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PCA Alternative

A recently published technique is said to be capable of finding good dense correspondence. It is described by Tony Jebara. Images are said to be better represented as sets of vectors for this specific purpose, as opposed to vectorisation where fixed ordering is imposed by concatenation of the vectors. Pixels are represented by the common tuple and the ordering of these tuples is arbitrary (they are said to analogically be placed in a bag so an alternative notion would be sets of pixel). Ways exist in which good configurations for ordering these pixels can be found. This implies that vectorisation of the pixels is not the sole option for effective image representation. As the process of pixel ordering takes place, dimensionality reduction is indirectly performed which transforms the image into a volumetrically minimal subspace and this reduction outperforms principal component analysis by orders of magnitude. This is one of the points that make this idea so appealing, but it is still extremely slow^A.2.

Figure pictures the difference between a common approach of pixel ordering versus the alternative bag of pixels.

Figure: Bag of pixels illustrated versus one conventional approach.