Hagit Zabrodsky

Using bilateral symmetry to improve 3D reconstruction from image sequences

Abstract In previous applications, bilateral symmetry of objects was used either as a descriptive feature in domains such as recognition and grasping or as a way to reduce the complexity of structure from motion. In this paper we demonstrate how bilateral symmetry can be used to improve the accuracy in 3D reconstruction. The symmetry property is used to “symmetrize” data before and after reconstruction. We first show how to compute the closest symmetric 2D and 3D configurations given noisy data. This gives us a symmetrization procedure, which we apply to images before reconstruction, and which we apply to the 3D configuration after reconstruction. We demonstrate a significant improvement obtained with real images. We demonstrate the relative merits of symmetrization before and after reconstruction using simulated and real data.

A measure of symmetry based on shape similarity

The authors view symmetry as a continuous feature, and define a continuous symmetry measure (CSM) of shapes. The general definition of symmetry measure allows a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape. Furthermore, the CSM is associated with the symmetric shape that is closest to the given one, enabling visual evaluation of the CSM.<<ETX>>

Completion of occluded shapes using symmetry

Following the view that symmetry is a continuous feature, a continuous symmetry measure (CSM) is developed to evaluate symmetrics of shapes and objects. The symmetry measure is extended to evaluate the symmetry of occluded shapes. Using the symmetry measure, occluded shapes are reconstructed by locating the center of symmetry of the shape.<<ETX>>

Utilizing symmetry in the reconstruction of three-dimensional shape from noisy images

In previous applications, bilateral symmetry of objects was used either as a descriptive feature in domains such as recognition and grasping, or as a way to reduce the complexity of structure from motion. In this paper we propose a novel application, using the symmetry property to “symmetrize” data before and after reconstruction. We first show how to compute the closest symmetric 2D and 3D configurations given noisy data. This gives us a symmetrization procedure, which we apply to images before reconstruction, and which we apply to the 3D configuration after reconstruction. We demonstrate a significant improvement obtained with real images. We demonstrate the relative merits of symmetrization before and after reconstruction using simulated and real data.

Symmetry of fuzzy data

Symmetry is usually viewed as a discrete feature: an object is either symmetric or non-symmetric. Following the view that symmetry is a continuous feature, a continuous symmetry measure (CSM) has been developed to evaluate symmetries of shapes and objects. In this paper the authors extend the symmetry measure to evaluate the imperfect symmetry of fuzzy shapes, i.e. shapes with uncertain point localization. The authors find the probability distribution of symmetry values for a given fuzzy shape. Additionally, for every such fuzzy shape, the authors find the most probable symmetric shape.

How to tell right from left (chirality for 2-D binary shapes)

The authors study the notion of chirality for two-dimensional binary shapes, and introduce measures to test whether a shape is symmetric, and if not whether it is left-handed or right-handed. The measures are based on boundary analysis, and perform well even when digital images of left-handed shapes differ from the mirror images of right-handed shapes. Such situations may occur due to natural variations and digitization errors. The measures can also successfully treat partially occluded shapes, and provide indications on the change of chirality as resolution changes.<<ETX>>