A recently published technique is said to be capable of finding good
dense correspondence. It is described by Jebara in [18].
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 slow7.
The figure below pictures the difference between common approach of pixel ordering versus the alternative bag of pixels.