Continuous symmetry measure definition

Following the definition of the continuous symmetry measure (CSM) in Section II, the CSM values are limited to the range 0. .. 1 (where 1 is the normalization scale). The lower bound of the CSM is obvious from the fact that the average of the square of the distances moved by the object points, is necessarily non-negative. The upper bound of the average is limited to 1 since the object is previously... 

Two general classes of chirality measures have been recognized in the first, the degree of chirality expresses the extent to which a chiral object differs from an achiral reference object, while in the second it expresses the extent to which two enantio-morphs differ from each other [Buda et al., 1992]. The continuous chirality measure (CCM) recently proposed [Zabrodsky and Avnir, 1995] is an example of chirality measure belonging to the first class and is based on the general definition of continuous symmetry measure defined as ... 

The continuous chirality measure is an example of first class chirality measure based on the general definition of continuous symmetry measure it is defined as [Zabrodsky and Avnir, 1995]... 

The proposed continuous symmetry measure (CSM) method which follows these guidelines is based on the following definition. Given a shape composed of rip points P, (/ = l...rip) and a symmetry group G, the symmetry measure 5(G) is a function of the minimal displacement the points P, of the shape must undergo in order to acquire G symmetry. The CSM method identifies the points P, of the nearest shape having the desired symmetry. Once the nearest P,- values are calculated, a continuous symmetry measure is evaluated as ... 

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