Empirical Analysis of Scale Invariance in Transform Coefficients

One of the necessary and useful image features in recognizing the images successfully is scale invariance. In this paper, we analyzed the effect of scaling on angular radial transform and polar harmonic transforms by computing deviation in each transform coefficient of scaled image and the original image at the same coefficient. These transforms help in extracting the features of an image which are useful for image recognition applications. But due to the presence of the sinusoidal functions, these transforms produce very high computational time complexity. Owing to this fact, we used few scale invariant coefficients instead of using all coefficients in face recognition application. On the basis of these results, the most tolerable coefficients are found out for each transform. Then, by using only 30% to 70% coefficients which produced the least scale deviation, in the application of face recognition, we reduced the time complexity while keeping the recognition rate intact.