## Recovery of 3-D Structure From Motion Is Neither Euclidean Nor Affine

Citations: | 10 - 2 self |

### BibTeX

@MISC{Pcrcepiion_recoveryof,

author = {Human Pcrcepiion and Fulvio Domini and Myron L. Braunstein},

title = {Recovery of 3-D Structure From Motion Is Neither Euclidean Nor Affine},

year = {}

}

### OpenURL

### Abstract

The relationship between simulated and judged depth separations for pairs of probe dots on planar surface patches was examined in a series of 6 experiments. The simulated slant of the patches was varied without varying the simulated depth separation of the probe dots by varying the depth gradient orthogonal to the direction determined by the probe dots on the image plane. Judged depth separation varied with mean slant for constant simulated depth separations. When observers judged depth separations along a closed path, the integral of the signed depths did not sum to zero, as would be required in Euclidean geometry. These results are inconsistent with the view that the mapping between simulated and perceived 3-D structure is alfme and indicate that, in general, the perceived structure cannot be represented in either a Euclidean space or an affine space. Moreover, these results are consistent with a first-order temporal analysis of the optic flow. A pattern of moving two-dimensional (2-D) features on a flat screen can give rise to a compelling impression of three-dimensionality. This phenomenon has been called the kinetic depth effect (Wallach & O'Connell, 1953) or structure

### Citations

518 |
The Interpretation of Visual Motion
- Ullman
- 1979
(Show Context)
Citation Context .... Such models can be characterized by two important features: the representational space and the mapping between the 3-D object and this space. The representational space of the Euclidean algorithms (=-=Ullman, 1979-=-) is the 3-D Euclidean space, and the mapping associates the projected 3-D features to elements of the perceived object by preserving the same Euclidean structure of the projected object. Because the ... |

310 | A±ne Structure from Motion - Koenderink, Doorn - 1991 |

161 |
The kinetic depth effect
- Wallach, O’Connell
- 1953
(Show Context)
Citation Context ...c flow. A pattern of moving two-dimensional (2-D) features on a flat screen can give rise to a compelling impression of three-dimensionality. This phenomenon has been called the kinetic depth effect (=-=Wallach & O'Connell, 1953-=-) or structure from motion (Uliman, 1979). Numerous attempts have been made to understand the underlying perceptual process and to answer the question of how the three-dimensional (3-D) properties of ... |

136 |
Facts on optic flow
- Koenderink, Doorn
- 1987
(Show Context)
Citation Context ...ressed as a tangent) of the planar patch (or) and its component of angular velocity (to) parallel to the image plane. This quantity is the deformation (def, see also Domini, Caudek, & Proffitt, 1997; =-=Koenderink, 1986-=-; Koenderink & van Doom, 1976, 1986): def = ~/def 2 + def 2 = tan orto. (1) From the first-order optic flow (i.e., from two views), it is possible to derive, up to a reflection, the tilt of the surfac... |

61 | Local Structure of Movement Parallax of the Plane - Koenderink, Doom - 1976 |

60 |
Visual perception of smoothly curved surfaces from double-projected contour patterns
- Todd, Reichel
- 1990
(Show Context)
Citation Context ...ding views does not substantially influence observers' performance in judgments about the structure (Liter, Braunstein, & Hoffman, 1993; Todd, Akerstrom, Reichel, & Hayes, 1988; Todd & Bressan, 1990; =-=Todd & Norman, 1991-=-). l Two orthographic views of a rigid object are compatible with a one-parameter family of 3-D rigid interpretations (Bennett, Hoffman, Nicola, & Prakash, 1989; Koenderink & van Doom, 1991; Todd & Br... |

42 |
The perception of 3-dimensional affine structure from minimal apparent motion sequences
- Todd, Bressan
- 1990
(Show Context)
Citation Context ... object has been questioned by a number of investigators. Empirical findings show that Euclidean quanrifles such as slant (Braunstein, Liter, & Tittle, 1993; Domini, Caudek, & Gerbino, 1995), angles (=-=Todd & Bressan, 1990-=-), and depth (Caudek & Proffitt, 1993) are misperceived by human observers. These findings are inconsistent with mathematical models that recover the 3-D Euclidean structure from moving images. Furthe... |

41 | Surface perception in pictures - Koenderink, Doorn, et al. - 1992 |

29 |
Systematic distortion of perceived three-dimensional structure from motion and binocular stereopsis
- Tittle, Todd, et al.
- 1995
(Show Context)
Citation Context ...pace. For example, it is possible to discriminate between parallel and nonparallel lines, compare segment lengths along parallel directions, and judge the coplanarity of points (Todd & Bressan, 1990; =-=Tittle, Todd, Perotti, & Norman, 1995-=-), but it is impossible to discriminate between 3-D structures that are related by linear stretching along the line of sight (Todd & Norman, 1991) and to make accurate metric judgments of. such quanti... |

25 | Differential techniques for optical flow - Verri, Girosi, et al. - 1990 |

24 |
Inferring local surface orientation from motion fields, 1
- Hoffman
- 1982
(Show Context)
Citation Context ...) From the first-order optic flow (i.e., from two views), it is possible to derive, up to a reflection, the tilt of the surface and the component of angular velocity perpendicular to the image plane (=-=Hoffman, 1982-=-). However, the slant of the surface (or) and the component of angular velocity (to) parallel to the image plane are undetermined. As can be seen in Equation 1, there are infinite pairs of or and to t... |

23 |
The visual perception of threedimensional length
- Norman, Todd, et al.
- 1996
(Show Context)
Citation Context ...view). Moreover, experiments have been presented assessing internal consistency of the metric judgments in shape from shading (Koenderik, van Doom, & Kappers, 1992) and full cues environmerits (F. N. =-=Norman, Todd, Perotti, & Tittle, 1996-=-). This issue has been addressed only recently for structure-from-motion (SFM) displays by Werkhoven and van Veen (1995), who found that observers are inaccurate in making depth relief judgments.3-D ... |

21 | Depth and shape from differential perspective in the presence of bending deformations - Koenderink, Doorn - 1986 |

19 | The perceptual buildup of three-dimensional structure from motion - Hildreth, Grzywacz, et al. - 1990 |

19 | Distortions of three-dimensional space in the perceptual analysis of motion and stereo - Todd, Tittle, et al. - 1995 |

18 |
Minimum points and views for the recovery of three-dimensional strucutre
- Braunstein, Hoffman, et al.
- 1987
(Show Context)
Citation Context ...nts that are sufficient for an ideal observer to recover the 3-D Euclidean structure of an object from 2-D moving images and to investigate the psychological validity of the theoretical findings (see =-=Braunstein, Hoffman, Shapiro, Andersen, & Bennett, 1987-=-, for a discussion). Recently, the view that the structure derived by the perceptual system has the same Euclidean properties as the Fulvio Domini, Cognitive Technology Laboratory (a collaboration bet... |

15 |
Inferring structure from motion in two-view and multiview displays
- Liter, Braunstein, et al.
- 1993
(Show Context)
Citation Context ...views of a moving object are sufficient for human observers to perceive a 3-D structure and that adding views does not substantially influence observers' performance in judgments about the structure (=-=Liter, Braunstein, & Hoffman, 1993-=-; Todd, Akerstrom, Reichel, & Hayes, 1988; Todd & Bressan, 1990; Todd & Norman, 1991). l Two orthographic views of a rigid object are compatible with a one-parameter family of 3-D rigid interpretation... |

12 | Misperceptions of angular velocities influence the perception of rigidity in the kinetic depth effect - Domini, Caudek, et al. - 1997 |

12 |
Apparent rotation in three-dimensional space: Effects of temporal, spatial, and structural factors
- Todd, Akerstrom, et al.
- 1988
(Show Context)
Citation Context ...ent for human observers to perceive a 3-D structure and that adding views does not substantially influence observers' performance in judgments about the structure (Liter, Braunstein, & Hoffman, 1993; =-=Todd, Akerstrom, Reichel, & Hayes, 1988-=-; Todd & Bressan, 1990; Todd & Norman, 1991). l Two orthographic views of a rigid object are compatible with a one-parameter family of 3-D rigid interpretations (Bennett, Hoffman, Nicola, & Prakash, 1... |

11 | Depth perception in motion parallax and stereokinesis
- Caudek, Proffitt
- 1993
(Show Context)
Citation Context ...umber of investigators. Empirical findings show that Euclidean quanrifles such as slant (Braunstein, Liter, & Tittle, 1993; Domini, Caudek, & Gerbino, 1995), angles (Todd & Bressan, 1990), and depth (=-=Caudek & Proffitt, 1993-=-) are misperceived by human observers. These findings are inconsistent with mathematical models that recover the 3-D Euclidean structure from moving images. Furthermore, evidence has been provided tha... |

11 |
Surface interpolation in three-dimensional structure from motion perception
- Husain, Treue, et al.
- 1989
(Show Context)
Citation Context ... Adding views may influence performance if the mount of rotation (degrees of angular rotation) displayed increases with an increase in the number of views (Hfldreth, Grzywacz, Adelson, & Inada, 1990; =-=Husain, Treue, & Andersen, 1989-=-). 12731274 oo1~a AND SRAUNSTF.IN make very precise predictions about the relationships between the 3-D properties of the perceived object and the moving projections. Such models can be characterized... |

7 |
The relationship of vertical and horizontal velocity gradients in the perception of shape, rotation, and rigidity
- Liter, Braunstein
- 1998
(Show Context)
Citation Context ...ing judged depth separation to def are consistent with results from a recent study showing a relationship between judged shape of a dihedral angle and the velocity gradients in orthogonal directions (=-=Liter & Braunstein, 1998-=-). The simulated objects in that study were dihedral angles consisting of two planes slanted about a horizontal axis and meeting at a horizontal edge. Different combinations of motion and projection w... |

3 |
Perception of surface attitude
- Domini, Caudek, et al.
- 1995
(Show Context)
Citation Context ... surface on the perceived depth separation of two dots that are located on the surface is predicted by a model that derives the slant from a first-order temporal property of the optic flow called def(=-=Domini et al., 1995-=-, 1997). Defis a function of angular velocity and simulated slant. In the present article we investigated the nature of the function relating perceived slant to simulated slant, for a constant value o... |

3 |
The visual perception of 3-D dimensional form
- Norman, Todd
- 1992
(Show Context)
Citation Context ...tulating a particular higher order geometry or set of geometries for either the mapping or the representation is necessary for an understanding of the recovery of 3-D structure from motion. (See J. E =-=Norman & Todd, 1992-=-, for a discussion of Klein's, 1893, hierarchy of geometries.) This does not imply, however, that perceived structure is not predictable from image motion. On the contrary, the present results, togeth... |

2 | Recovering 3-D shape from perspective translations and orthographic rotations - Braunstein, Liter, et al. - 1994 |

2 |
V ision
- Marr
- 1982
(Show Context)
Citation Context ...ensional (3-D) properties of the perceived object are related to characteristics of the moving pattern. Much of the research on this topic has been influenced by the computational approach to vision (=-=Marr, 1982-=-) and has sought algorithms that could recover the real structure of the distal objects from moving patterns. Indeed, the main issue has been to find the minimal conditions and constraints that are su... |

1 | Decoding principles, heuristics and inference in visual perception - Brannstein - 1994 |

1 |
A critical review of Luneburg's model with 3-D STRUCTURE FROM MOTION 1291 (Appendixes follow) regard to global structure of visual space
- Indow
- 1991
(Show Context)
Citation Context ...reasing function of defand that the tilt "r' is correctly derived: or' = f(def) (2) "r' = ~. (3) 2 An extensive literature exists on the intrinsic geometry of the perceptual space for stereopsis (see =-=Indow, 1991-=-, for a review). Moreover, experiments have been presented assessing internal consistency of the metric judgments in shape from shading (Koenderik, van Doom, & Kappers, 1992) and full cues environmeri... |

1 | Vergleichende Betrachtungen ueber neuere geometrische Forschungen ("Erlanger Programm") [Comparative observations on recent research in geometry ("Erlanger program - Klein - 1893 |