Perception of 3D Symmetrical and Nearly Symmetrical Shapes

Vijai Jayadevan,Zygmunt Pizlo,Edward Delp,Tadamasa Sawada

doi:10.3390/sym10080344

Abstract

The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes. We also showed that binocular perception of symmetric shapes can be well modeled by the above-mentioned priors and binocular depth order information. In this study, which used a shape-matching task, we show that these priors can also be used to model perception of near-symmetrical shapes. Our near-symmetrical shapes are asymmetrical shapes obtained from affine distortions of symmetrical shapes. We found that the perception of symmetrical shapes is closer to veridical than the perception of asymmetrical shapes. We introduce a metric to measure asymmetry of abstract polyhedral shapes, and a similar metric to measure shape dissimilarity between two polyhedral shapes. We report some key observations obtained by analyzing the data from the experiment. A website was developed with all the shapes used in the experiment, along with the shapes recovered by the subject and the shapes recovered by the model. This website provides a qualitative analysis of the effectiveness of the model and also helps demonstrate the goodness of the shape metric.

Highlights

Research on human 3D shape perception started with two seminal papers published in the same year in the same journal [1,2]
We show in the present paper that the unique and veridical percept is produced by the application of a priori constraints to 2D retinal images.) If the percept is sometimes asymmetrical, it is obvious that a symmetry prior competes with other priors and with binocular data, when the session involves binocular viewing
It has to be pointed out that the 3D shape recovery is quite robust to perturbation of the weights around their optimal values

Summary

Introduction

Research on human 3D shape perception started with two seminal papers published in the same year in the same journal [1,2]. Hans Wallach, who received his training with one of the founding fathers of Gestalt psychology, started his paper with a note of disappointment that, despite numerous attempts, no Gestalt psychologist, nor anyone else, was able to show how Prägnanz or the simplicity principle could produce veridical 3D percepts of shapes He turned his attention to the competing tradition of empiricism, and set out to demonstrate that it is learning based on motion cues, rather than any innate simplicity predilection, that teaches human observers about the three-dimensionality of objects. When the 3D object rotates, the changing shadow of the rotating object leads to a 3D percept (they called this “kinetic-depth-effect”) This way, Wallach and O’Connell provided evidence that motion, in the absence of any other cue, can produce a 3D percept. The computational theory is called, after Ullman [4], the structure from motion

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Conclusion