Scale co-occurrence matrix: Difference between revisions

Revision as of 13:21, 4 March 2015

Revision as of 10:20, 7 March 2016

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=== [[Discrete wavelet transform|Discrete wavelet]] frame (DWF) ===

In order to do SCM we have to use discrete wavelet frame (DWF) transformation first to get a series of sub images. The discrete wavelet frames is nearly identical to the standard wavelet transform,<ref>{{cite journal|last1=Kevin|first1=Lund|last2=Curt|first2=Burgess|title=Producing high-dimensional semantic spaces from lexical co-occurrence|journal=Behavior Resesrch Methods|date=June 1996|volume=28|issue=2|pages=203–208}}</ref> except that one upsamples the filters, rather than downsamples the image. Given an image, the DWF decomposes its channel using the same method as the wavelet transform, but without the subsampling process. This results in four filtered images with the same size as the input image. The decomposition is then continued in the LL channels only as in the wavelet transform, but since the image is not subsampled, the filter has to be upsampled by inserting zeros in between its coefficients. The number of channels, hence the number of features for DWF is given by 3&nbsp;×&nbsp;l&nbsp;−&nbsp;1.<ref>{{cite journal|last1=Mallat|first1=S.G.|title=A theory for multiresolution signal decomposition: The wavelet representation|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence,|date=1989|pages=674–693}}</ref>

One dimension discrete wavelet frame decompose the image in this way: