Inferring the relative three-dimensional positions of two moving points

Hoffman, Donald D.; Bennett, Bruce M.

doi:10.1364/josaa.2.000350

Cited by 36 publications

(34 citation statements)

References 2 publications

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“…(4) Are two views sufficient for accurate detections of surface curvature, as suggested by Droulez and Comilleau-Peres (1990), Koenderink and van Doom (1991), and Todd and Bressan (1990)? Most alternative computational models (e.g., Hoffman & Bennett, 1985, 1986Ullman, 1979) need three "distinct" views to recover the 3-D structure of a moving object.…”

Section: •mentioning

confidence: 99%

The detection of surface curvatures defined by optical motion

Norman

Lappin

1992

Perception & Psychophysics

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The detectability of surface curvatures defined by optical motion was evaluated in three experiments. Observers accurately detected very small amounts of curvature in a direction perpendicular to the direction of rotation, but they were less sensitive to curvatures along the direction of rotation. Variations in either the number of points (between 91 and 9) or the number of views (from 15 to 2) had little or no effect on discrimination accuracy. The results of this study demonstrate impressive visual sensitivity to surface curvature. Several characteristics of this sensitivity to curvature are inconsistent with many computational models for deriving three-dimensional structure from motion.The results of nearly a century of research have shown that optical motion is a powerful source of information about an object's three-dimensional (3-D) shape. To this day, however, it remains unclear exactly which 2-D image properties are detected and exactly which 3-D structural relations are perceived when observers view structurefrom-motion displays. As recently as 1989, Sperling, Landy, Dosher, and Perkins asked: "Does the observer perceive the correct shape in a display? The correct depths? The correct depth order? The correct curvature?' , (p. 826). Contemporary research, they argued, has failed to resolve such issues.Most current computational models operate on a number of discrete points contained within a set of distinct "views." These models typically assume that appropriate correspondences have been established between the same physical object points across the discrete views. Given this assumption, such models recover depth and/or orientation values for each identifiable feature. When the set of all such pointwise depths has been recovered, a primary computational problem has been solved, but other substantial problems remain. What remains is to parse this collection of depths into separate objects and to interpolate This research was supported in part by National Research Service Award EY-07007-10 to the first author and Nlli Grant EY-05926 to the second author. Many of the analyses accompanying the empirical results contained in this manuscript were aided by Grant 89-00 16 from the Air Force Office of Scientific Research, Grant BNS-8908426 from the National Science Foundation, and grants from the Office of Naval Research, and the Air Force Office of Scientific Research to James Todd. We are grateful to James Todd for his helpful comments on an earlier version of this manuscript. Correspondence should be addressed to J. F. Norman, Department of Psychology, Brandeis University, Waltham, MA 02254-9110. smooth surfaces between connected feature points. Object surfaces and properties such as curvature are thought to be secondarily derived from the more elementary features and their depths.One problematic phenomenon for such models is the finding of directional anisotropies. Rogers and Graham (1983) and Rogers and Cagenello (1989) have documented anisotropies for both stereopsis and motion parallax. Rogers and Grah...

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Section: •mentioning

confidence: 99%

The detection of surface curvatures defined by optical motion

Norman

Lappin

1992

Perception & Psychophysics

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“…Examples of algorithms that derive a 3D configuration from a set of n points (or similar features) displayed in each of m frames are Hoffman and Bennett (1985) and Ullman (1979Ullman ( , 1985, or see Braunstein, Hoffman, Shapiro, Andersen and Bennett (1987) for a more empirical treatment. A list of visual features is identified and located in 2D space on each frame.…”

Section: Feature -~Orre~~onde~~e Modelsmentioning

confidence: 99%

“…It is interesting to contrast this with a manipulation which eliminates the ability to track individual image features (dots) over multiple frames. Models that emphasize the extraction of specific image features and their image plane location (Hoffman & Bennett, 1985;Ullman, 1979Ullman, , 1985 might predict that eliminating feature stability should have an equally large impact on the shape identification. We investigated this hypothesis by comparing feature stability over a full 30 frame image sequence with stimuli in which features (surface dots) were stable for only 3 and 2 frames, after which they were replaced with a different random sample of dots (Fig.…”

Section: Equated Intensity Control (Experiments 2)mentioning

confidence: 99%

Kinetic depth effect and optic flow—I. 3D shape from Fourier motion

1989

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Abstract-Fifty-three different 3D shapes were defined by sequences of 2D views (frames) of dots on a rotating 3D surface. (1) Subjects' accuracy of shape identifications dropped from over 90% to less than 10% when either the polarity of the stimulus dots was alternated from light-on-gray to dark-on-gray on successive frames or when neutral gray interframe intervals were interposed. Roth manipulations interfere with motion extraction by spatio-temporal (Fourier) and gradient first-order detectors. Second-order (non-Fourier) detectors that use full-wave rectification are unaffected by alternating-polarity but disrupted by interposed gray frames. (2) To equate the accuracy of two-alternative forced-choice (ZAFC) planar dir~tion-of-motion ~~ri~nation in standard and zloty-alternated stimuli, standard contrast was reduced. 3D shape discrimination survived contrast reduction in standard stimuli whereas it failed completely with polarity-alternation even at full contrast. (3) When individual dots were permitted to remain in the image sequence for only two frames, performance showed little loss compared to standard displays where individual dots had an expected lifetime of 20 frames, showing that 3D shape identification does not require continuity of stimulus tokens. (4) Performance in all discrimination tasks is predicted (up to a monotone transformation) by considering the quality of first-order information (as given by a simple computation on Fourier power) and the number of locations at which motion information is required. Perceptual first-order analysis of optic flow is the primary substrate for st~cture-from-motion computations in random dot displays because only it offers suBicient quality of perceptual motion at a sufficient number of locations.

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“…One way to recover the structure and motion of corresponding points is from discrete views of the points. Using the assumption of rigid, fixed-axis rotation Hoffman and Bennett (1985) showed that it is possible to recover the structure and motion of two points given five discrete views. Thus, when five views of two corresponding points exist, both the axis of rotation and the angular velocity can be obtained from the profile sequence.…”

Section: Recovering the Global Properties Of Motionmentioning

confidence: 99%

“…Much current research has concentrated on the recovery of shape under the assumption that the shape-recovery algorithm is provided with the motion of identifiable points (the correspondence problem is solved). Some of these theories state the minimal conditions which are necessary to recover a unique structure from general 3-D rigid motion (Huang and Lee, 1989;Longuet-Higgins & Prazdny, 1980;Ullman, 1979) or more constrained motion (Hoffman & Bennett, 1985Hoffman & Flinchbaugh, 1982;Longuet-Higgins, 1982;Webb & Aggarwal, 1981). Other theories describe how the instantaneous 2-D motion limits, but does not uniquely specify, the possible 3-D interpretations (Koenderink & van Doorn 1975, Todd & Bressan, 1990Ullman, 1983) or similarly how 2 discrete views limit the possible interpretations of 3-D shape (Bennett, Hoffman, Nicola & Prakash, 1989;Huang & Lee, 1989, Koenderink & van direction just grazes an object's surface (see Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Human Recovery of Shape from Profiles

Pollick¹,

Giblin

Rycroft

et al. 1992

Behaviormetrika

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A single profile of a solid object contains much information about the shape of the object. Viewing the changing profiles of a moving object provides even greater information about the shape of the object. Few computational models of this process have been applied to the human ability to recover the shape and motion of solid objects from their changing profiles. We propose a theory that relates measurable quantities of changing two-dimensional (2-D) profiles to structural properties of three-dimensional (3-D) surfaces in motion. The relevance of this theory to human perception is shown by relating theoretical predictions to existing psycho physical results as well as additional demonstrations of human recovery of shape from profiles.

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Inferring the relative three-dimensional positions of two moving points

Cited by 36 publications

References 2 publications

The detection of surface curvatures defined by optical motion

The detection of surface curvatures defined by optical motion

Kinetic depth effect and optic flow—I. 3D shape from Fourier motion

Human Recovery of Shape from Profiles

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