A Bayesian model of binocular perception of 3D mirror symmetrical polyhedra

Li, Yunfeng; Sawada, Tadamasa; Shi, Yun Q.; Kwon, Tae-Kyu; Pizlo, Zygmunt

doi:10.1167/11.4.11

Cited by 33 publications

(71 citation statements)

References 32 publications

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“…Evidence that bilaterally symmetric 3-D objects share the perceptual salience found for mirror-image symmetry in the frontoparallel plane comes from other studies as well, which suggest that symmetry may be an a priori expectation brought to bear in the course of object recognition [10,11,19,[36][37][38][39][40]. The symmetrical stimuli used here have a reflection about a plane in 3-D space, a property they share with many animals, plants, and man-made objects.…”

Section: Discussionsupporting

confidence: 57%

The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

Farell¹

2015

Symmetry

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Abstract:The visual system is sensitive to symmetries in the frontoparallel plane, and bilateral symmetry about a vertical axis has a particular salience. However, these symmetries represent only a subset of the symmetries realizable in three-dimensional space. The retinal image symmetries formed when viewing natural objects are typically the projections of three-dimensional objects-animals, for example-that have a symmetry in depth. To characterize human sensitivity to depth symmetry, experiments measured observers' ability to discriminate stereo displays that were symmetrically distributed in depth and those that were asymmetrically distributed. Disparity values were distributed about one of four planes passing through the z-axis and differing in frontoparallel orientation. Asymmetrical patterns were generated by perturbing one of these disparities. Symmetrical-asymmetrical discrimination thresholds were lowest for symmetry about the vertical plane and highest for the horizontal plane. Thresholds for discriminating repetitions and non-repetitions of depth values did not differ across the four planes, whereas discriminations for depth gradients differed from both the symmetry and repetition cases. The heightened sensitivity to symmetry in depth about the vertical plane is a 3-D analog of 2-D mirror-image symmetry performance and could be its source.

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Section: Discussionsupporting

confidence: 57%

The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

Farell¹

2015

Symmetry

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“…There is empirical evidence showing that the human visual system relies on the 3-D symmetry constraint. 7 The symmetry constraint is responsible for our veridical perception of 3-D shapes. By "veridical," we mean that we see shapes the way they are out there.…”

Section: Figure-ground Organization Based On Three-dimensional Symmetmentioning

confidence: 99%

“…7 Symmetry is also important in "shape constancy." Shape constancy refers to the phenomenon in which the perceived shape of an object is constant despite changes in the shape of the retinal image caused by changes in the 3-D viewing direction.…”

Section: The Generality Of the Symmetry Priormentioning

confidence: 99%

Figure-ground organization based on three-dimensional symmetry

Michaux

Jayadevan

Delp

et al. 2016

J. Electron. Imaging

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Abstract. We present an approach to figure/ground organization using mirror symmetry as a general purpose and biologically motivated prior. Psychophysical evidence suggests that the human visual system makes use of symmetry in producing three-dimensional (3-D) percepts of objects. 3-D symmetry aids in scene organization because (i) almost all objects exhibit symmetry, and (ii) configurations of objects are not likely to be symmetric unless they share some additional relationship. No general purpose approach is known for solving 3-D symmetry correspondence in two-dimensional (2-D) camera images, because few invariants exist. Therefore, we present a general purpose method for finding 3-D symmetry correspondence by pairing the problem with the two-view geometry of the binocular correspondence problem. Mirror symmetry is a spatially global property that is not likely to be lost in the spatially local noise of binocular depth maps. We tested our approach on a corpus of 180 images collected indoors with a stereo camera system. K -means clustering was used as a baseline for comparison. The informative nature of the symmetry prior makes it possible to cluster data without a priori knowledge of which objects may appear in the scene, and without knowing how many objects there are in the scene. IntroductionAccording to most studies of human vision, the first step in visual perception is determining whether there are objects in front of the observer: where they are and how many there are. This step (visual function) is called figure-ground organization (FGO). 1 The computer vision community refers to this problem as object discovery. As with all natural visual functions of human observers, FGO operates in three-dimensional (3-D) space, as opposed to the two-dimensional (2-D) retinal image. It follows that it is natural to think about visual mechanisms underlying FGO as based on 3-D operations. However, the fact that the input to the visual system is one or more 2-D retinal images encouraged previous researchers to look for a theory of FGO based on 2-D operations. This is how the human vision community studied FGO. Consider the prototypical example of Edgar Rubin's vase-faces stimulus.2 In this 2-D stimulus, there are two possible interpretations depending on which region is perceived as a "figure" as opposed to the "ground." Similar bistable stimuli have been used during the last several dozen years of FGO research in human vision.3,4 This research provided a large body of results, but few theories and computational models. Furthermore, the proposed models are usually not suitable for real retinal or camera images representing 3-D scenes. This paper breaks with this tradition and looks for 3-D operations that can establish the correct 3-D FGO.

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“…The primary benefit for a Bayesian analysis is when informative priors strongly influence the interpretation of the data (e.g., Li et al (2011) and Vanpaemel (2010). Poor models and poor priors can lead to poor analyses; and these difficulties are not alleviated by simply broadening the prior to express ever more uncertainty (Gelman, 2013;Rouder et al, 2016).…”

Section: Bayes Factorsmentioning

confidence: 99%

Equivalent statistics and data interpretation

Francis

2016

Behav Res

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Recent reform efforts in psychological science have led to a plethora of choices for scientists to analyze their data. A scientist making an inference about their data must now decide whether to report a p value, summarize the data with a standardized effect size and its confidence interval, report a Bayes Factor, or use other model comparison methods. To make good choices among these options, it is necessary for researchers to understand the characteristics of the various statistics used by the different analysis frameworks. Toward that end, this paper makes two contributions. First, it shows that for the case of a two-sample t test with known sample sizes, many different summary statistics are mathematically equivalent in the sense that they are based on the very same information in the data set. When the sample sizes are known, the p value provides as much information about a data set as the confidence interval of Cohen's d or a JZS Bayes factor. Second, this equivalence means that different analysis methods differ only in their interpretation of the empirical data. At first glance, it might seem that mathematical equivalence of the statistics suggests that it does not matter much which statistic is reported, but the opposite is true because the appropriateness of a reported statistic is relative to the inference it promotes. Accordingly, scientists should choose an analysis method appropriate for their scientific investigation. A

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A Bayesian model of binocular perception of 3D mirror symmetrical polyhedra

Cited by 33 publications

References 32 publications

The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

Figure-ground organization based on three-dimensional symmetry

Equivalent statistics and data interpretation

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