Thursday, September 13, 2012

Why rotational invariant (complex moments) is affine invariant(or covariant)?

How orientation is defined in moments?[1]

Straightforward cases:
Principal component analysis is used to define the orientation. However, it suffers from following disadvantages.



A so called "Complex Moments [2] " comes into rescue to compute the orientation.

References:
[1] J Crespo, P Aguiar Revisiting Complex Moments For 2D Shape Representation and Image Normalization  - Image Processing, IEEE Transactions on, 2010
[2] Abu-Mostafa Y, Psaltis D (1985) Image Normalization by Complex Moments.IEEE Transactions on Pattern Analysis and Machine Intelligence7(1)

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