Empirical Analysis of Invariance of Transform Coefficients under Rotation

Rotationally invariant transforms, namely, angular radial transform and polar harmonic transforms such as polar cosine transform, polar sine transform and polar complex exponential transforms, are used to characterize image features for a number of applications like logo recognition, face recognition etc. But the computation of features using these transforms is an expensive process due to their sinusoidal basis functions which are quite computationally expensive. In this paper, the transform coefficients are analyzed to observe the effect of rotation on each coefficient. The experimentation is done to find most robust transform coefficients under rotation for each transform. Further, analysis is done to trace the effect of observed robust transform coefficients in face recognition application. The results show that the recognition rate remains same for cases when all transform coefficients are used for extracting image features and when only 50% to 60% observed robust moments are used whereas the execution time decreases resulting in fast execution of application.