An energy of asymmetry for accurate detection of global reflection axes

We define in this paper two energy terms, symmetric energy term and asymmet ric energy term, which respectively correspond to the symmetric and asymmet ric components of an object. The asymmetric energy term must be zero, if th e studied object is invariant under a reflection about the x-axis. Accordin gly, we formulate the problem of detecting reflectional symmetries as a pro blem of minimising the asymmetric energy term. From the local minima of the asymmetric energy term, we can detect all the symmetric axes of any object . Since the asymmetric energy term is expressed as a summation of a set of generalised complex (GC) moments computed for an object, the proposed symme try detection method is robust against both noise and slight deformation. W e nse the steepest descent technique to calculate the local minima of the a symmetric energy term, whose initialisation is calculated from the most dom inant GC moment. Experiments on typical logo images and human brain image h ave shown the effectiveness and the robustness of the proposed method. To o ur knowledge, this is the first theory on energy functions that describe th e symmetric and asymmetric components of a 2D pattern. (C) 2001 Elsevier Sc ience B.V. All rights reserved.