from two circular arcs. Each circular arc is tangent to its sponsoring contour at o... |

81 |
A Combinatorial Introduction to Topology
- Henle
- 1979
(Show Context)
Citation Context ...odel of a surface consisting of a set of paper panels taped together in prescribed ways. Panelings will be described in greater detail in the next chapter. More formal treatments of the subject (e.g. =-=[18]-=-) employ triangulations, which are panelings satisfying other criteria (e.g. all panels must be three-sided). 18 m+1 m n n n m 0 m m n+1 n m n 0 Figure 1.6: A boundary labeling scheme. The image of th... |

72 | The curve of least energy
- Horn
- 1983
(Show Context)
Citation Context ...from the family of possible curves of this form, the pair of circular arcs which minimizes total bending energy (i.e. E = R (s) 2 ds, wheresis curvature) models the shape of the illusory contour. Horn=-=[22]-=- subsequently proposed that the shape of the contour joining two boundary fragments is described by the true curve of least energy, to which Ullman's curve is a two arc approximation. More recently, K... |

61 |
The Perception of the Visual
- Gibson
- 1950
(Show Context)
Citation Context ...ides and solid interiors. The existence of a visual world, distinct from the "real world," but "going beyond " that which is plainly visible is familiar to philosophers of human pe=-=rception. See Gibson[13]-=- or Kanizsa[29] for especially lucid accounts. The field of computer vision, in contrast, has for all practical purposes ignored the problem of visual reconstruction of environmental structure that is... |

52 |
The 2.1-D sketch
- Nitzburg, Mumford
- 1990
(Show Context)
Citation Context ...nctional models the shape of an illusory contour with the same end conditions and demonstrate this agreement on a number of figures which elicit illusory contours in human vision. Nitzberg and Mumford=-=[39] point out-=- that the problem of computing the shape of the curve of least energy was first studied by Euler, and have used "elastica" to represent potential completions in a combinatorial optimization ... |

37 |
Obtaining Shape from Shading Information,” The Psychology of Computer Vision
- Horn
- 1975
(Show Context)
Citation Context ... q 2 [p; q; \Gamma1] T The methods proposed for computing the 2 1 2 -D sketch are generally referred to as "shape-from" methods. The inspiration for these methods is the influential early wo=-=rk of Horn[21]-=- on shape-from shading. Surface orientation can be computed directly from image brightness when the direction of illumination is known and surface reflectance is predominantly diffuse. Where these ass... |

36 |
S.: Comparison of three curve intersection algorithms
- SEDERBERG, PARRY
- 1986
(Show Context)
Citation Context ...ssings exploits two properties of the Bezier representation. First, a Bezier 7 For descriptions and comparisons of different methods for finding points where two Bezier curves intersect, see Sederberg=-=[55]-=-. 117 Figure 4.8: Before overlap pruning. A magnified view of a portion of G non\Gammaplanar (k = 3) for the Ehrenstein test figure is shown prior to overlap pruning. Boundary fragments are drawn thic... |

33 |
Method and Means for Recognizing
- Hough
- 1962
(Show Context)
Citation Context ...severe, their application is limited in practice to mappings between low dimensional parameter spaces. A typical example is a network which detects straight lines by computing a global Hough transform=-=[24]-=-, where the components of the percept vector represent individual straight lines parameterized by their orientation and distance from the origin. In a recent paper, Guy and Medioni[16] describe an abs... |

31 |
Model Dependent Inference of 3D Information from a Sequence of 2D Images
- Kumar
- 1992
(Show Context)
Citation Context ...y the many members of the computer vision group at the University of Massachusetts who have applied 111 it to a large number of problems requiring stable descriptions and accurate spatial localization=-=[7, 36, 53]-=-. 4 Boldt's algorithm begins by creating an initial set of unit length line segments with orientation normal to the direction of maximum gradient along zero crossing contours of the Laplacian convolve... |

23 |
Principles of Gestalt
- Koffka
- 1935
(Show Context)
Citation Context ... statement is actually somewhat of a misrepresentation. Gestalt philosophy, in small part, was an early 20th century attempt to describe a set of phenomena in human vision using metaphors from physics=-=[34, 35]. For exam-=-ple, the Gestalt "field" is the medium through which visual stimuli exhert influence on one another in the process of perceptual organization. This is analogous to the electromagnetic field,... |

21 |
Computing curvilinear structure by token-based grouping
- Dolan, Riseman
- 1992
(Show Context)
Citation Context ...ional complexity. In general, if there are n boundary fragments with 2n endpoints, there will be O(n 2 ) potential completions and O(n 4 ) crossing vertices in 4 In his forthcoming dissertation, Dolan=-=[9]-=- studies the problem of generalizing Boldt's algorithm to compute image curves other than straight lines. 112 Figure 4.6: G input for the four test figures. The line segments are produced by Boldt's a... |

20 |
Natural computation
- Richards
- 1988
(Show Context)
Citation Context ... effect of clutter by producing exactly the conditions required for illusory contours. 1.3 Thesis Overview This thesis approximately follows the "natural computation" methodology advocated b=-=y Richards[45]-=- (see Table 1.1). This methodology is based upon Marr's[38] belief that complex information processing systems can only be understood by analyzing them at the three levels of 1) computational theory; ... |

12 |
The Use of Grouping in Visual Object Recognition
- Jacobs
- 1988
(Show Context)
Citation Context ...rse, the combinatorial problem is often aggravated by extraneous contours originating in background clutter and contours which are absent because of occlusion. It is the opinion of Lowe[37] and Jacobs=-=[28]-=- that the necessary computational savings can only be achieved if grouping processes are used to collect together subsets of contours likely to belong to the same object prior to matching. Kanizsa's c... |

12 |
Nuove ricerche sperimentali sulla totalizzazione percettiva
- Petter
- 1956
(Show Context)
Citation Context ...e between pairs of contours exhibiting bilateral symmetry, although this tendency is weaker than the others. Another very interesting phenomenon, important in preference, is known as the Petter effect=-=[43]-=-. The Petter effect occurs when two surfaces of equal reflectance overlap. Because the reflectances of the two surfaces are the same, their relative depth can not be determined from figural informatio... |

11 |
Perceptual organization of occluding contours
- Williams
- 1990
(Show Context)
Citation Context ...e observations were incorporated into a set of necessary constraints on the appearance of edges in these simple scenes. 8 These constraints formed the basis of the integer linear program described in =-=[59]-=-. The requirement that the depth of the occluding surface be less than or equal to the depth of the occluded surface was among the constraints that were readily apparent. However, because this particu... |

9 |
Identifying Salient Circular Arcs on Curves
- Saund
- 1993
(Show Context)
Citation Context ... to the full Huffman labeling scheme, leading to a computational theory sufficient to explain the full range of perceptual completion phenomena at work in human vision. 1 See the recent paper by Saund=-=[52]-=- for a review of the literature on this topic. A P P E N D I X GLOSSARY This appendix is a glossary of general and specific terms used in Chapter 2. General Terms ffl boundary The set of points of a s... |

8 |
Perceptual rivalry between illusory and real contours
- Fahle, Palm
- 1991
(Show Context)
Citation Context ... recent evidence seems to suggest that the human visual system has not heard of this theory. Consider the stimulus depicted in Figure 5.2(a) which is a variation of a figure designed by Fahle and Palm=-=[12]-=-. Although only one illusory rectangle is physically 136 (a) (b) (c) (a) (b) (c) Figure 5.2: Prediction of surface organization model. (a) A variation of a figure designed by Fahle and Palm[12]. Altho... |

8 |
On the Role of Structure
- Witkin, Tenenbaum
- 1983
(Show Context)
Citation Context ... regards to be the purpose of perceptual organization: Grouping of image measurements of one kind or another into collections likely to belong to individual objects. Ten years ago Witkin and Tenenbaum=-=[60] wrote what many con-=-sider to be a kind of "P.O." manifesto. In "On the Role of Structure in Vision" they argued that the purpose of perceptual organization is to provide an explicit representation of ... |

6 |
Receptive Fields, Binocular Interaction and
- Hubel, Wiesel
- 1962
(Show Context)
Citation Context ...oes play a role in the organization of outline stimuli, but seems to governed by different logic depending on whether contrast or outline stimuli are involved. It has been known since Hubel and Wiesel=-=[25]-=- that simple cells in the human visual cortex have oriented receptive fields of either odd or even symmetry. Hubel and Wiesel conjectured that these neurons are feature detectors which respond to edge... |

6 |
An object perception approach to static and kinetic subjective contours
- Kellman, Loukides
- 1987
(Show Context)
Citation Context ...ions can determine topological aspects of the organization (i.e. unit and depth), topological aspects do not determine completion shape. A still more radical notion is advanced by Kellman and Loukides=-=[32], who theorize that -=-"unit formation" occurs prior to and independently of "depth placement." This possibility will be considered in detail in Chapter 5. 3.3.1 Curves of Least Energy Even if we assume ... |

5 |
ªThe Role of Illusory Contours in Visual Segmentation,º The Perception of Illusory Contours
- Grossberg, Mingolla
- 1987
(Show Context)
Citation Context ...) of different orientations. More recently, it has been hypothesized that figural completion phenomena are the result of integrating simple cell responses over extended spatial areas (see for example =-=[15]-=-). A possible explanation for the qualitatively different completion effects in contrast and outline stimuli is that the output of cortical simple cells with odd and even receptive fields are integrat... |

5 |
From features to perceptual categories
- Richards, Feldman, et al.
- 1992
(Show Context)
Citation Context ...ealistic given the complexity of the real world. They are only prepared to say that these densities achieve their maximum at zero 3 This idea has been further developed by Richards, Feldman and Jepson=-=[46] who propo-=-se that perceptually significant categories correspond to the "non-tranverse modes" of feature probability densities. We will have more to say about this in the next chapter, where the featu... |

5 |
Spatial and Temporal Grouping in the Interpretation of Image Motion
- Sawhney
- 1992
(Show Context)
Citation Context ...y the many members of the computer vision group at the University of Massachusetts who have applied 111 it to a large number of problems requiring stable descriptions and accurate spatial localization=-=[7, 36, 53]-=-. 4 Boldt's algorithm begins by creating an initial set of unit length line segments with orientation normal to the direction of maximum gradient along zero crossing contours of the Laplacian convolve... |

4 |
Token based extraction of straight lines
- Boldt, Weiss, et al.
- 1989
(Show Context)
Citation Context ...oes in fact exist. 1 To simplify implementation of the experimental system, "off-the-shelf" components were used wherever possible. For example, the straight-line grouping algorithm develope=-=d by Boldt[6]-=- was used to generate the input set of boundary fragments. Consequently, the experimental system was tested with straight-sided figures. This limitation is not as significant as it may seem, since it ... |

4 |
Matching 2D Images to Multiple 3D Objects Using View Description Networks
- Burns
- 1992
(Show Context)
Citation Context ...y the many members of the computer vision group at the University of Massachusetts who have applied 111 it to a large number of problems requiring stable descriptions and accurate spatial localization=-=[7, 36, 53]-=-. 4 Boldt's algorithm begins by creating an initial set of unit length line segments with orientation normal to the direction of maximum gradient along zero crossing contours of the Laplacian convolve... |

4 |
Singularities and plane maps
- Callahan
- 1974
(Show Context)
Citation Context ...f the smooth manifold-solid. 58 r'(t) n(t) |r'(t) n(t)| r'(t) n(t) (a) (b) Figure 2.14: Anterior scene constructed from smooth manifold-solid. (a) A smooth manifold-solid and its image (after Callahan=-=[8]). The ima-=-ge of the contour generator contains two cusps which form a "swallowtail." (b) Anterior scene A 0 is formed by slicing the manifold-solid along the contour generator, discarding the backward... |

3 |
Recovering Instrinsic Scene Characteristics from Images, Computer Vision Systems
- Barrow, Tenenbaum
- 1978
(Show Context)
Citation Context ...ce orientation, reflectance and illumination of 6 a visible surface point in the environment. In theory, a solution of the image irradiance equation would consist of a set of what Barrow and Tenenbaum=-=[3]-=- call intrinsic images, each of which represents one of the physical parameters underlying image brightness. The intrinsic images representing depth and surface orientation together form what Marr[38]... |

3 |
The Integration of Figure Fragments into Representations of Planar Shape
- Elder, Zucker
- 1993
(Show Context)
Citation Context ...sities for each category are: C corner = 2 6 6 6 6 6 6 4 1:0 \Theta 10 9 0 0 0 0 0 5:0 0 0 0 0 0 0:05 0 0 0 0 0 1:0 \Theta 10 9 0 0 0 0 0 1:0 \Theta 10 \Gamma9 3 7 7 7 7 7 7 5 (4.7) 3 Elder and Zucker=-=[11]-=- investigate the relationship between number and size of boundary gaps and the degree of perceptual closure. They measure latency time in a visual search task where the target and distractor elements ... |

3 |
Snakes: Active Minimum Energy Seeking Contours
- Kass, Witkin, et al.
- 1987
(Show Context)
Citation Context ... the shape of the contour joining two boundary fragments is described by the true curve of least energy, to which Ullman's curve is a two arc approximation. More recently, Kass, Witkin and Terzopolous=-=[30] have demonstrated t-=-he utility of active minimum energy seeking contours called "snakes" in a variety of computer 71 vision applications. The "internal" energy in the snake active contour model is def... |

3 | A Problem Solving Approach to Illusory Contours, The Perception of Illusory Contours - Rock - 1987 |

2 |
Geometry and the imagination (translation from German original
- Hilbert, Cohn-Vossen
- 1952
(Show Context)
Citation Context ...Moebius strip. 30 a a b b a a b b a a b b b b a a Figure 2.2: The torus. The torus is constructed by identifying the opposite edges of a rectangular panel as illustrated (after Hilbert and Cohn-Vossen=-=[19]-=-). 31 non-orientable surface which does not contain an occluding contour. 1 Non-orientable surfaces cannot be immersed in the plane. For this reason, we adopt the convention (simplifying later argumen... |

2 |
The Shape of Smooth Objects and the Way Contours
- Koenderink
- 1988
(Show Context)
Citation Context ... by luminance change in the image. However, where bound7 Local homeomorphism is violated only at points where the direction of the contour generator coincides with the viewing direction (i.e. at cusps=-=[33]-=-). 16 p p' (a) p q p' (b) Figure 1.5: The difference between embedding and immersion. (a) An embedding is a global homeomorphism between visible surface neighborhoods and image neighborhoods first inc... |

2 |
Co-Circularity and the Role of Curvature in Curve Detection
- Parent, Zucker
- 1985
(Show Context)
Citation Context ...on is used as an estimate of the dominant direction. 2 The second type consists of processing elements with local spatial support coupled in a locally connected network. For example, Parent and Zucker=-=[41]-=- describe a network method for computing a discrete tangent and curvature field consistent with local orientation and curvature measurements produced by operators analogous to simple cells in the visu... |

2 |
Algebra and its Applications, Harcourt Brace
- Strang, Linear
- 1988
(Show Context)
Citation Context ...tions has a solution if and only if the sums of the weights of every cycle in its corresponding network equal zero (where the weight of an edge is 1 or \Gamma1 depending on the direction of traversal)=-=[56]-=-. We demonstrate not only that a solution to this system of difference constraints always exists but also that a solution exists where the value of fl for every planar region is greater than the large... |

1 |
An Extension of a Theorem
- Heller, Tompkins
- 1956
(Show Context)
Citation Context ...ng problem with a totally unimodular constraint matrix. The basic feasible solutions all lie on the integer lattice. 155 singular submatrix is \Sigma1. The following theorem, due to Heller and Tomkins=-=[17]-=- establishes a sufficient condition for total unimodularity. Theorem 5.1 (Heller and Tompkins) An integer matrix A with a ij = 0; \Sigma1 is TUM if no more than two nonzero entries appear in any colum... |

1 |
Contributions to the Analysis of Visual Perception--First Paper
- Schumann
- 1987
(Show Context)
Citation Context ..., which is ambiguity in identifying which contour fragments match which to form boundaries. The word "unit" is used here in the manner it is used by the Gestalt psychologists (see for exampl=-=e Schumann[54]-=-), and in this thesis refers to the boundary components which are the products of the grouping process. Unit ambiguity is illustrated in Figure 3.3. Rock[48] calls the interpretation in Figure 3.3(b) ... |