Thank you for the details Michael! (cc-ing to Dr. Koutsias, this discussion might be of his interest)
Michael Barton: > > [...] > >> However, my question is about performing an *inverse pca*--getting back > >> to the original values from the principal components maps. Nikos: > > Michael, getting back to the original values can _only_ be done if one > > does not "touch" the data in any of the intermediate steps, i.e. Input > > > EVD (or SVD) > Inverse PCA > Original values. > > If one alters the data at any step prior to the Eigenanalysis or SVD, I > > don't think it is possible to land back on "level 1". From the moment > > that global stats of a multivariarte dataset, subject to PCA, are > > changed, one will probably jump into a "new" reality. This means that it > > takes an extra effort to interpret the "new" stuff. Michael: > Right. That is why I'm not doing any alteration of the data after > transforming to PC's. > >> The idea of pca sharpening is that you perform a pca, then do an inverse > >> pca substituting the pan band for pc1 to enhance the resolution. Nikos: > > I haven't tried PCA sharpening. So, apologies for my simplistic > > question(s), I just want to understand the trick here. > > Which resolution is to be enhanced? The geometric? Is it meant to keep > > PC1 and mix it with the rest, or keep the Pan and throw away PC1? > > Principal Component 1 will contain the highest variance of your input data > > -- which, in fact, is a composition of different amount of information > > originated from all input bands. If you throw that away you are left with > > a dataset which is likely to be useless! Michael: > The way this works is to: > > 1) transform 3 lower resolution bands to 3 principal components > 2) replace PC1 with the higher resolution panchromatic band (under the > reasonable assumption that the pan band will include more of the total > spectral variability than will any more spectrally limited band). Histogram > matching the pan band to PC1 is recommended here. This assumption is, indeed, necessary and sounds pretty rational. Interesting stuff. > 3) do an inverse PCA to get back to the original bands with a similar range > of spectral response but with higher spatial resolution. > There have been--and continue to be--studies of the performance of different > pan sharpening algorithms from various perspectives. For myself, pan > sharpening can help with visually resolving more features in greater > detail. But this is at the cost of making it considerably more difficult to > understand what the pixel values of the enhanced bands mean. > >> The equations I show below seem to work, but what I've read indicates > >> that it is not possible to *exactly* get the original values back; you > >> can only approximate them. Nikos: > > As Markus' demonstration showed in another post, the results can be close > > enough so the differences can be disregarded. As far as I have understood > > PCA, it depends on how many decimals are taken into account, while doing > > all the math and _not_ effectively altering the data at any of the > > intermediate steps. Michael: > Yes. Markus' demo made me more comfortable with the algorithm overall. When > you replace PC1 with the pan band, of course, you don't get back to the > original values. But the ranges look pretty good now. > I'll attach the script here in case you want to try it. Ver. 2 and 3 > represent different kinds of optimizing for calculation speed. v3 only > works with a new GRASS python function that Hamish committed to trunk > yesterday. V2 should work with all current versions of GRASS. Thanks a lot. Noted on my ToDo list: "Check MichaelB's pan-sharpening scripts (after next week)". > Here are some helpful references: > Amarsaikhan, D., & Douglas, T. (2004). Data fusion and multisource image > classification. International Journal of Remote Sensing, 25(17), 3529–3539. > Behnia, P. (2005). Comparison between four methods for data fusion of ETM+ > multispectral and pan images. Geo-spatial Information Science, 8(2), > 98–103. doi: 10.1007/BF02826847 > Du, Q., Younan, N. H., King, R., & Shah, V. P. (2007). On the Performance > Evaluation of Pan-Sharpening Techniques. Geoscience and Remote Sensing > Letters, IEEE, 4(4), 518 –522. doi: 10.1109/LGRS.2007.896328 > Karathanassi, V., Kolokousis, P., & Ioannidou, S. (2007). A comparison study > on fusion methods using evaluation indicators. International Journal of > Remote Sensing, 28(10), 2309–2341. doi: 10.1080/01431160600606890 _______________________________________________ grass-dev mailing list [email protected] http://lists.osgeo.org/mailman/listinfo/grass-dev
