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 we extend the symmetry measure to evaluate the symmetry of occluded shapes. Additionally, using the symmetry measure, we recon...

Symmetry plays an important role in optimization. The usual approach to cope with symmetry in discrete optimization is to try to eliminate it by introducing artificial symmetry-breaking conditions into the problem, and/or by using an ad-hoc search strategy. In this paper we argue that symmetry is instead a beneficial feature that we should preserve and exploit as much as possible, breaking it o...

Fluctuating asymmetry is mainly interpreted as an indicator of developmental instability, while directional asymmetry of the upper limbs is associated with handedness. The association patterns between adult androgen levels and fluctuating as well directional asymmetry patterns are still unclear. In the present study, the association between adult androgen levels, body size and directional as we...

In order to analyze energy levels, bonding, and spectroscopy, it is of great importance to be able to determine the symmetry of a molecule. The symmetry of a molecule or atom can be analyzed strictly from the molecule itself, or from the environment of the atom. Symmetry properties are classified according to different groups determined by sets of symmetry operations. Different elements are con...

This paper concerns sprinklings into Minkowski space (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sp...

Symmetry is usually viewed as a discrete feature: an object is either symmetric or non-symmetric. In this presentation, symmetry is treated as a continuous feature and a continuous measure of symmetry (the Symmetry Distance) is defined. This measure can be easily evaluated for any shape or pattern in any dimension. A preliminary study presented here shows that the Symmetry Distance is commensur...