# Are discrete wavelet transform based statistical features invariant to rotation/translation/scale?

I'm reading a paper where image classification is done. Their approach is to use the discrete wavelet transform with bi-orthogonal wavelets of degree 3.5 and decomposition of level 3 on images. Based on the 2d coefficients gotten from the DWT they calculate statistical features such as standard deviation, skew, kurtosis, mean, absolute deviation. These statistical features are used as input for classification.

My question is now, are these statistical features based on the DWT rotation/scale/translation invariant ? I personally do not think so. But I can't motivate my answer. Can someone explain this, I'd appreciate if you can quote a source if you anwer.

• are the wavelets symmetrical? I don't think it could be rotation-invariant otherwise – endolith Oct 27 '14 at 18:15
• Yes bior3.5 wavelets are symmetric: wavelets.pybytes.com/wavelet/bior3.5 – Olivier_s_j Oct 27 '14 at 18:29
• It will depend of the wavelet family of course but I would say mostly no either. See stationary wavelet transform and scattering transform (cmap.polytechnique.fr/~mallat/papiers/ScatCPAM.pdf). – matovitch Nov 3 '14 at 10:37
• Can you please give the exact mathematical expression of at least one of the features they calculate? – Jazzmaniac Nov 3 '14 at 11:23
• @Jazzmaniac this is the paper I am talking about: buet.ac.bd/me/icme2013/icme2009/Proceedings/PDF/… . The statistical features are: Skew, Kurtosis, Mean absolute deviation, Mean, Entropy and standard deviation – Olivier_s_j Nov 3 '14 at 11:44