Structure from two orthographic views of rigid motion

Bennett, Bruce M.; Hoffman, Donald D.; Nicola, J. E.; Prakash, Chetan

doi:10.1364/josaa.6.001052

Cited by 86 publications

(67 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…tain the information to determine whether or not the projections have a rigid interpretation (Bennett, Hoffman, Nicola, & Prakash, 1989;Koenderink & van Doorn, 1991;Ullman, 1977). Ullman (1979) has shown that three parallel projections ofat least four points uniquely define the 3-D structure up to a reflection about the image plane (and a uniform scaling).…”

mentioning

confidence: 99%

Monocular discrimination of rigidly and nonrigidly moving objects

Hogervorst

Kappers

Koenderink

1997

Perception & Psychophysics

View full text Add to dashboard Cite

Wemeasured thresholds for the monocular discrimination of rigidly and nonrigidly moving objects defined by motion parallax. The retinal projections of rigidlymoving objects are subject to certain constraints. By applying smooth 2-Dtransformations to the projections of rigidly moving objects, we created stimuli in which these constraints were affected. Thresholds for (generic) nonrigidtransformations that in theory can be detected from rigid ones by processing pairs of views depended not only on the extent to which the rigidity constraints were affected, but also on the structure and the movement of the simulated object. Nonrigid transformations under which every three successive views had a rigid interpretation were not discriminable from rigid transformations, except in cases where the distortions were very large. Under the rigidity assumption, this would mean that a large class of nonrigidly moving objects is erroneously perceived as rigidly moving.When moving around in the world, we have the impression that the world is stable, rigid, and three-dimensional. This is perhaps remarkable considering the fact that the retinal images change over time. Many experiments show that the visual system is capable of extracting useful information about 3-D structure from these retinal changes. The process involved is usually called structure-frommotion (SfM).Unless assumptions are made about how the world changes over time, motion parallax does not provide us with information about depth. Without such assumptions there is a large class ofpossible interpretations ofthe underlying scene, including an interpretation formed by a set ofmarkers moving in the frontal plane. An assumption frequently used in the literature is the rigidity assumption.

show abstract

mentioning

confidence: 99%

Monocular discrimination of rigidly and nonrigidly moving objects

Hogervorst

Kappers

Koenderink

1997

Perception & Psychophysics

View full text Add to dashboard Cite

show abstract

“…4 noncoplanar points in 3 views suffice to uniquely determine motion and structure, modulo the unrecoverable signs and values of the overall camera-object distances [16,17,34]. Many algorithms have been published for this problem, including linear methods in [16,20], nonlinear algebric methods in [1,17] and a nonlinear numerical method in [27]. A good review can be found in [27].…”

Section: Minimal Data For Euclidean Reconstructionmentioning

confidence: 99%

Some Results on Minimal Euclidean Reconstruction from Four Points

2006

View full text Add to dashboard Cite

Abstract. Methods for reconstruction and camera estimation from miminal data are often used to boot-strap robust (RANSAC and LMS) and optimal (bundle adjustment) structure and motion estimates. Minimal methods are known for projective reconstruction from two or more uncalibrated images, and for "5 point" relative orientation and Euclidean reconstruction from two calibrated parameters, but we know of no efficient minimal method for three or more calibrated cameras except the uniqueness proof by Holt and Netravali. We reformulate the problem of Euclidean reconstruction from minimal data of four points in three or more calibrated images, and develop a random rational simulation method to show some new results on this problem. In addition to an alternative proof of the uniqueness of the solutions in general cases, we further show that unknown coplanar configurations are not singular, but the true solution is a double root. The solution from a known coplanar configuration is also generally unique. Some especially symmetric point-camera configurations lead to multiple solutions, but only symmetry of points or the cameras gives a unique solution.

show abstract

“…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). These points (the critical set) map onto the viewplane to form a profile ; hence for each possible viewing direction there is a critical set and its corresponding profile.…”

Section: Introductionmentioning

confidence: 99%

Human Recovery of Shape from Profiles

Pollick¹,

Giblin

Rycroft

et al. 1992

Behaviormetrika

View full text Add to dashboard Cite

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.

show abstract

Structure from two orthographic views of rigid motion

Cited by 86 publications

References 20 publications

Monocular discrimination of rigidly and nonrigidly moving objects

Monocular discrimination of rigidly and nonrigidly moving objects

Some Results on Minimal Euclidean Reconstruction from Four Points

Human Recovery of Shape from Profiles

Contact Info

Product

Resources

About