Determination of symmetry parameters of objects in noisy images

Measures and functionals of global asymmetry of noisy and noise-free images are axiomatically introduced. Explicit expressions are obtained that make these functionals applicable for determining the symmetry axes of noisy images. It is shown that some asymmetry functionals are unstable against noise levels of images; i.e., the symmetry axis obtained using these functionals may deviate significantly if the signal-to-noise ratio is large. Sufficient and necessary conditions are obtained under which the symmetry axes calculated using asymmetry functionals remain unchanged.