Reconstruction of shapes of 3D symmetric objects by using planarity and compactness constraints

Abstract

We present a new algorithm for reconstructing 3D shapes. The algorithm takes one 2D image of a 3D shape and reconstructs the 3D shape by applying a priori constraints: symmetry, planarity and compactness. The shape is reconstructed without using information about the surfaces, such as shading, texture, binocular disparity or motion. Performance of the algorithm is illustrated on symmetric polyhedra, but the algorithm can be applied to a very wide range of shapes. Psychophysical plausibility of the algorithm is discussed.

Binocular disparity only comes into play when everything else fails; a finding with broader implications than one might suppose

“…The perception of depth provided by binocular disparity does not, and cannot, contribute to the veridical perception of shape (see Note 2). Chan et al (2006), Li and Pizlo (2007), Pizlo et al (2006) and Pizlo (2008) used these psychophysical results to develop a computational model of shape constancy, in which a priori constraints they called symmetry, planarity of contours, minimum variance of angles, and maximal 3D compactness were used to reconstruct a 3D shape from a single 2D image of the 3D shape. The symmetry, planarity and minimum variance of angles constraints had been used before, but maximal compactness of the 3D shape was entirely new.…”

Symmetric Non-rigid Structure from Motion for Category-Specific Object Structure Estimation

“…Many man-made objects have symmetric structures [15,16]. Motivated by this, symmetry has been studied extensively in the past decades [16][17][18][19][20][21][22]. However, this information has not been exploited in recent works on 3D object reconstruction [23,24], nor used in standard non-rigid structure from motion (NRSfM) algorithms [3][4][5][6][7][8][9][10]14].…”

Detecting mirror-symmetry of a volumetric shape from its single 2D image

“…This seems to be the first such algorithm. Prior algorithms for recovering 3D symmetric shapes needed either four [17] or three [6] non-coplanar symmetric pairs of vertices. It follows that these prior algorithms cannot recover planar symmetric figures.…”

“…In order to produce a unique 3D shape, one has to restrict the family of possible 3D interpretations, by using a priori constraints. Here we use the algorithm described by Li & Pizlo [6]. Specifically, given a 2D orthographic image of a symmetric 3D shape, the algorithm begins by producing a virtual image of this shape (see Appendix).…”