## A new approach to qualitative stereo

Citations: | 1 - 0 self |

### BibTeX

@MISC{Hel-Or_anew,

author = {Yacov Hel-Or and Shimon Edelman},

title = {A new approach to qualitative stereo },

year = {}

}

### OpenURL

### Abstract

Nonmetric multidimensional scaling (MDS) allows one to derive aquantitative representation from a set of qualitative data which satisfy certain simple constraints. As a tool for vision, MDS combines the advantages of both qualitative and classical approaches, by relying, on the one hand, on an ordinal-scale input representation, and by supporting, on the other hand, the extraction of metric information. The proposed approach is illustrated on the example of stereopsis, although it is applicable also to the processing of other visual cues, as well as to the integration of several cues within a common computational framework.

### Citations

269 |
Nonmetric multidimensional scaling: a numerical method
- Kruskal
- 1964
(Show Context)
Citation Context ...ic MDS, the cost function penalizes instead deviations from the given rank order of the pairwise distances. In our implementation, the algorithm followed the monotone regression approach described in =-=[7]-=-. We first tested the nonmetric MDS stereo algorithm (NMDS) on artificial data sets generated by hand (see Figure 4). The results of these tests showed that NMDS is a viable approach to qualitative st... |

124 | A computational framework for determining stereo correspondence from a set of linear spatial filters
- Jones, Malik
- 1992
(Show Context)
Citation Context ...ge was represented by a large number (typically, 20; 000) of linear RFs, each of which consisted of several Gabor filters of different orientation (the response of each RF was therefore a vector; cf. =-=[6]). To add -=-biological realism, the RFs were highly overlapping and were placed at random locations chosen independently (for each RF and each "eye") from a uniform distribution. Each left-image RF was ... |

111 |
Discussion of a set of points in terms of their mutual distances
- Young, Householder
- 1938
(Show Context)
Citation Context ...the points can be recovered essentially by an eigenvalue decomposition of the distance matrix, the rank of which, in the absence of errors, must be equal to the dimensionality of the underlying space =-=[18]-=-. In many applications, the exact distances may be unknown, but a set of quantities monotonically related to the true distances may be available. The problem in this case is known as nonmetric MDS. Be... |

89 |
Multidimensional Scaling, Tree-Fitting and Clustering
- Shepard
- 1980
(Show Context)
Citation Context ...--- a family of algorithms that allow the recovery of the geometric structure of a set of points from information related to their pairwise distances (for a concise and readily accessible review, see =-=[13]-=-). If the distances themselves are given, the problem is called metric MDS. In this case, the coordinates of the points can be recovered essentially by an eigenvalue decomposition of the distance matr... |

82 | Maximising Rigidity : the incremental recovery of 3-D structure from rigid and nonrigid motion", in Perception Vol 13
- Ullman
- 1984
(Show Context)
Citation Context ...ing as an additional term in the MDS cost function. Integration of motion information may also be possible (note that Ullman's incremental rigidity algorithm for the recovery of structure from motion =-=[15]-=- minimizes a cost function expressed in terms of inter-point distances). The proposed approach to the recovery of depth from stereo has interesting biological connotations. Psychophysicists in the pas... |

55 |
The JISCT stereo evaluation
- Bolles, Baker, et al.
- 1993
(Show Context)
Citation Context ... used for testing the NMDS algorithm. Left: a fire extinguisher scene (original resolution 384 \Theta 288 pixels). Middle: a ball on a slanting surface (256 \Theta 256; courtesy of the JISCT database =-=[3]-=-). Right: a face (234 \Theta 218 pixels). 2.6 Real stereo pairs: NEC matcher We then tested the NMDS method on a few natural images using two different matching algorithms. 3 The first one is the inte... |

41 |
Researches in binocular vision
- Ogle
- 1964
(Show Context)
Citation Context ...e values are recovered up to a relief transformation. This ambiguity may be removed by combining results from two pairs of images, taken from different viewpoints. disparity values by oblique viewing =-=[10]-=-. Mitchison and Westheimer [8] pointed out that the linear disparity gradient introduced by oblique viewing can be eliminated by basing the computation of depth on differences of disparities instead o... |

34 |
The analysis of stereopsis
- Poggio, Poggio
- 1984
(Show Context)
Citation Context ... assumed to be known. 2 Of these there are two main varieties: cells tuned to zero disparity, and cells with a highly nonlinear sigmoidal response which prefer either crossed or uncrossed disparities =-=[11]-=-. a b d e c f Figure 4: An illustration of the MDS-based stereo algorithm applied to synthetic disparity data. Each of the panels (a through f) shows the real configuration of a triplet of points (on ... |

33 | Stereo without disparity gradient smoothing: A Bayesian sensor fusion solution
- Cox, Hingorani, et al.
- 1992
(Show Context)
Citation Context ...pixels). 2.6 Real stereo pairs: NEC matcher We then tested the NMDS method on a few natural images using two different matching algorithms. 3 The first one is the intensity-based matcher described in =-=[5]-=-. 4 This matcher produces a dense disparity field, in which the value of pixels designated as occluded is set to 0. To facilitate further processing and the display of the results, we have subjected t... |

21 |
Cooperative neural processes involved in stereoscopic acuity
- Westheimer
- 1979
(Show Context)
Citation Context ...s. Psychophysicists in the past have advanced computational arguments in favor of the use of disparity differences instead of raw disparities, based on observations of human performance in stereopsis =-=[17, 8, 12]-=-. The present work indicates that multidimensional scaling (both metric and 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 0 20 40 60 80 0 10 20 30 40 50 60 F... |

17 |
Foundations of multidimensional scaling
- Beals, Krantz, et al.
- 1968
(Show Context)
Citation Context ...pplications, the exact distances may be unknown, but a set of quantities monotonically related to the true distances may be available. The problem in this case is known as nonmetric MDS. Beals et al. =-=[2]-=- have identified a set of simple conditions that must be fulfilled by distance ranks if the points that gave rise to the distances are to be embeddable in a metric space. As we shall see below, both t... |

15 | Qualitative depth from stereo, with applications
- Weinshall
- 1990
(Show Context)
Citation Context ...rtinent to the task are retained. In binocular stereopsis, for example, one may process disparity data to compute qualitative characteristics of the surface such as the sign of its Gaussian curvature =-=[16]-=-, instead of trying to recover surface depth. In the present work, we show that it is possible to derive a quantitative representation from an intermediate set of qualitative data which satisfy certai... |

14 |
Disparity curvature and the perception of three-dimensional surfaces
- Rogers, Cagenello
- 1989
(Show Context)
Citation Context ...s. Psychophysicists in the past have advanced computational arguments in favor of the use of disparity differences instead of raw disparities, based on observations of human performance in stereopsis =-=[17, 8, 12]-=-. The present work indicates that multidimensional scaling (both metric and 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 0 20 40 60 80 0 10 20 30 40 50 60 F... |

10 |
Purposive and qualitative vision
- Aloimonos
- 1990
(Show Context)
Citation Context ...asurements A growing body of work in computer vision and visual perception is aimed at exploiting the advantages of the qualitative approach to the representation and processing of visual information =-=[1]-=-. According to the proponents of qualitative vision, trading precision for robustness can yield stable and noise-free representations without sacrificing utility for real-world tasks. A typical qualit... |

8 |
Integration of stereo. shading and texture
- H, Mallot
- 1990
(Show Context)
Citation Context ... distribution) than at perceiving the metrics of the viewed shapes (this result has been established for the perception of shape from shading [14], although it seems to hold also for binocular stereo =-=[4]-=-). Surprisingly, retaining just the qualitative information (e.g., the ranks of \Deltad ij ) in the data submitted to MDS does not preclude the possibility of recovering the geometry of the configurat... |

7 |
Binocular fixation in the rhesus monkey: Spatial and temporal characteristics
- Motter, Poggio
- 1984
(Show Context)
Citation Context ... 2 seem to be better suited to signal the sign of disparity difference rather than its exact value. ffl Functional considerations. Implementational factors such as imprecise binocular control of gaze =-=[9]-=- may create a bias in favor of the use of disparity ranks. ffl Psychophysical observations. Experimental data on shape perception indicate that human subjects are better at perceiving quantities relat... |

7 | Multidimensional scaling, tree- tting, and clustering - Shepard - 1980 |

6 |
Viewing geometry and gradients of horizontal disparity
- Mitchison, Westheimer
- 1990
(Show Context)
Citation Context ...relief transformation. This ambiguity may be removed by combining results from two pairs of images, taken from different viewpoints. disparity values by oblique viewing [10]. Mitchison and Westheimer =-=[8]-=- pointed out that the linear disparity gradient introduced by oblique viewing can be eliminated by basing the computation of depth on differences of disparities instead of the disparities themselves. ... |

1 |
Perception of ordinal depth relations from patterns of shading
- Todd, Reichel
- 1990
(Show Context)
Citation Context ... points in depth (e.g., a global characterization of their distribution) than at perceiving the metrics of the viewed shapes (this result has been established for the perception of shape from shading =-=[14]-=-, although it seems to hold also for binocular stereo [4]). Surprisingly, retaining just the qualitative information (e.g., the ranks of \Deltad ij ) in the data submitted to MDS does not preclude the... |

1 | Binocular xation in the Rhesus monkey: spatial and temporal characteristics - Motter, Poggio - 1984 |